AP Physics B - Course Notesmrbadenphysics.weebly.com/uploads/8/7/5/8/8758160/conceptual... · Show the answer above in a different color on your ... AP Physics B - Conceptual Inventory

AP Physics B - Course Notes

Please choose from the following drop down menu:

Conceptual Inventory - Test #1 Conceptual Inventory - Test #1- Answers

Conceptual Inventory - Test #2 Conceptual Inventory - Test #2 - Answers

Conceptual Inventory - Test #3 Conceptual Inventory - Test #3 Answers





Exam Review - Answers to Selected Problems Kinematics Example Projectile Example

Newton's Laws Example Circular Motion Example

Work and Energy Example Momentum Example

Torque Example Thermo/Heat Example

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AP Physics B - Course Notes

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AP Physics B - Conceptual Inventory Test I

A.P. Physics B Forum- Test #1 Conceptual Inventory

1. Conceptually explain what the velocity doing during the time interval 0-4, ? The displacement? The acceleration?

2. During the time interval 4-6, what is the velocity doing? The displacement? The acceleration?

3. Where on the graph is the acceleration "0"?

4. How many time intervals are shown above?

5. If you were sketching an acc vs t or a disp vs t graph, how many lines must you have?

6. If the slope on a V vs T graph is constant, the lines on a A vs T graph will be?

7. Sketch the A vs T graph for the V vs T graph below

http://bowlesphysics.com/apinv1.html (1 of 6) [1/23/2004 5:36:33 PM]


What is the acceleration due to gravity?

Why is it negative?

Is it ever zero?

Does it work horizontally?

In the three boxes above, write the 3 equations for the kinematics.

Consider the following problem:

A particle starts from rest from the top of an inclined plane and slides down with constant acceleration.



The inclined plane is 2.00 m long, and it takes 3.00 seconds for the particle to reach the bottom. Find (a) the acceleration (b) its speed at the bottom of the incline (c) the time it takes the particle the middle of the incline (d) its speed at the midpoint.

What is the initial velocity?

What is the displacement?

What is the time?

What are you looking for?

What are you NOT looking for?

Which equation is best suited for this data?

Solve for (a)

What are you looking for in (b)?

Which equation(s) is best suited for this data?

Solve for (b)

What is the displacement for (c)?

What are you looking for in (c)?


Solve for (c)

What are you looking for in (d)?


Solve for (d)

Consider the following example:



A car travels 2000 meters north then 3500 m, 60 degrees W of N. Find the magnitude and direction of the car's displacement.

Draw this scenario without lifting your pencil off the paper.

What do you do to the vector at an angle?

Show the answer above in a different color on your drawing.

How many arrows do you have in the x direction?

How many arrows do you have in the y direction?

What do you do to the arrows in the y direction?

How do you find the resultant?

How do you find the direction?

Draw the complete and reduced triangle below and label all sides.

Find the magnitude and direction of the car's displacement.

If you have 3 or more vectors, what will you have to set up?

If they are at angles, you must _______________________________________

What do you do to all the x-components? y-components?



When will a component be negative?

Solve the following:

The driver of a car drives 3000 m north, 2000 m 42 degrees E of N, 4000 m,W then 3000 m , 55 degrees E of S. Where does he end up relative to where he started?

Consider the following: A bomber flies horizontally with a speed of 275 m/s at an altitude of 3000 m.

In the spaces above, write the formulas for the vertical and horizontal motion of a projectile.

What is the initial "y" velocity ( Voy) of an object if it starts off horizontally?

In the formula, x = voxt + 1/2at2, what is the acceleration in the x direction?

Why?

What is another thing you can say about vox?

In the problem above, vox =

What is the displacement in the y direction?

Aside from a method of substitution, can these #s ever be in the same formula ?

Solve for the time the projectile is in the air

Solve for the "x" displacement



A skier leaves the ramp of an elevated 35 degree ski jump with a velocity of 10 m/s.

What is the first thing you are going to do?

Vx = Voy =

What is the displacement of the skier in the vertical direction?

How long is he in the air?

How long does it take to reach his maximum height?

How high does he rise?

How far away does he land?


AP Physics B - Conceptual Inventory Test I - Answers

A.P. Physics B Forum- Test #1 Conceptual Inventory

1. Conceptually explain what the velocity doing during the time interval 0-4, ? The displacement? The acceleration? The velocity is increasing, the displacement is increasing, the acceleration is constant.

2. During the time interval 4-6, what is the velocity doing? The displacement? The acceleration? The velocity is constant, the displacement is increasing , the acceleration is zero.

3. Where on the graph is the acceleration "0"? t = 4 to t = 6 seconds, t = 11 to t = 13 seconds.

4. How many time intervals are shown above? eight

5. If you were sketching an acc vs t or a disp vs t graph, how many lines must you have? eight

6. If the slope on a V vs T graph is constant, the lines on a A vs T graph will be? horizontal

7. Sketch the A vs T graph for the V vs T graph below

http://bowlesphysics.com/apinv1a.html (1 of 7) [1/23/2004 5:36:38 PM]


What is the acceleration due to gravity? -9.8 m/s/s

Why is it negative? because it works DOWNWARD

Is it ever zero? NO!

Does it work horizontally? NO!

v = vo + at

x = vot + 1/2at2 v2 = vo2 + 2ax

In the three boxes above, write the 3 equations for the kinematics.

Consider the following problem:

A particle starts from rest from the top of an inclined plane and slides down with constant acceleration. The inclined plane is 2.00 m long, and it takes 3.00 seconds for the particle to reach the bottom. Find (a) the acceleration (b) its speed at the bottom of the incline (c) the time it takes the particle the middle of the incline (d) its speed at the midpoint.



What is the initial velocity? it is ZERO, it started from REST!

What is the displacement? 2.0 m

What is the time? 3.0 s

What are you looking for? The acceleration

What are you NOT looking for? The final velocity

Which equation is best suited for this data? x = vot + 1/2at2 (because it DOES NOT have the final velocity in it)

Solve for (a) 2 = 0 + (0.5)(a)(3)2 a = 0.44 m/s/s

What are you looking for in (b)? The final velocity

Which equation(s) is best suited for this data? v = vo + at , it is the smallest and easiest to use

Solve for (b) v = 0 + (0.44)(3) = 1.32 m/s

What is the displacement for (c)? 1.00 m, because it said IN THE MIDDLE of the incline

What are you looking for in (c)? The time

Which equation(s) is best suited for this data? x = vot + 1/2at2 (because acceleration is constant you can use your answer from above)

Solve for (c) 1 = 0 + (0.5)(0.44)(t)2 t = 2.13 seconds

What are you looking for in (d)? the final velocity at the midpoint

Which equation(s) is best suited for this data? v = vo + at

Solve for (d) v = 0 + (0.44)(2.13) = 0.93 m/s

Consider the following example:



A car travels 2000 meters north then 3500 m, 60 degrees W of N. Find the magnitude and direction of the car's displacement.

Draw this scenario without lifting your pencil off the paper.

What do you do to the vector at an angle? Break it into Components

Show the answer above in a different color on your drawing. See Above

How many arrows do you have in the x direction? One

How many arrows do you have in the y direction? Two

What do you do to the arrows in the y direction? Add them

How do you find the resultant? Use the Pythagorean theorem ( after you ad the 2 vecotrs in the y-direction)

How do you find the direction? Use Inverse Tangent

Draw the complete and reduced triangle below and label all sides.



