Newton’s Laws

Newton’s Laws

--Don’t cross the Newton.You’ll get figged.

Newton’s laws

1) An object in motion tends to stay in motion

unless acted upon by an outside, net force2) An object accelerates proportional to the net

force exerted upon it, inversely proportional to its mass.

3) For every action, there is an equal and opposite reaction.

Newton’s First Law

• …also known as “inertia”

• An object in motion tends to stay in motion, an object at rest tends to stay at rest…

Newton’s First Law

• …also known as “inertia”

• An object in motion tends to stay in motion, an object at rest tends to stay at rest…

…unless acted upon by an outside force!

Does anything remain in motion?

• So what causes objects to come to rest?

Does anything remain in motion?

• So what causes objects to come to rest?

Friction Happens

Friction opposes motion

V

The surfaces in contact cause friction

F

Decrease friction• Wheels• Skates/skis• Sleds• Lubricants• Magnetic levitation

Increase friction• Brakes• Rubber tires• Tread on tires/shoes• Spikes

Even without a surface…

V

…air resistance will slow moving objects

Air resistance

Decrease air resistance• Streamlining• Slowing down

(Professional cyclists shave their legs!)

Increase air resistance• Parachutes• Sails• Airfoils

Frames of reference

• Suppose a kayaker can paddle at 1.8 m/s, and she is on a river flowing at 1.5 m/s.

1. If she is paddling downstream, how fast is she moving with respect to:

a. The water?b. The riverbank?

2. If she is paddling upstream, how fast is she moving with respect to:

a. The water?b. The riverbank?

Definition

--A push or a pull.--must be exerted on an object

Forces

• A force is a push or a pull.– It has a DIRECTION!

5N East

15N North

7N West

Forces

• A force can cause acceleration.

• …this object accelerates to the east

5N East

Forces

• A force can cause acceleration.

• …or not.

The object’s weight pushes it against the surface

Forces

• The acceleration of an object is a result of the forces acting upon it.

A object’s weight pulls it down

The cart starts to move west as the horse begins to pull

Forces

• The units on a force are Newtons

• (Remember? Newton’s Laws of motion?)

Forces

• A one Newton force will accelerate a 1 kg object at one m/s2

1N=1kgm/s2

A 1 N force will accelerate a 1kg object at 1 m/s2

1 kg

Forces


1N=1kgm/s2

A 1 N force will accelerate a .5kg object at 2 m/s2

.5 kg

Forces


1N=1kgm/s2

A 1 N force will accelerate a 2kg object at .5 m/s2

2 kg

Newton’s Second Law

• The acceleration of an object is proportional to the net force acting on it, and inversely proportional to the object’s mass.

a=F/m or F=ma

Centripetal force

An object moving in a curved path is acted upon

by a centripetal force

Weight

Weight is the force exerted upon an object by

the acceleration of gravity.

Weight is a force!

1) What is the weight of a 5.8 kg object?

2) What is the weight of a 865 g object?

3) What is the mass of a 580 N object?

The acceleration of gravity = 9.8 m/s2

1) What is the weight of a 5.8 kg object?57N

2) What is the weight of a 865 g object?8.5 N

3) What is the mass of a 580 N object?59 kg

What is the acceleration?

1) A 850 kg car gets a force of 2700 N (from the friction between the tires and the road)

2) A tugboat provides a force of 70,000 N of tension on its tow cables to pull a ship with a mass of 15,000,000 kg away from the dock.

3) The Saturn-V rocket has a mass of 2.8x106 kg, while its engines provide 3.3x107 N of thrust

What is the acceleration?

1) A 850 kg car gets a force of 2700 N (from the friction between the tires and the road)

3.2 m/s2

2) A tugboat provides a force of 70,000 N of tension on its tow cables to pull a ship with a mass of 15,000,000 kg away from the dock.

.0047 m/s2

3) The Saturn-V rocket has a mass of 2.8x106 kg, while its engines provide 3.3x107 N of thrust

12 m/s2

What is the force?

1) A 72 kg sprinter leaves the blocks at 15 m/s2

2) A fighter jet with a mass of 4500 kg accelerates at 35 m/s2 while taking off.

3) A quarterback throws a 1.2 kg football at 21 m/s, accelerating it from rest in .32 s

What is the force?

1) A 72 kg sprinter leaves the blocks at 15 m/s2

1100 N2) A fighter jet with a mass of 4500 kg accelerates at 35 m/s2 while taking off.

160,000 N3) A quarterback throws a 1.2 kg football at 21 m/s, accelerating it from rest in .32 s

79 N

What is the braking distance?• The road can offer a car exactly 1/3 of its weight in

friction with the tires at full braking. Suppose the car has a mass of 1100 kg (weight = 10800 N)

a) How much friction does the road provide?

b) What is the acceleration of the car at full braking?

c) If the car is moving at 25 m/s, how far does it travel before coming to rest?



a) How much friction does the road provide?-3600 N

b) What is the acceleration of the car at full braking?-3.26 m/s2


97 m











97 m











380 m

Vector addition

• If two vectors lie in the same direction, add their magnitudes. The sum lies in the same direction.

