Mechanics (2)

This is the classic physics topic. Here is where physics began, and where physics has most

influenced other sciences (especially economics).Mechanics is a huge subject, that we divide into

“kinematics” (description of motion) and “dynamics” (causes of motion).

Mr. KlapholzShaker Heights

High School

A special challenge

• Nowhere else in the IB physics curriculum is so much material covered in so little time.

• Clearly IB does not ask us to learn it thoroughly, and this can be hard on students and awkward for teachers.

• The challenge for us is to learn it well enough, but not to dwell on it too long.

A mistake by Tsokos

• After looking at other IB texts, it seems clear that our author has messed up with ‘displacement’.

• What follows is what the majority of IB texts use.

• Even so, different cultures use the words in slightly different ways, so we’ll need to be on our toes in the IB world.

IB vs. USA• They say “Gradient of a line”, we say:• “Slope of a line”• They call it a “lift”, we call it an:• Elevator.• They say “Lorry”, we say:• “Truck”• They say “Trolly”, we say:• “Cart”• They say “Torch”, we say• “Flashlight”

• I say: “GOOD LUCK!”

Position (x)

• We use “x” to say __________ on the number line an object is located.

• “Position” is a lot like the __________ of a point.

Position (x)

• We use “x” to say where on the number line an object is located.

• “Position” is a lot like the __________ of a point.

Position (x)

• We use “x” to say where on the number line an object is located.

• “Position” is a lot like the address of a point.

Distance (d or s)

• “Distance” describes how far apart two points are.

• Simply: it is how much string it would take to connect two points.

• Distance is never negative.• Distance is a scalar.

Displacement (s) 1 of 3

• “Displacement” is like distance, but it is a __________ . Displacement has _________ .

• Positive and negative depend on how we set up our x-y axes.

• The magnitude (the size, the amount) of displacement, is __________ .

Displacement (s) 1 of 3

• “Displacement” is like distance, but it is a vector. Displacement has __________ .

• Positive and negative depend on how we set up our x-y axes.

• The magnitude (the size, the amount) of displacement, is __________ .

Displacement (s) 1 of 3

• “Displacement” is like distance, but it is a vector. Displacement has direction.

• Positive and negative depend on how we set up our x-y axes.

• The magnitude (the size, the amount) of displacement, is __________ .

Displacement (s) 1 of 3

• “Displacement” is like distance, but it is a vector. Displacement has direction.

• Positive and negative depend on how we set up our x-y axes.

• The magnitude (the size, the amount) of displacement, is distance.

Displacement (s) 2 of 3

• If you travel 100 m East, that could be a positive displacement. Then, if you traveled 100 m West, that would be a negative displacement.

• Displacement is the change in __________ .• s = x2 – x1

• s = xf – xi

• s = Dx {memorize this}

Displacement (s) 2 of 3

• If you travel 100 m East, that could be a positive displacement. Then, if you traveled 100 m West, that would be a negative displacement.

• Displacement is the change in position.• s = x2 – x1

• s = xf – xi

• s = Dx {memorize this}

Displacement (s) 3 of 3

• Draw a number line so that it is like a football field: 10 yards, 20, 30 , 40, 50.

• An object starts at the 40 yard line.• The object then moves to the 30.• What is the displacement of the object?

s = Dx = x2 – x1

s = 30 yd – 40 yds = -10 yards

Speed (v)

• You are traveling on the highway. What are the units for your speed?

• What is the equation for speed?• Speed = __________ • If you travel 110 miles in 2 hours then your

speed is?

Speed (v)

• You are traveling on the highway. What are the units for your speed?

• What is the equation for speed?• Speed = Distance ÷ Time• If you travel 110 miles in 2 hours then your

speed is?

Velocity (v)

• Velocity is like speed, but it is a vector. Velocity has __________ .

• Guess the equation for velocity:• Velocity =• v =• The magnitude (the size, the amount) of

velocity, is __________ .

Velocity (v)

• Velocity is like speed, but it is a vector. Velocity has direction.

• Guess the equation for velocity:• Velocity =• v =• The magnitude (the size, the amount) of

velocity, is __________ .

Velocity (v)

• Velocity is like speed, but it is a vector. Velocity has direction.

• Guess the equation for velocity:• Velocity = displacement / time• v =• The magnitude (the size, the amount) of

velocity, is __________ .

Velocity (v)

• Velocity is like speed, but it is a vector. Velocity has direction.

• Guess the equation for velocity:• Velocity = displacement / time• v = s ÷ t• The magnitude (the size, the amount) of

velocity, is __________ .