Find the magnitude and direction of the car's displacement. (3750)2 + (3031.0)2 = c2 c = 4821.8 m

Inv Tan = (3031.0) / (3750) = 38.9 degrees West of North

If you have 3 or more vectors, what will you have to set up? A table of components

If they are at angles, you must BREAK THEM INTO COMPONENTS!

What do you do to all the x-components? y-components? Add them up

When will a component be negative? if it is moving West or South

Solve the following:

The driver of a car drives 3000 m north, 2000 m 42 degrees E of N, 4000 m,W then 3000 m , 55 degrees E of S. Where does he end up relative to where he started?

X Y

0 3000 m

2000Sin42 = 1338.3 m 2000Cos42 = 1486.3 m

-4000 m 0

3000Sin55 = 2457.5 m 3000Cos55 = -1720.7 m ( it is negative because it is SOUTH!)

Total = -204.2 m Total = 2765.6 m



(-204.2)2 + (2765.6)2 = c2 c = 2773.1 m

Inv tan (2765/204.2) = 85.8 degress N of W

Consider the following: A bomber flies horizontally with a speed of 275 m/s at an altitude of 3000 m.

y = voyt + 1/2gt2 x = voxt

In the spaces above, write the formulas for the vertical and horizontal motion of a projectile.

What is the initial "y" velocity ( Voy) of an object if it starts off horizontally? ZERO

In the formula, x = voxt + 1/2at2, what is the acceleration in the x direction? ZERO

Why? Gravity DOES NOT work in the "x" direction

What is another thing you can say about vox? it is CONSTANT

In the problem above, vox = 275 m/s

What is the displacement in the y direction? - 3000 m, because it is falling

Aside from a method of substitution, can these #s ever be in the same formula ? NEVER!

Solve for the time the projectile is in the air -3000 = 0 + 1/2(-9.8)t2 t = 24.7 s

Solve for the "x" displacement x = (275)(24.7) = 6792.5 m

A skier leaves the ramp of an elevated 35 degree ski jump with a velocity of 10 m/s.

What is the first thing you are going to do? Break the speed into components



Vx = 10Cos35 = 8.2 m/s Voy = 10 Sin35 = 5.74 m/s

What is the displacement of the skier in the vertical direction? ZERO, he goes up and down!

How long is he in the air? 0 = 5.74t + 1/2(-9.8)t2 -5.74t = -4.9t2 time and negative both CANCEL OUT! t = 1.2 seconds

How long does it take to reach his maximum height? Half the time or 0.59 seconds

How high does he rise? y = 5.74(0.59) + 1/2(-9.8)(0.59)2 = 1.68 m

How far away does he land? x = (8.2)(1.2) = 9.84 m


AP Physics B - Concept Inventory #2 - Newton's Laws

A.P. Physics B – Concept Inventory #2 – Mechanics

I. Newton’s First Law Newton’s first law is concerned with 2 types of sub-conditions. What are they?

What do you call the MAIN condition?

A 15-kg box is pushed at a constant speed, with friction, horizontally by a rope with tension of 55 N . The direction is in the +x.

Draw the free body diagram of the box

How many forces are in the Y direction?

How many forces are in the X direction?

What state of condition is the box in? Explain.

Write the equation for the x direction? (no #s)

Write the equation for the y direction? (no #s)

What is the Force Normal equal to?

What is Friction equal to?

Below, show the complete substitution and solve for µk.



Suppose the box was on a 25 degree incline and the 55 N was applied downward parallel to the incline. What 2 things will you do before any calculations?

Show the free body diagram for the box to the left

What is the Force Normal equal to?

What is Friction equal to?


II – Newton’s Second Law Complete the following statements:

If force on an object increases, the acceleration of the object ___________________________

If the mass of a system decreases, the acceleration of the system ________________________



What does the slope of the graph above show?

Determine the ________ of the object:

A wooden block of mass 9-kg accelerates down an incline sloped at 20 degree. The block starts from rest and is located 5.0 m from the bottom of the incline.

What 2 things must you do before you begin any calculations?

What does the Force Normal equal?

What is the traditional formula for Friction?

What does friction equal in this case?

Write an equation in the direction of the acceleration?

If the coefficient of friction is 0.33, determine the acceleration of the block:



What equation would you use to determine the speed at the bottom of the incline?

Determine the final velocity of the block.

M1 = 4-kg is attached via a string to a hanging M2= 6 kg. Friction is

present.

On the figure, draw the free body diagram

How many forces are on M2?

Which force on M2 is larger?

Which way does M2 accelerate?

How many forces act on M1?

Which way does M1 accelerate?

In which direction is M1 at equilibrium?

What to M1 and M2 have in common?

Which force on M1 is larger in the direction of acceleration?

Write a force equation for M2

What does the Force Normal on M1 equal?

Suppose M2 starts from rest and moves a total displacement of 1.75 meters in 2.5 seconds.

What equation would be appropriate to find the acceleration?

Find the acceleration of M2



Is this value the same for M1? Explain

Below determine µk for M1

III- Newtons 3rd Law How many objects are there concerning in this law?

How many Forces?

According to Newton, these force are ____________and ______________

Finish the following: A boy steps off of a curb and onto the street. If the action force is the earth pulling the boy the reaction force is _______________________________


AP Physics B - Conceptual Inventory #2 - answers

A.P. Physics B – Concept Inventory #2 Answers – Mechanics

I. Newton’s First Law Newton’s first law is concerned with 2 types of sub-conditions. What are they? Moving at a constant velocity OR being AT REST

What do you call the MAIN condition? EQUILIBRIUM A 15-kg box is pushed at a constant speed, with friction, horizontally by a rope with tension of 55 N . The direction is in the +x.

Draw the free body diagram of the box

How many forces are in the Y direction? TWO

How many forces are in the X direction? TWO

What state of condition is the box in? Explain. The box is in equilibrium because , it is moving at a constant speed.

Write the equation for the x direction? (no #s) T = Ff



Write the equation for the y direction? (no #s) Fn = mg

What is the Force Normal equal to? The Weight

What is Friction equal to? The Tension


Ff = µFn Ff =µmg T=µmg

55 = µ(15)(9.8) µ = 0.374

Suppose the box was on a 25 degree incline and the 55 N was applied downward parallel to the incline. What 2 things will you do before any calculations? Rotate axis & break the weight into components

Show the free body diagram for the box to the left



What is the Force Normal equal to? mgcosθ

What is Friction equal to? Fa + mgsinθ


Ff = Fa + mgsinθ µFn = 55 + mgsinθ µmgcosθ = 55 + mgsinθ µ(15)(9.8)cos25 = 55 + (15)(9.8)sin25 µ = 0.879

II – Newton’s Second Law Complete the following statements:

If force on an object increases, the acceleration of the object INCREASES

If the mass of a system decreases, the acceleration of the system INCREASES



What does the slope of the graph above show? MASS

Determine the MASS of the object: Rise = 60 Run = 10 Mass = 60/10 or 6 kg

A wooden block of mass 9-kg accelerates down an incline sloped at 20 degree. The block starts from rest and is located 5.0 m from the bottom of the incline.

What 2 things must you do before you begin any calculations? Rotate axis and break weight into components

What does the Force Normal equal? Fn = mgcosθ

What is the traditional formula for Friction? F = µFn

What does friction equal in this case? Ff = µmgcosθ

Write an equation in the direction of the acceleration? mgsinθ - Ff = ma mgsinθ - µmgcosθ = ma gsinθ - µgcosθ = a

If the coefficient of friction is 0.33, determine the acceleration of the block:



(9.8)sin20 - (0.33)(9.8)Cos20 = a 0.31 m/s/s = a

What equation would you use to determine the speed at the bottom of the incline? v2 = vo

2 + 2ax

Determine the final velocity of the block. v2 = 0 + 2(0.31)(5) v2 = 3.1 v = 1.76 m/s

M1 = 4-kg is attached via a string to a hanging M2= 6 kg. Friction

is present.