5N (north) + 10N (north) = 15N (north)

75m/s (east) + 40m/s (east) = 115m/s (east)

Vector addition• If two vectors lie in opposite directions, subtract

their magnitudes. The sum lies in the same direction as the longer vector.

5N (south) + 12N (north) = 7N (north)

75m/s (east) + 40m/s (west) = 35m/s (east)

What is the net force?

1) A 20 N object is lifted with 36 N. .2) A 45N object is lifted by a 850 N man.

.3) A two guys push a desk with 350 N

each. .4) I pull a desk with 400 N against 180 N

friction. .

What is the net force?

1) A 20 N object is lifted with 36 N. +16 N

2) A 45N object is lifted by a 850 N man. -895N

3) A two guys push a desk with 350 N each. +700N

4) I pull a desk with 400 N against 180 N friction. +220N

Draw two vectors at right angles:

• On your graph paper, draw a 5.0 cm vector east and a 7.0 cm vector north.


• On your graph paper, draw a 5.0 cm vector east and a 7.0 cm vector north.

• These vectors might represent x and y components of velocity

vx

vy


• So, what direction is the object going?

vx

vy


• So, what direction is the object going?

• Up and to the right —right?

vx

vy


• Draw the vectors TIP to TAIL

• (re-draw the north vector so its tail starts at the tip of the east vector)

vx

vy


• The RESULTANT vector is the sum of the two vectors.

vx

vy

v R



• Measure and record the length of the resultant vector (in cm.) and the angle it makes with vx

vx

vy

v R



• Measure and record the length of the resultant vector (in cm.) and the angle it makes with vx

vx

vyv R

=8.6

cm at

54o

To add two vectors at right angles

Draw them tip to tail

The sum is the hypotenuse


Find the length using the Pythagorean theorem.

Find the angle using an inverse tangent.


Find the length using the Pythagorean theorem.

vR=√(72+52)=8.6 cm

Find the angle using an inverse tangent.

ϴ=tan-1(7/5)=54o

Try it. What is the resultant?

1) Pulling a wagon with a force of 55N up and 75 N forwards.2) Flying at 90 m/s north with a 50 m/s crosswind to the east.3) Rowing at 2.0 m/s across a river with a

current of 3.0 m/s downstream4) Accelerating at 27 m/s2 forwards while

dropping at -9.8 m/s2 down

Components of forces

It is often useful to separate a force into two

forces at right angles (e.g. right/left and up/down forces)

Resolving a vector

A length and angle are given

ϴ

L

Resolving a vector

A length and angle are given —how do you find the x and y components of the vector?ϴ

L

Resolving a vector

X direction:vx=L cos ϴ

ϴ

LY direction:vy=L sin ϴ

To resolve a vector

• On your graph paper, draw a 6.5 cm vector at an angle of 25o N of E

To resolve a vector

• On your graph paper, draw a 6.5 cm vector at an angle of 25o N of E

• This could represent the initial velocity of a thrown object. (65 m/s at 25o)

To resolve a vector

What are the x and y components of this velocity?

vyvx

To resolve a vector

• vx=6.5 cos25=5.9 cm

• vy=6.5 sin25=2.7 cm

vyvx

To resolve a vector

• vx=6.5 cos25=5.9 cm(59 m/s forwards)• vy=6.5 sin25=2.7 cm(27 m/s up)

vyvx

Try it. What are the components?

1) Pulling a wagon with a force of 70 N at an angle of 50o

2) Flying at 90 m/s east northeast (22.5o N of E)3) Crossing a river at 4.6 m/s at an angle of 75o

to the bank of the river.4) Accelerating at 26 m/s2 at 21o down (21o

below the line of level flight)

…is dropped from a height of…

• Two things are given here!

1) vi=0 m/s and2) a=-9.8 m/s2

…is thrown horizontally…

1) viy=0 m/s2) ay=-9.8 m/s2

3) vx is given, and constant4) Time is the same for both x and y

motion

Try it.

1) A ball is dropped from a 38 m building. How long is it in the air?

2) A ball is thrown horizontally from the same building at a velocity of 25 m/s. How far does it travel before it hits the ground?

3) A car drives off an 11 m cliff at 35 m/s.a. How long is it in the air?b. How far does it travel before it hits the ground?c. What is its vertical velocity as it hits the ground?d. What is its total velocity (using vx and vy)?

…is thrown vertically…

1) a=-9.8 m/s2

2) The object rises as long as v>0 m/s, then it turns around and falls. 3) Rising time = falling time

Rising time

=Falling time

a=-9.8 m/s2

Up!

1) A pop fly goes up at 45 m/sa. How long does it rise?b. How high does it go?c. How long is it in the air?

2) A piece of candy is thrown up at 15 m/sa. How long does it rise?b. How high does it go?c. How long is it in the air?