Velocity (v)

• Velocity is like speed, but it is a vector. Velocity has direction.

• Guess the equation for velocity:• Velocity = displacement / time• v = s ÷ t• The magnitude (the size, the amount) of

velocity, is speed.

Velocity (v)

• If you walk from the 40-yard line of a football field to the 10-yard line in 5 seconds, what is your velocity?

• v = Dx / t• v = (10 yd – 40 yd) / 5 s• v = (–30 yd) / 5 s• v = –6 yd s-1

Acceleration (a)

• Acceleration is the rate of change of velocity.• a = Dv / t

Acceleration (a)

• If you (in a sports car) go from 0 mph to 60 mph in 6 seconds, then your acceleration is:

• 10 mph per second (10 mph s-1)• If I go from 0 to 60 mph in 10 seconds, then

my acceleration is just 6 mph s-1.• We have the same change in velocity, but

different accelerations.

Acceleration and Velocity

• a = Dv / t• a = (v2 – v1) / t• Do a little algebra and see:• v2 = v1 + at• This says that the final velocity is equal to the

initial velocity, plus the product of acceleration and time.

• Some IB news…

Acceleration and Velocity

• IB does not write it as: v2 = v1 + at• Instead we have: v = u + at• This saves us from the subscripts.• What does “v” represent?• What does “u” represent?

Velocities and Displacement (1 of 2)

• 1: Average Velocity = Displacement / Time • 2: (u + v)÷2 = s / t• 3: s = {(u + v)÷2}•t

Velocities and Displacement (2 of 2)

• If you accelerate, then of course that affects how far you go.

• s = ut + (1/2)at2

• Combine some of the equations, and rearrange to get our last equation:

• v2 = u2 + 2as

Graphs of Position vs. Time

• The gradient (or slope) of a position graph is the velocity.

• So, if an object is moving at constant velocity, then its x vs. t graph is a line. Draw.

• If an object is not moving, then its position graph is a horizontal line. Draw.

• If an object’s velocity is increasing, then the slope of its position graph is increasing. Draw.

Graphs of Velocity against Time

• The gradient (or slope) of a velocity graph is the acceleration.

• So, If an object is moving at constant velocity, then its velocity graph is a horizontal line. Draw.

• If an object is moving at constant acceleration, then its v vs. t graph is a line. Draw.

• The area under a graph of v vs. t is displacement.

Force (the cause of motion)

• A force is a push or a pull.• Force is a vector.• An example of a force is when you push a

button on your calculator.• Another example of a force is weight. Weight

is the force that the earth puts on an object. The weight vector is always downward.

Mass

• Mass is the amount of matter that an object possesses.

• Mass is not a vector; mass does not have direction.

• If an astronaut brings the key to her house with her on a mission, then the weight of the key will decrease, but the mass of the key will stay the same.

Sum of the forces. Net Force. SF

• If you add up the forces that act on one object, you have the ‘sum’ of the forces or the ‘net force’.

• What is the sum of the forces that act on a book that sits on a table? Is it zero?

• Drop the book. Is the net force zero during the fall?

First Law of Motion

• If the net force is zero, then the acceleration is zero.

• If a = 0, then SF = 0.• This is the “Law of Inertia” discovered by

Galileo (and embraced by Newton).• If the forces on an object add up to zero, then

the object will continue to do what it was doing.

Second Law of Motion

• Acceleration is determined by the _____ force and by the mass.

• a = SF / m• If you see “F = ma”, then that ‘F’ must be the

net force or “unbalanced force” or the “sum of the forces.”

Example of the Second Law of Motion

• A book is resting on a table.• The mass of a book is 2 kg.• A person pushes Northward on the book with a

force of 10 N.• Friction opposes this push with a force of 4 N.• What is the net force?• The net force is 6 N.• What is the acceleration?• a = (6 N) / (2 kg) = 3 m s-2.

Third Law of Motion

• If object A puts a force on object B, then object B will put an equal and opposite force on object A.

• This is sometimes called the “Action - Reaction” law.

If you stretch something, it pulls back.If you let it be, then there is no force.

If you compress something, then it pushes back.

http://cecs.boardeducation.net/dynamics-forum-f12/spring-force-hooke-s-law-t19.htm

Hooke’s Law

• Always compare a spring to its ‘natural’ length.• If you compress the spring a distance Dx, then

the spring will push back. And, the greater the Dx, the greater the push back.

F = -Dx• Interestingly, it also works if you stretch the

spring, and again the force that the spring exerts is opposite in direction to the change in length.