On the figure, draw the free body diagram

How many forces are on M2? TWO

Which force on M2 is larger? THE WEIGHT

Which way does M2 accelerate? DOWN

How many forces act on M1? FOUR

Which way does M1 accelerate? To the right

In which direction is M1 at equilibrium? Horizontal

What to M1 and M2 have in common? Tension

Which force on M1 is larger in the direction of acceleration? Tension

Write a force equation for M2

m2g - T = m2a

What does the Force Normal on M1 equal? m1g

Suppose M2 starts from rest and moves a total displacement of 1.75 meters in 2.5 seconds.



What equation would be appropriate to find the acceleration? x = vot + 1/2at2

Find the acceleration of M2

1.75 = 0 + 1/2(a)(2.5)2 a = 0.56 m/s/s

Is this value the same for M1? Explain Yes , they are attached to the same rope, therefore they have the same motion.

Below determine µk for M1

T - Ff = m1a

T - mFn = m1a

m2g - m2a - µm1g = m1a

(6)(9.8) - (6)(0.56) - µ(4)(9.8) = 4(0.56)

µ = 1.36

III- Newtons 3rd Law How many objects are there concerning in this law? TWO

How many Forces? TWO

According to Newton, these force are equal and ______OPPOSITE_____

Finish the following: A boy steps off of a curb and onto the street. If the action force is the earth pulling the boy the reaction force is The boy pulling on the earth


A.P. Physics - Test #3 - Conceptual Inventory

A.P. Inventory #3 – Circular Motion/Work-Energy/ Momentum

Circular Motion1. As something moves in a circle, the speed is constant but the velocity is NOT. Why?

2. What is the formula for constant speed?

3. Symbolically, what is the distance around a circle?

4. What is the formula for the speed if one is moving around in a circle?

5. What is the formula for the centripetal acceleration?

6. What does centripetal mean?

7. What is the formula for centripetal force?

8. A person swings a 0.65 kg rock in an old fashion slingshot around in a vertical circle. The length of the slingshot is 0.85 m. If the person swings the rock around once in 0.55 seconds, determine: a) The slingshot’s speed

b) The slingshot’s tension when the rock is at the bottom of the swing

c) The slingshot’s tension when the rock is at the lowest point of the swing

9. Suppose the same person swung the rock around horizontally at an angle of 20 degrees below the horizontal.

Draw the free body diagram of the rock in a sling below



How many forces are in the y?

Is it moving in the y direction?

What condition is the y direction in?

How many forces are in the x direction?

What part of the circle does the horizontal force point?

What does the horizontal force equal?

Write an equation in the y direction.

What can you solve for? Solve for it!

Write an equation in the x direction.

Solve for the radius of the circle using Geometry then solve for the velocity of the rock

Work and Energy

What is the basic formula for work?

What one thing must you remember conceptually about the formula above?

Can work be negative? If so, the force must be what?

If the force is at an angle, and the displacement along the + X: What must you do to the force before you apply the formula?

A man pushes down on a lawnmower with a force of 50 N at 55 degrees above the horizontal along the +x. a) If the displacement is 6 m, how much work does the man do on the lawnmower?

Work equals a change in what?



b) If the lawnmower starts from rest, how fast is it moving at the end of the 6 m if its mass is 100 kg?

A crane pulls a 250 kg box 35 m upward with a constant speed in 5.5 seconds.

a) What is the formula and units for Power?

b) What is the force in this case?

c) Solve for Power.

What is the formula for potential energy?

What is the formula for kinetic energy?

What is the unit for energy?

Suppose the crane in the problem above has a giant 400 kg ball at the end of a 15 m cable. If the ball is above the ground in such a way that the cable makes an angle of 25 degrees with the vertical, determine: Draw a sketch of this situation below

What do you have to subtract to find the height?

Solve for the height

What kind of energy does it have at this point?

If it suddenly was released, what kind of energy would it have at the bottom?

Solve for the velocity at the bottom



Momentum

What is the formula for momentum?

Symbolically, show the conservation of momentum formula below

What would the formula look like if you had an ELASTIC collision between 2 objects

What would the formula look like if you had an INELASTIC collision between 2 objects

What would the formula look like if you had 1 object that split into 2 objects.

A 675 kg car traveling at 15 m/s strikes another car at rest. The second car ( 525 kg) moves at what velocity if the 1st car comes to rest?

What velocity would BOTH cars move had they become connected?

A loaded cannon with ball has a mass of 250 kg. What is the velocity of a 5 kg ball if the cannon moves backwards at 0.5 m/s?

A 145 kg linebacker moving at 1.5 m/s to the west strikes a 165 Kg runningback who momentarily stops before the collision. The linebacker moves at 32 degrees N of W after the collision and the runningback moves at 66 degrees S of W.

Draw the sketch for this situation below

Due to the angles you must use the what to solve this problem?

Write an equation for the X direction



Write an equation for the Y direction

Solve simultaneously for the velocity of each player


A.P. Physics B - Test 3 Conceptual Inventory Answers

A.P. Inventory #3 Answers – Circular Motion/Work-Energy/ Momentum

Circular Motion1. As something moves in a circle, the speed is constant but the velocity is NOT. Why? Because the velocity's DIRECTION is instantaneously changing at every point on the circle

2. What is the formula for constant speed? Speed = distance / time

3. Symbolically, what is the distance around a circle? the circumference(2πr)

4. What is the formula for the speed if one is moving around in a circle? Speed = 2πr / time

5. What is the formula for the centripetal acceleration? ac = v2 / r

6. What does centripetal mean? Center seeking

7. What is the formula for centripetal force? Fc = mac or Fc = mv2 / r

8. A person swings a 0.65 kg rock in an old fashion slingshot around in a vertical circle. The length of the slingshot is 0.85 m. If the person swings the rock around once in 0.55 seconds, determine: a) The slingshot’s speed

b) The slingshot’s tension when the rock is at the bottom of the swing

c) The slingshot’s tension when the rock is at the lowest point of the swing



9. Suppose the same person swung the rock around horizontally at an angle of 20 degrees below the horizontal.

Draw the free body diagram of the rock in a sling below

How many forces are in the y? Two

Is it moving in the y direction? No

What condition is the y direction in? Equilibrium

How many forces are in the x direction? one

What part of the circle does the horizontal force point? towards the center

What does the horizontal force equal? the centripetal force

Write an equation in the y direction. Tsinθ = mg

What can you solve for? Solve for it! Tension! T = mg/ sinθ = 18.6 N



Write an equation in the x direction. TCosθ = Fc

Solve for the radius of the circle using Geometry then solve for the velocity of the rock

Work and Energy

What is the basic formula for work? Work equals Force times displacement

What one thing must you remember conceptually about the formula above? Force and displacement MUST be on the same axis

Can work be negative? If so, the force must be what? Yes, it could be friction or any other resistive force

If the force is at an angle, and the displacement along the + X: What must you do to the force before you apply the formula? You must break it into components and use the horizontal component in the formula

A man pushes down on a lawnmower with a force of 50 N at 55 degrees above the horizontal along the +x. a) If the displacement is 6 m, how much work does the man do on the lawnmower?

Work equals a change in what? Kinetic energy (∆KE)

b) If the lawnmower starts from rest, how fast is it moving at the end of the 6 m if its mass is 100 kg?