…is thrown at an angle of…

• This is the big one—ballistic motion.1) Separate motion into x and y components.2) Calculate time in the air by the vy component3) Motion in the x direction is constant.

4) Highest point is halfway through the flight5) Rising and falling times are equal if the height

is the same.

Draw a picture (1 frame every .1 s)

1) A ball is dropped from a height of 2 m.2) A ball rolls at a constant velocity of 1 m/s right.3) A ball rolls off a 2 m high table at a horizontal

speed of 1 m/s4) A ball is thrown up with a vertical velocity of

+1 m/s 5) A ball is thrown with a vertical velocity of +1

m/s and a horizontal velocity of 1 m/s right

Draw a velocity vector on each ball

1) A ball is dropped from a height of 2 m.2) A ball rolls at a constant velocity of 1 m/s right.3) A ball is thrown with a vertical velocity of +1

m/s 4) A ball rolls off a 2 m table at a horizontal speed

of 1 m/s5) A ball is thrown with a vertical velocity of +1

m/s and a horizontal velocity of 1 m/s right

Ballistic motion

Ballistic motion

Ballistic motion

Ballistic motion

Ballistic motion

Ballistic motion

Ballistic motion

Ballistic motion

Equilibrant of a vector

A force is represented as a vector.

An equal and opposite force is the equilibrant of a vector.

An object subjected to a force and its equilibrant has no net force

(For an object that is not accelerating)

Force up=force down

andForce left=force right

Newton’s Third Law of Motion

• Usually applied to forces, but we will use it with momentum later

For every action, there is an equal and opposite reaction.


• If you push on something, it pushes back!

• The forces are equal and opposite.


• Two ways to use it:

1) If something is accelerating, what is it pushing against?

2) If something is not accelerating, what are the opposing forces?

What is it pushing against?

1) A helicopter takes off2) A sailboat leaves the dock3) A car comes to a stop4) A rock climber climbs up a cliff5) A planet circles the Sun (pulling, not pushing)

Statics

If acceleration is zero, then net force is zero.

If an object stays motionless, then acceleration is zero

Therefore….

Statics

If acceleration is zero, then net force is zero.

If an object stays motionless, then acceleration is zero

Therefore….

If an object stays motionless, the net force is zero!

Statics

?

10N 20N

Statics

50N

?

?

?

10N

40o

?

? ?

Statics

60N

60o 60o

? ?

?

Statics

60N

30o 30o

?

?

?

Statics (much harder!)

60N

50o 30o

? ?

?

Statics

20N

20o 40o

? ?

?

Statics

20N35o

?

?

?

Friction

Friction is a force exerted by touching surfaces

that opposes motion

Friction

• The magnitude depends on the force pushing the surfaces together and the surfaces

• The direction always opposes motion.

Friction

• The magnitude depends on the force pushing the surfaces together and the surfaces– Friction is directly related to the normal force– Sometimes we want to increase friction

• The direction always opposes motion.

Friction

• The magnitude depends on the force pushing the surfaces together and the surfaces– Friction is directly related to the normal force– Sometimes we want to increase friction

• The direction always opposes motion.– Slows down moving objects– Prevents slipping

Decrease friction• Wheels• Skates/skis• Sleds• Polishing / Lubricants• Magnetic levitation

Increase friction• Brakes• Rubber tires• Tread on tires/shoes• Spikes

m: the coefficient of friction

• m is the ratio of friction to normal force

m = F friction F normal

(please notice that the Newtons cancel!)

In general:

Smoother surfaces have smaller m = Less friction

In general:

Larger objects have a greater normal force= More friction

In general:

Surface area has very little effect= Same friction

What is m?

1) I (at 830 N) get 390N of traction (friction) between my shoes and the floor.

2) A 55 kg woman gets 150 N of friction between the floor and her Manolo Blahnik pumps

3) A 1500 kg car skids to a stop at -6.2 m/s2

4) A 75 kg cyclist on a 5 kg bike skids to a stop from 15 m/s in a distance of 25 m

The ramp problem

Force up=force downandForce left=force right

The ramp problem

Force out of the ramp=force into the ramp

andForce uphill=force downhill

The ramp problem

The ramp problem

The ramp problem

The ramp problem

Θ

The ramp problem

ΘΘ

That’s the ramp!

On the ramp problem:• Since the force into and out of the ramp are not

directly up and down, force up the ramp and down the ramp are not directly left and right.

• F in =F weight cos Θ• F out = -F in = F Normal

• F down = F weight sin Θ• F friction = m F Normal (can be up or down the ramp)

What is F Normal and F down?

• If Θ = …. F Normal F down

10o?20o?30o?45o?60o?

10N

For your test1) How long does it take

an object to fall:a) 1.5 m?b) 5.8 m?c) 15.5 m?

2) How long will an object be in the air if is tossed straight up at :

a) 11 m/s?b) 21 m/s?c) 35 m/s?

3) If the objects in q 1 and 2 are moving at a horizontal velocity of 5.0 m/s, how far will they travel?

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Newton’s Laws