Momentum and Energy

PHYS 1090 Unit 3

Question

If a car collides with a bug, which experiences the greatest force?

A. The car.

B. The bug.

C. It’s a tie.

D. Insufficient information to answer.

Force Meters

Newton’s Third Law

• Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first, along the same line of interaction.

• To every action there is always an opposed equal reaction.

• If object A exerts force F on object B, object B exerts force –F on object A.

FA→B = −FB→A

Bug + Windshield

Small car: 1250 kg

From the same force, the bug accelerates a lot more!

Large insect: 0.00025 kg

Forces are the same—the accelerations are different.

Interaction Forces

All forces are interaction forces!– gravity– wind– jumping– everything!

• This means: whenever something accelerates, something else accelerates in the opposite direction! Whoa!

Pulleys

Pulleys

• Change the direction but not magnitude of the tension in the cable

• Lift force is tension times number of segments lifting

• Lift height is pull divided by number of segments

Levers

Levers

• To balance a load, the force closest to the fulcrum must be larger

Levers

• To balance a load, the force closest to the fulcrum must be larger

• The load farthest from the fulcrum moves the most

Inclined Planes

Inclined Planes

• The steeper the plane, the greater the force required

• The steeper the plane, the shorter the distance pulled to reach the same height

Simple Machines

• All are a trade-off between force and distance (or force and speed)

• The greater force moves the least distance

F1d1 = F2d2

Work

Formula

work = F·d

F = force appliedd = distance traveled

Simple Machines

F1d1 = F2d2

Work input = Work output

• Forces are different

• Distances are different

• Work is the same.

Work and Energy

• Doing work on something changes its energy.

• Energy: “the ability to do work”

Conservation of Energy

• Energy can be transferred between objects or transformed into different forms, but the total amount of energy can never change.

Rail Cart Collisions

Rail Cart Collisions

• Accelerations are in opposite directions

• More massive cart accelerates the least

• Equal-mass carts have equal accelerations (in opposite directions)

• Total Mass·Velocity the same before and after collisions

Air Hockey Collisions

Air Hockey Collisions

• Accelerations are in opposite directions

• More massive disk accelerates the least

Momentum

• “Inertia in motion”

• Massive objects are hard to get going.

• Massive objects are hard to stop.• It is hard to give an object a high speed.• It is hard to stop a high-speed object.

Momentum

Formula

momentum is a vector.

p = mv

Momentum Changes and Newton’s Third Law

• At any instant:

p = (mv) = mv = mat = m(F/m)t = Ft

• For interacting objects, FA = −FB, so:

pA = FAt

pB = FBt = −FAt

pA = −pB

Conservation of Momentum

• Momentum can be transferred between objects, but the total momentum can never change.

p1 + p2 = 0

Rollerballs and Drag Meters

Rollerballs and Drag Meters

• The lighter the meter, the farther it drags.• The heavier the ball, the farther it drags a meter.• The higher the ramp, the farther a ball drags a

meter.• The higher the ramp, the faster a ball rolls at the

bottom.• The mass of the ball has no influence on how

fast it rolls at the bottom.

Some Forms of Energy

• Potential Energy

• Kinetic energy

Work Against Gravity

Force = –w = mg

distance = h

work = mgh

Source: Griffith, The Physics of Everyday Phenomena

Get It Back?

Gravity exerts force mg as object drops distance h.

work = mgh

Source: Griffith, The Physics of Everyday Phenomena

Potential Energy

The energy of relative position of two objects

gravity

springs

electric charges

chemical bonds

Potential Energy

Gravitational potential energy =

the work done by gravity in lowering an object

– or –

the work to raise an object to a height

Gravitational PE = mgh

A Moving Object Can Do Work

Source: Griffith, The Physics of Everyday Phenomena

Kinetic Energy

the work that a moving object does in stopping

– or –

the work to bring a motionless object to speed

KE = 12 mv2

Rollerball Energy Conversions

work

Potential energy

Kinetic energy

work

The more work you put in, the more work you get out!