A crane pulls a 250 kg box 35 m upward with a constant speed in 5.5 seconds.

a) What is the formula and units for Power? Power = Work divided by Time or force times velocity; Power is measure in WATTS

b) What is the force in this case? The box's weight

c) Solve for Power.

What is the formula for potential energy? PE = mgh

What is the formula for kinetic energy? KE = 0.5mv2

What is the unit for energy? JOULES

Suppose the crane in the problem above has a giant 400 kg ball at the end of a 15 m cable. If the ball is above the ground in such a way that the cable makes an angle of 25 degrees with the vertical, determine: Draw a sketch of this situation below



What do you have to subtract to find the height? L - LCos 25 = h

Solve for the height 15 - 15Cos25 = h =1.40 m

What kind of energy does it have at this point? Potential

If it suddenly was released, what kind of energy would it have at the bottom? Kinetic

Solve for the velocity at the bottom =

E(before) E(after)

PE KE

mgh 1/2mv2

= v = 5.24 m/s

Momentum

What is the formula for momentum? p = m∆v

Symbolically, show the conservation of momentum formula below p(before) = p(after)

What would the formula look like if you had an ELASTIC collision between 2 objects m1vo1 + m2vo2 = m1v1 + m2v2

What would the formula look like if you had an INELASTIC collision between 2 objects m1vo1 + m2vo2 = mtvt

What would the formula look like if you had 1 object that split into 2 objects. mtvt = m1v1 + m2v2



A 675 kg car traveling at 15 m/s strikes another car at rest. The second car ( 525 kg) moves at what velocity if the 1st car comes to rest?

What velocity would BOTH cars move had they become connected?

A loaded cannon with ball has a mass of 250 kg. What is the velocity of a 5 kg ball if the cannon moves backwards at 0.5 m/s?

A 145 kg linebacker moving at 1.5 m/s to the west strikes a 165 Kg runningback who momentarily stops before the collision. The linebacker moves at 32 degrees N of W after the collision and the runningback moves at 66 degrees S of W.

Draw the sketch for this situation below



Due to the angles you must use the what to solve this problem? You must use the components! Write an equation for the X direction see pic below Write an equation for the Y direction see pic below Solve simultaneously for the velocity of each player see pic below




AP Physics B - Conceptual Inventory - Torque and SHM

A.P. Inventory #4 – Torque, & Simple Harmonic Motion

Torque

What is the formula for torque?

What must we conceptually understand before applying this formula to a situation?

If the Στ = 0, what can you say about the torque in the clockwise and counter-clockwise direction?

Consider τ= rFsinθ

r is the displacement from where?

Why do we use sin θ?

If a force is acting at the POR the torque produced by that force is equal to what?

Why?



An artist wishes to construct a birds-and-bees mobile as shown. If the bee on the lower left has a mass of 0.10 kg and each vertical support string has a length of 30 cm, what are the masses of the other birds and bees? ( Neglect the masses of the bars and strings)

Lets focus on the lower bar! Write an equilibrium expression for the lowest bar. Show work below!

Torque Clockwise = F ( x)

= Torque Counter-Clockwise = F ( x)

Solve for the mass of the bee on the right

What is the magnitude AND direction of the tension equal to in the lowest string?

Let’s focus on the middle bar! ( use your force from above!) Relative to the middle bar, what is the direction in the lowest string?

Show work below!

Torque Clockwise = F ( x) = Torque Counter-Clockwise = F ( x)

Solve for the mass of the bird on the right

What is the magnitude AND direction of the tension equal to in the middle string? Let’s focus on the upper bar! ( use your force from above!) Relative to the upper bar, what is the direction in the middle string?

Show work below!



Torque Clockwise = F ( x) = Torque Counter-Clockwise = F ( x)

Solve for the mass of the bird on the left

Springs and pendulums

According to Hooke’s Law, the force is _________________ proportional to the _________________.

When dealing with springs, what is the slope of a Force vs. Displacement graph?

Show why the above sentence is true.

What is the formula for Elastic Potential Energy?

What is the formula for the period of an oscillating spring?

What is the formula for the frequency of an oscillating spring?

A 500-g block is released from rest and slides down a frictionless track that begins 2.00 m above the horizontal as shown in the figure. At the bottom of the track, where the surface is horizontal, the block strikes and sticks to a light spring with a constant of 20 N/m.

What kind of energy does the block have initially?

Once the block sticks to the spring, what kind of energy is present?

Solve for the displacement that the spring is compressed.



Assume that the spring now oscillates in simple harmonic motion

Calculate the period of the spring’s motion

The frequency?

What is the formula for the period of a pendulum?

The frequency?

A simple 2.00-m long pendulum oscillates on earth. How many complete oscillations does it make in 5.0 minutes?


AP Physics B - Torque and SHM Inventory answers

A.P. Inventory #4 – Torque, & Simple Harmonic Motion

Torque

What is the formula for torque? The product of the force and the lever arm displacement What must we conceptually understand before applying this formula to a situation? The force and displacement MUST be perpendicular If the Στ = 0, what can you say about the torque in the clockwise and counter-clockwise direction? The must be equal Consider τ= rFsinθ

r is the displacement from where? The POINT OF ROTATION

Why do we use sin θ? Because the force and the lever arm must be perpendicular. Sin q is used to get the necessary perpendicular component.

If a force is acting at the POR the torque produced by that force is equal to what? ZERO! Why? Because there is no "X" displacement



An artist wishes to construct a birds-and-bees mobile as shown. If the bee on the lower left has a mass of 0.10 kg and each vertical support string has a length of 30 cm, what are the masses of the other birds and bees? ( Neglect the masses of the bars and strings)

Lets focus on the lower bar! Write an equilibrium expression for the lowest bar. Show work below!

Torque Clockwise = F (

x)

= Torque Counter-Clockwise = F ( x)

(x)(9.8)(0.20) (0.10)(9.8)(0.40)

Solve for the mass of the bee on the right 0.20 kg

What is the magnitude AND direction of the tension equal to in the lowest string? Tension up = Weight of BOTH bees T = (0.10)(9.8) + ( 0.20)(9.8) = 2.94 N

Let’s focus on the middle bar! ( use your force from above!) Relative to the middle bar, what is the direction in the lowest string? Down

Show work below!

Torque Clockwise = F ( x) = Torque Counter-Clockwise = F ( x)(x)(9.8)(0.15) (2.94)(0.25)

Solve for the mass of the bird on the right 0.5 kg

What is the magnitude AND direction of the tension equal to in the middle string? Tension up = Weight of bird + first tension T = 2.94 + (0.5)(9.8) = 7.84 N



Let’s focus on the upper bar! ( use your force from above!) Relative to the upper bar, what is the direction in the middle string? Down

Show work below!

Torque Clockwise = F ( x) = Torque Counter-Clockwise = F ( x)(7.94)(0.15) (x)(9.8)(0.30)

Solve for the mass of the bird on the left 0.40 - kg

Springs and pendulums

According to Hooke’s Law, the force is _____Directly____________ proportional to the _____displacement____________.

When dealing with springs, what is the slope of a Force vs. Displacement graph? the spring constant

Show why the above sentence is true. F= kx k = F/x Slope = Rise/Run k = slope, F = rise, x = run

What is the formula for Elastic Potential Energy? Us = 1/2kx2

What is the formula for the period of an oscillating spring?

What is the formula for the frequency of an oscillating spring?



A 500-g block is released from rest and slides down a frictionless track that begins 2.00 m above the horizontal as shown in the figure. At the bottom of the track, where the surface is horizontal, the block strikes and sticks to a light spring with a constant of 20 N/m.

What kind of energy does the block have initially? Gravitational Potential Energy

Once the block sticks to the spring, what kind of energy is present? Elastic Potential Energy

Solve for the displacement that the spring is compressed. mgh = 1/2kx2 (0.500)(9.8)(2) = (0.5)(20)(x2) x = 0.99 m Assume that the spring now oscillates in simple harmonic motion

Calculate the period of the spring’s motion

The frequency? 1/0.99 = 1.01 Hz



What is the formula for the period of a pendulum?

The frequency?

A simple 2.00-m long pendulum oscillates on earth. How many complete oscillations does it make in 5.0 minutes?

0.35 cyles x 300 seconds ( 5 minutes converted to sec) = 105 cycles


AP Physics B - Thermodynamics Concept Inventory

AP Test #5 – Concept Inventory – THERMODYNAMICS

What is the formula for pressure based on its definition?

What could the force be in this case?

What could you substitute in for MASS?

Suppose the object was a cylinder, could could you find the Volume?

What is the formula for absolute pressure?

The pressure exerted by a person's lungs can be measured by having the person blow as hard as possible into one side of a manometer.( see page 317 in the blue book and page 315 in the white book for reference as to what a manometer looks like). If a person blowing into one side of an open tube manometer produces a 70 cm difference in heights of the columns of water in the manometer arms, what is the lung pressure?

According to Archimedes, the buoyant force is equal to the ______________ of fluid it displaces.

Once again, what can you substitute in for the MASS?

What is the formula for the buoyant force?

An irregularly shaped piece of metal has a mass of 90 grams in air. It is suspended from a scale and the scale reads 75 grams when the piece is submerged in water. What are the volume and density of piece of metal?

What are the 3 points that define an IDEAL fluid?

●

●

●

What kind of flow do you have when every particle moves exactly along the smooth path as every



particle that follows it?

What do you call the path of the flow mentioned above?

What kind of flow do you have in which the paths are irregular?

What do you call the path of this kind of flow?

Fill in the blank: Concerning a closed pipe system, the mass that flows into a region will ____________ the mass that flows out of a region.

What is the equation of flow continuity?

Water flows from a 2.0 cm pipe at a speed of 0.35 m/s. How long will it take to fill a 10-L container?

What is Bernoulli's Equation?

In an industrial cooling process, water is circulated through a system. If the water pumped from the first floor through a 6.0 cm pipe with a speed of 0.45 m/s under a pressure of 53,157.9 Pa, what will be the pressure on the next floor 4.0 m above in a pipe with a diameter of 2.0 cm?

Consider the formula Q = mc∆T

What are the units of Q? What are the units of m?

What are the units of ∆T?

Re-write the formula above and solve it in terms for c :

What are the units of c?



What is the significance of the ∆?

According to Conservation of Energy, Heat _____________ equals Heat _____________

A thin copper cup of mass 150-g containing 500-g of water is at a temperature of 20 degrees Celsius. A 225-g sample of an unidentified material at 508 degrees Celsius is lowered into the bath and the cup is sealed. After a few minutes, the system reaches a constant final temperature of 40 degrees Celsius. Determine the specific heat of the sample.

How many objects are losing heat? How many objects are gaining heat?

Solve for c

If something has specific heat it MUST be CHANGING in what?

If an object is NOT undergoing the answer above it must be involved in what type of heat?

Write the formula for _______________ heat. (use answer above)

Re-write the formula above and solve it in terms for L :

What are the units for L:

Write the appropriate “ Heat of ………” word for the following processes

Melting = _________________ Freezing = __________________ evaporating = _________________

Condensing = ____________________

How much heat must be added to a 1.0 Kg mass of ice at – 10 degrees Celsius in order to transform it into 110 degree Celsius steam? (c(steam) = 2020 J/kgxC) How many processes or states does this piece of ice go through?

Solve for Q



1 mole equals what three things · · ·

How many grams are in 3.75 moles of NaF2 ?

How many molecules are in 16.3 L of Cl2 at STP?

Consider the formula PV = nRT

What does P stand for? Units: OR

What does V stand for? Units:

What does n stand for?

What does T stand for? Units:

Re-Arrange the formula above and solve for R: Units:

If 23.8 grams of Ammonia gas ( NH3 ) are to be put into a 10.0-L container at a pressure 202.6 kPa, at

what temperature should the gas be maintained?

What needs to be determined before you begin this problem?

Solve for T?



What must the units of temperature be in when dealing with gas laws?

If a gas is placed in a piston at a specific pressure, yet there is no change in volume, the work done by the gas is?

Losing heat has what sign?

Gaining?

What is the sign of work if the gas does the work?

What is the sign of work if work is done on the gas?

Both Q(heat) and W(work) correspond to the transfer of energy. What do you call the difference of Q and W? Hint: this answer depends on a change in temperature

A cylinder containing a gas is sealed with a nearly frictionless piston at a pressure of 0.20 MPa. The cylinder is placed in contact with a source of heat and the gas very slowly expands, moving the piston, in such a way that the volume changes by 5 x 10-3 m3 . Assuming the process is isobaric, and given that 300 J of heat enters the system, determine its change in internal energy

What exponent will Mpa get?

What do you have to determine first?

Solve

Solve for ∆U:

Fill in chart below



Process Isothermal Isobaric Isovolumetric Adiabatic

Constant?

Changing?

Special things To remember?

What can you determine when you know what you get OUT of an engine based on what you put IN?

What do you call the MAXIMUM or IDEAL situation according to your answer above?

What must you remember about the temperature in an IDEAL situation?

1 mole of an ideal gas is taken through the cyclic process shown to the left.

If the situation involves an ideal gas, what formula do you use?

By what value will you multiply your units of pressure by?

At what temperature is point B?

At what pressure is point B?

Using the ideal gas law and point B, solve for V1?

Solve for the volume at point A



(a) Compute the work (W) for each of the four processes.

If this process is cyclic, meaning that it returns to its original starting position, what is its change in internal energy?

∆U =

(b) What is the NET work?

(c) What is T3?

An internal combustion engine using natural gas and air as a working substance has a temperature in the spark-ignited firing chamber of 2150 K and an exhaust temperature of 900 K. The difference between the heat supplied and the work done by the engine in one complete cycle is 460 J.

What does the word “difference” suggest?

What is another way to state “heat supplied”?

If the difference between the heat supplied and the work done by the engine in one complete cycle is 460 J, what are they really saying 460 J is?

If you were asked to find the ideal efficiency, what kind of engine are we suggesting?

Solve for the maximum efficiency

How much work is done if the heat input is 790 J?

What is the ACTUAL efficiceny (meaning don’t use Carnot)




AP Physics B - Conceptual Inventory Test #5 - Answers

AP Test #5 – Concept Inventory – THERMODYNAMICS

What is the formula for pressure based on its definition? P = F/A ( Force per unit Area)

What could the force be in this case? The weight

What could you substitute in for MASS? Since density is equal to mass over volume, you can substitute volume x density for mass

Suppose the object was a cylinder, could could you find the Volume? Area times the displacement(height)

What is the formula for absolute pressure?

The pressure exerted by a person's lungs can be measured by having the person blow as hard as possible into one side of a manometer.( see page 317 in the blue book and page 315 in the white book for reference as to what a manometer looks like). If a person blowing into one side of an open tube manometer produces a 70 cm difference in heights of the columns of water in the manometer arms, what is the lung pressure?

According to Archimedes, the buoyant force is equal to the ____WEIGHT__________ of fluid it displaces.

Once again, what can you substitute in for the MASS? Density times volume

What is the formula for the buoyant force?

An irregularly shaped piece of metal has a mass of 90 grams in air. It is suspended from a scale and the scale reads 75 grams when the piece is submerged in water. What are the volume and density of the piece of metal? First you find the weight in air and in water. Subtract the two values to find the BUOYANT force.



What are the 3 points that define an IDEAL fluid?

● non-viscous● incompressible● non-turbulent

What kind of flow do you have when every particle moves exactly along the smooth path as every particle that follows it? Laminar Flow What do you call the path of the flow mentioned above? Streamlines What kind of flow do you have in which the paths are irregular? Turbulent Flow What do you call the path of this kind of flow? Eddy Currents

Fill in the blank: Concerning a closed pipe system, the mass that flows into a region will _EQUAL___________ the mass that flows out of a region.

What is the equation of flow continuity?

Water flows from a 2.0 cm pipe at a speed of 0.35 m/s. How long will it take to fill a 10-L container?



What is Bernoulli's Equation?

In an industrial cooling process, water is circulated through a system. If the water pumped from the first floor through a 6.0 cm pipe with a speed of 0.45 m/s under a pressure of 53,157.9 Pa, what will be the pressure on the next floor 4.0 m above in a pipe with a diameter of 2.0 cm? You first must use the equation for continuity to solve for the velocity of water on the second floor!

Then use Bernoulli's equation to solve for the Pressure. Keeping in mind that the initial height is zero.



Consider the formula Q = mc∆T

What are the units of Q? JOULES What are the units of m? KILOGRAMS

What are the units of ∆T? DEGREES CELSIUS

Re-write the formula above and solve it in terms for c : Q/m∆Τ=c

What are the units of c? J/kgxC

What is the significance of the ∆? It means CHANGE or DIFFERENCE

According to Conservation of Energy, Heat __LOST___________ equals Heat ____GAINED_________

A thin copper cup of mass 150-g containing 500-g of water is at a temperature of 20 degrees Celsius. A 225-g sample of an unidentified material at 508 degrees Celsius is lowered into the bath and the cup is sealed. After a few minutes, the system reaches a constant final temperature of 40 degrees Celsius. Determine the specific heat of the sample.

How many objects are losing heat? ONE How many objects are gaining heat? TWO

Solve for c:

If something has specific heat it MUST be CHANGING in what? TEMPERATURE

If an object is NOT undergoing the answer above it must be involved in what type of heat? LATENT



Write the formula for ___LATENT____________ heat. (use answer above)

Q = mL

Re-write the formula above and solve it in terms for L : L= Q/m

What are the units for L: Joules/Kg

Write the appropriate “ Heat of ………” word for the following processes

Melting = __Fusion_______________ Freezing = ______Solidification____________ evaporating = __vaporization_______________

Condensing = ___condensation_________________

How much heat must be added to a 1.0 Kg mass of ice at – 10 degrees Celsius in order to transform it into 110 degree Celsius steam? (c(steam) = 2020 J/kgxC) How many processes or states does this piece of ice go through? FIVE

Solve for Q:

1 mole equals what three things

● Mass from periodic table● Avogadro's # of molecules● 22.4 Liters of a gas at STP

How many grams are in 3.75 moles of NaF2 ?

How many molecules are in 16.3 L of Cl2 at STP?



Consider the formula PV = nRT

What does P stand for? Pressure Units: Pascals OR Newtons/meter

What does V stand for? Volume Units: Meters cubed

What does n stand for? moles

What does T stand for? temperature Units: Kelvin

Re-Arrange the formula above and solve for R: Units:

If 23.8 grams of Ammonia gas ( NH3 ) are to be put into a 10.0-L container at a pressure 202.6 kPa, at what

temperature should the gas be maintained?

What needs to be determined before you begin this problem? Convert your grams to moles, Liters to cubic meters, and kilopascals to pascals.

Solve for T?

What must the units of temperature be in when dealing with gas laws? KELVIN

If a gas is placed in a piston at a specific pressure, yet there is no change in volume, the work done by the gas



is? ZERO

Losing heat has what sign? NEGATIVE

Gaining? POSITIVE

What is the sign of work if the gas does the work? POSITIVE

What is the sign of work if work is done on the gas? NEGATIVE

Both Q(heat) and W(work) correspond to the transfer of energy. What do you call the difference of Q and W? (Hint: this answer depends on a change in temperature) The change in internal energy or ∆U

A cylinder containing a gas is sealed with a nearly frictionless piston at a pressure of 0.20 MPa. The cylinder is placed in contact with a source of heat and the gas very slowly expands, moving the piston, in such a way that the volume changes by 5 x 10-3 m3 . Assuming the process is isobaric, and given that 300 J of heat enters the system, determine its change in internal energy

What exponent will Mpa get? x 106

What do you have to determine first? The work! W = P∆V Solve for ∆U:

Don’t let the sign fool you! This piston expands at the expense of a reduction!

Fill in chart below

Process Isothermal Isobaric Isovolumetric Adiabatic

Constant? Temperature Pressure Volume Nothing

Changing? Pressure, VolumeVolume, temperature

Pressure, temperature

Pressure,Volume, Temp.



Special things To remember? ∆U=0, Q = W ∆V=0, W=0, ∆U=Q Q=0, ∆U= -W

What can you determine when you know what you get OUT of an engine based on what you put IN? The EFFICIENCY

What do you call the MAXIMUM or IDEAL situation according to your answer above? CARNOT EFFICIENCY

What must you remember about the temperature in an IDEAL situation? They must be in KELVIN

1 mole of an ideal gas is taken through the cyclic process shown to the left.

If the situation involves an ideal gas, what formula do you use? PV=nRT

By what value will you multiply your units of pressure by?1.01x105

At what temperature is point B? 200 K

At what pressure is point B? 1.01x105 Pa

Using the ideal gas law and point B, solve for V1?

Solve for the volume at point A

(a) Compute the work (W) for each of the four processes. Work is the Area under the line. W = 0 for the process from D to A and from B to C because there is NO CHANGE in volume or NO AREA.



If this process is cyclic, meaning that it returns to its original starting position, what is its change in internal energy?

∆U = ZERO

(b) What is the NET work? 3312.8 + (-1656.4) = 1656.4 J

(c) What is T3? Since the Volume doubles from C to D thus the temperature must DOUBLE according to Charles' Law T3 = 800 K

An internal combustion engine using natural gas and air as a working substance has a temperature in the spark-ignited firing chamber of 2150 K and an exhaust temperature of 900 K. The difference between the heat supplied and the work done by the engine in one complete cycle is 460 J.

What does the word “difference” suggest? SUBTRACT

What is another way to state “heat supplied”? Heat Absorbed, Heat taken in

If the difference between the heat supplied(Qh) and the work(W) done by the engine in one complete cycle is

460 J, what are they really saying 460 J is? The Heat expelled to the COLD RESERVIOR, Qc = 460 J

If you were asked to find the ideal efficiency, what kind of engine are we suggesting? Carnot

Solve for the maximum efficiency

How much work is done if the heat input is 790 J?



What is the ACTUAL efficiceny (meaning don’t use Carnot)


AP Physics B - Concept Inventory- Waves,Sound, Optics

A.P. Inventory – Test 6 – Waves, Sound, and Optics

Waves and Sound

1. Sound occurs at this part of a standing wave?

2. Sound DOES NOT occur at this part of a standing wave?

3. For an open pipe, sound occurs every ____________ wavelength?

4. For a closed pipe, sound occurs every ____________ wavelength?

5. Open pipes play ________ harmonics.

6. Closed pipes play only ______ harmonics.

7. Suppose the fundamental frequency of a resonating sound wave in a pipe is 325 Hz, What would be the next highest frequency that emits a sound in an open pipe? Closed pipe?

8. If a police siren emits a sound at a frequency of 60 Hz, as it moves towards you it appears that the frequency does this?

As the car moves away?

9. What do we call the phenomenon in #8?

10. For a wave traveling on a string, the velocity is directly proportional to?

Inversely proportional to?

Optics On the Horizontal Line below, draw what would happen to an incident ray in air striking water and then refracting.



What does “n” stand for?

“n” is a ratio of what 2 things?

What happens to light when it enters a medium of low “n” to a medium of high “n”?

ALL ANGLES when dealing with refraction MUST be measured from the?

If a light ray comes up from a medium of high “n” into a medium of low “n”, yet the ray does not refract you have said to have exceeded the what?

After you exceeded the answer above you have Total ___________ _____________.

A ray of light comes up from water into air. The incident angle in water is 27 degrees. Calculate the refracted angle in air.

A ray of light travels from diamond ( n = 2.36) into air. Calculate the minimum angle that would result in a refracted ray.

What is the sign of the image distance if it located in the following places?

Same side of a Converging mirror as the object?



Opposite side of a Converging mirror as the object?

Same side of a Converging lens as the object?

Opposite side of a Converging lens as the object?

What is the sign of the focal point for a Diverging Lens or Mirror?

What kind of image will you have if the object is inside the focal point of a converging lens or mirror?

What kind of image will you have from a diverging lens or mirror?

An object is placed 40 cm in front of a diverging lens with a focal length of 13 cm. a) Calculate the image distance b) Calculate the magnification

What are the characteristics of the image mentioned above?

Diffraction

Bright fringes occur at every _______ wavelength.

Dark Fringes occur at every _______ wavelength.

The distance one ray travels more than the other is known as the?

Bright fringes are a result of what type of interference?

Dark fringes are a result of what type of interference?

“d” represents:

“L” represents



“y” represents

“m” represents

The bright central has what order?

The dark fringe on each side of the bright central has what order?

If a diffraction grating has 15,450 lines per cm, what is the distance between the slits?

What is the path difference at the 4th order dark fringe?


AP Physics B - Conceptual Inventory - Test 6 - answers

A.P. Inventory – Test 6 – Waves, Sound, and Optics

Waves and Sound

1. Sound occurs at this part of a standing wave? The antinode

2. Sound DOES NOT occur at this part of a standing wave? The node

3. For an open pipe, sound occurs every ___1/2_________ wavelength?

4. For a closed pipe, sound occurs every ____1/4________ wavelength?

5. Open pipes play __ALL______ harmonics.

6. Closed pipes play only _ODD_____ harmonics.

7. Suppose the fundamental frequency of a resonating sound wave in a pipe is 325 Hz, What would be the next highest frequency that emits a sound in an open pipe? Closed pipe? Open: 650 Hz Closed: 975 Hz

8. If a police siren emits a sound at a frequency of 60 Hz, as it moves towards you it appears that the frequency does this? gets louder

As the car moves away? gets softer

9. What do we call the phenomenon in #8? The Doppler effect

10. For a wave traveling on a string, the velocity is directly proportional to? The Tension(T)

Inversely proportional to? The linear mass density of the string(M/L)

Optics On the Horizontal Line below, draw what would happen to an incident ray in air striking water and then refracting.



What does “n” stand for? index of refraction

“n” is a ratio of what 2 things? The speed of light in a vaccum and the speed of light in that medium

What happens to light when it enters a medium of low “n” to a medium of high “n”? The rays bend TOWARDS the normal. In other words the angle of refraction is LESS THAN the angle of incidance.

ALL ANGLES when dealing with refraction MUST be measured from the? NORMAL

If a light ray comes up from a medium of high “n” into a medium of low “n”, yet the ray does not refract you have said to have exceeded the what? The critical angle

After you exceeded the answer above you have Total INTERNAL REFLECTION

A ray of light comes up from water into air. The incident angle in water is 27 degrees. Calculate the refracted angle in air.

A ray of light travels from diamond ( n = 2.36) into air. Calculate the minimum angle that would result in a refracted ray.



What is the sign of the image distance if it located in the following places?

Same side of a Converging mirror as the object? Positive

Opposite side of a Converging mirror as the object? Negative

Same side of a Converging lens as the object? Negative

Opposite side of a Converging lens as the object? Positive

What is the sign of the focal point for a Diverging Lens or Mirror? Negative

What kind of image will you have if the object is inside the focal point of a converging lens or mirror? Virtual

What kind of image will you have from a diverging lens or mirror? Virtual

An object is placed 40 cm in front of a diverging lens with a focal length of 13 cm. a) Calculate the image distance

b) Calculate the magnification



What are the characteristics of the image mentioned above? VIRTUAL, REDUCED, UPRIGHT

Diffraction

Bright fringes occur at every __1_____ wavelength.

Dark Fringes occur at every ___1/2____ wavelength.

The distance one ray travels more than the other is known as the? path difference

Bright fringes are a result of what type of interference? Constructive

Dark fringes are a result of what type of interference? Destructive

“d” represents: slit separation distance

“L” represents: Distance the slit is from the screen

“y” represents: Distance between the bright central and a fringe

“m” represents: the order( the numerical # of wavelengths)

The bright central has what order? ZERO

The dark fringe on each side of the bright central has what order? ZERO

If a diffraction grating has 15,450 lines per cm, what is the distance between the slits? Convert this distance to meters, them invert. d = 6.47 x 10-7m

What is the path difference at the 4th order dark fringe? 4 1/2λ




AP Physics B - Conceptual Inventory -E & M

A.P. Inventory #7 – Electricity & Magnetism

What is the symbol for charge?

What is the unit for charge?

What is the charge for a proton and electron?

What do like charges do?

What do unlike charges do?

According to Coulomb’s Law, “ The Force is _______________ related to the ___________ of the

charges and ________________ related to the ____________ of the separation distance.

When a proportionality becomes a formula, what must be added?

What is the value for the answer above?

3 metal spheres have charges of (sphere 1=) –12µC , (sphere 2=) +4 µC, and (sphere 3=) +3 µC. Sphere 1 touches sphere 2 leaving what charge on each sphere?

Sphere 2 now touches sphere 3 leaving what charges on each sphere?

If Sphere 1 is now placed at +y = 3 cm, sphere 2 at the origin, and sphere 3 at x= -2. Calculate the magnitude and direction of the NET electrostatic force on the particle at the origin.

Answer with the words, “ Leave” or “Enter”.

The electric field lines ___________ a positive charge and ___________ a negative charge.

The electric field is _______________ proportional to the force and _______________ proportional to the _____________.



According to the statement above, what would the formula look like?

Substitute Coulomb’s Law into the formula above and show an alternate formula for electric field

What is another unit for voltage besides volts? Show this below V =

If the numerator was a symbol rather than a unit it would be?

If the denominator was a symbol rather than a unit it would be?

If the above concept looked like a formula it would look like?

Sometimes you might substitute __________ ____________ for work, especially if the particle is moving.

Insert the basic formula for work into the formula above and show it below?

Insert Coulomb’s Law into the formula above and show it below.

Calculate the Electric field on the y axis due to Sphere 1at the origin

Calculate the electric field on the x axis due to sphere 3 at the origin



Calculate the magnitude of the electric field due to Sphere 1 & 3 as well as the direction at the origin

Calculate the electric potential at the origin due to sphere 1


Calculate the NET potential at the origin due to Sphere 1 & 3

What is the unit for Capacitance?

What does a µF stand for numerically?

What does the q or charge of a capacitor equal?

To find the total capacitance of a series circuit you must:

To find the total capacitance of a parallel circuit you must:

What happens between the 2 oppositely charges plates of a capacitor

Can we find the voltage of these plates? How?

What is the formula for storing energy in a capacitor?

Substitute the Capacitance formula into the energy formula and show below.



What is the total capacitance of the circuit to the left?

What is the formula for the energy stored in a capacitor?

How much energy is stored in this capacitor.

What is the formula for Ohm’s law?

What does the voltage do in a series circuit? Parallel?

What does the current do in a series circuit? Parallel?

What is the basic electrical formula for Power?

Substitute Ohm’s law into the formula above and show me 2 alternate formulas for Power.



The picture above represents?

What does the VT represent graphically?

What does the ε represent graphically?

What does the I represent graphically?

What does “r” represent?

A particle can become a magnet as long as the particle itself is ______________________

What is the formula for the magnetic force on a moving particle?

According to the Right Hand Rule(RHR), do the fingers represent and include units?

According to the Right Hand Rule(RHR), does the thumb represent and include units?

According to the Right Hand Rule(RHR), does the palm represent and include units?

The left hand is used for what type of particle? Right hand?

What is the unit for a magnetic field?

When particles move into a magnetic area, the shape of their path often resembles a ?

What 2 forces are at work here?



Set them equal to each other and solve for r.

If the electrons were in a wire, would you use F = qvb? If not, what formula is appropriate?

For there to be Magnetic Flux, there must be a changing _______________ ______________.

What is the formula for Magnetic Flux?

How do you find the voltage in a Rod or a coil of wire? Show me two ways!

A long, straight wire is in the same plane as a rectangular, conducting loop. The wire carries a constant current I as shown in the figure. Which one of the following statements is true if the wire is suddenly moved toward the loop?

A) There will be no induced emf and no induced current. B) There will be an induced emf, but no induced current. C) There will be an induced current that is clockwise around the loop. D) There will be an induced current that is counterclockwise around the loop. E) There will be an induced electric field that is clockwise around the loop.


AP Physics B - Conceptual Inventory - E & M Answers

A.P. Inventory #7 – Electricity & Magnetism

What is the symbol for charge? q What is the unit for charge? Colomb or "C" What is the charge for a proton and electron? 1.6 x 10-19 C What do like charges do? repel What do unlike charges do? Attract According to Coulomb’s Law, “ The Force is ___directly____________ related to the __product_________ of the

charges and __inversely______________ related to the ___square_________ of the separation distance.

When a proportionality becomes a formula, what must be added? a constant

What is the value for the answer above? 9 x 109 Nm2/C2

3 metal spheres have charges of (sphere 1=) –12µC , (sphere 2=) +4 µC, and (sphere 3=) +3 µC. Sphere 1 touches sphere 2 leaving what charge on each sphere? -4µC on each sphere

Sphere 2 now touches sphere 3 leaving what charges on each sphere? -0.5µC on each sphere

If Sphere 1 is now placed at +y = 3 cm, sphere 2 at the origin, and sphere 3 at x= -2. Calculate the magnitude and direction of the NET electrostatic force on the particle at the origin. Using the NEW charges after the touching of all the spheres!



The direction is below the negative x axis!

The electric field lines ___LEAVE________ a positive charge and ___ENTER________ a negative charge.

The electric field is ___DIRECTLY____________ proportional to the force and _INVERSELY____ proportional to the ____CHARGE______.

According to the statement above, what would the formula look like?

Substitute Coulomb’s Law into the formula above and show an alternate formula for electric field



What is another unit for voltage besides volts? Show this below V = Joules/ Coloumb

If the numerator was a symbol rather than a unit it would be? WORK(W) If the denominator was a symbol rather than a unit it would be? Charge(q) If the above concept looked like a formula it would look like?

Sometimes you might substitute _Kinetic__Energy______ for work, especially if the particle is moving.

Insert the basic formula for work into the formula above and show it below?

Insert Coulomb’s Law into the formula above and show it below.

Calculate the Electric field on the y axis due to Sphere 1at the origin

Calculate the electric field on the x axis due to sphere 3 at the origin



Calculate the magnitude of the electric field due to Sphere 1 & 3 as well as the direction at the origin

The direction is above the positive X axis, because electric field lines enter negativeCalculate the electric potential at the origin due to sphere 1




Calculate the NET potential due to Sphere 1 & 3

What is the unit for Capacitance? Farad What does •F stand for numerically? Micro ( 10-6) What does the q or charge of a capacitor equal? Q = CV To find the total capacitance of a series circuit you must: Use the parallel resistor formula To find the total capacitance of a parallel circuit you must: Add the individual capacitances What happens between the 2 oppositely charges plates of a capacitor And electric field sets up between them Can we find the voltage of these plates? How? Yes, If you know the electric field strength and the distance between the plates you can use V = Ed What is the formula for storing energy in a capacitor?



What is the total capacitance of the circuit to the left?

How much energy is stored in this capacitor.

What is the formula for Ohm’s law? V = IR What does the voltage do in a series circuit? Parallel? Individual voltages add up to the total in a series and are equal to the total in a parallel What does the current do in a series circuit? Parallel? Individual currents are equal to the total in a series and add up to the total in a parallel What is the basic electrical formula for Power? P=VI Substitute Ohm’s law into the formula above and show me 2 alternate formulas for Power.



The picture above represents? A battery with internal resistance

What does the VT represent graphically?

It is usually plotted on the y-axis

What does the ε represent graphically? The y- intercept of the graph. It is the emf or the MAXIMUM voltage OR the voltage when the current is equal to ZERO, thus being the y-intercept.

What does the I represent graphically? I ,or the current, is plotted on the x-axis The maximum current occurs when the Y=0 What does “r” represent? The "internal" resistance of the battery

A particle can become a magnet as long as the particle itself is ___MOVING___________________

What is the formula for the magnetic force on a moving particle?

According to the Right Hand Rule(RHR), do the fingers represent and include units? The B-Field(magnetic field) in TESLAS According to the Right Hand Rule(RHR), does the thumb represent and include units? The velocity in m/s According to the Right Hand Rule(RHR), does the palm represent and include units? The force in Newtons



The left hand is used for what type of particle? Right hand? Right hand for proton, left hand for electron, right hand for wires and rods

What is the unit for a magnetic field? TESLA When particles move into a magnetic area, the shape of their path often resembles a ? A circle

What 2 forces are at work here? Magnetic and centripetal Set them equal to each other and solve for r.

If the electrons were in a wire, would you use F = qvb? If not, what formula is appropriate?

NO!!!!



For there to be Magnetic Flux, there must be a changing ____AREA___________ ______________.

What is the formula for Magnetic Flux?

How do you find the voltage in a Rod or a coil of wire? Show me two ways!

A long, straight wire is in the same plane as a rectangular, conducting loop. The wire carries a constant current I as shown in the figure. Which one of the following statements is true if the wire is suddenly moved toward the loop? Pointing thumb in the direction of current we see that the wire's magnetic field goes INTO the page where the loop is located, thus the loop's

magnetic field must be OUT of the page inside the loop. Using our right hand, we place our fingers out of the page and wrap arounf the loop to discover the current goes counter-clockwise. Answer = D A) There will be no induced emf and no induced current. B) There will be an induced emf, but no induced current. C) There will be an induced current that is clockwise around the loop. D) There will be an induced current that is counterclockwise around the loop. E) There will be an induced electric field that is clockwise around the loop.



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