Momentum and Energy

Chapter 4ISCI 2002

Momentum and Inertia• (1). Momentum is inertia in motion

– Momentum = mv

• (2). A heavy object in motion will have a great deal of momentum

• (3). Mass is constant; momentum changes – Change in velocity • Acceleration occurs

Impulse• (1). Force produces acceleration which

changes velocity (changes the momentum)– Time of force • Longer force applied, more change in momentum• Impulse = (F)(t)

• (2). Impulse-Momentum Relationship – Ft = (mv)• Net force applied over a period of time changes

momentum

Examples• (1). Why are cannons barrels so long?

– Applied force on ball is extended• Increased impulse, increased momentum ,

• (2). Your Choice: Hitting a wall or soft surface when driving a car? – Of course the soft surface• Relate momentum , impulse and impact

• When you hit a soft surface you extend time your momentum is brought to zero, extend impact which reduces force that will be incurred.

Conservation of Momentum(1). Mirrors Newton’s Third Law

As the cannonball gains momentum the cannon also gains momentum by recoiling Net momentum = zero

(2). If an object has momentumNo change unless affected by unbalance forceWhich Law?

Collisions and Momentum • (1). One object in motion – with a specific momentum hits

second object at rest– First object collides and stops– Second object moves with Vi of first ball – “elastic collision”– Momentum is transferred from one ball to another. “rebound”– Conservation of momentum

• (2). Object one collides with static object two– No rebound (freight cars) “inelastic” – Object one (moves 10 m/s) so

• (net mv)before = (net mv)after • (m x 10)b = (2m x v)a *2m refers to twice mass or two cars moving• V = 5 m/s (using the formula, velocity of object hit can be predicted)

Energy • (1). Impulse = (F)(t)

– (F)(d)? Force over a specific distance– Refers to energy – work

• (2). Energy – Sun, food, heat, etc.

• (3). Work = (F)(d)– When work is done energy is transferred to an

object – Unit of work = Nm or the joule (J)

Power(1). Work done/time interval

Measure or rate of how fast work is doneRate at which energy is changed from one form

to anotherUnit: watt

One watt = used when one joule of work is done in one second.

PE vs KE• (1). PE

– Stored energy – Chemical energy (fuels, glucose)

• Chemical changes occurs makes energy available – Can do work

• Gravitational PE– Work to elevate objects against gravity – GPE of an object raised = work done lifting against gravity – PE = mgh

• (2). KE– Object in motion or moving and energy involved

• Object hits another transfers energy • GPE of object transforms into KE when object is dropped • KE = ½ mv2

Work-Energy Theorem(1). Work = ΔKE

Or (F)(d) = ΔKEWork done on an object basically equals gain in

KE by that object Push on a box

it slides (you are doing work) It gains KE (moving)

KE vs Momentum (1). Properties of moving things but:

Momentum is a vector – movement in a directionKE is scalar – can never be cancelled (like mass)

Momentum depends on velocity (mv) KE depends on the square of velocity (1/2 mv2) Two objects with same mass

Object 1 moves with 2x velocity as object 2 Object 1 has 2x the momentum and 4x the KE

If a car travelling 2x velocity crashes, will crash with 4x more energy

Machines • (1). Machines

– Change direction of force• Lever – push on one end does work on load end (4.24)• Work input = work output

– Multiply forces• Fulcrum is close to load, small force input produces large output force

• (2). Examples of machines– Car jack – push it down 25 cm lifts car 0.25 cm

• Applies 100x the force – Pulley

• Pull on it (a little) multiplies force applied • Remember fD input = Fd output !• Car example

– She applies 50N x 25cm = 5000N x 0.25

• (3). Efficiency – Work done / energy used – 100J work done and 98J of productive work = 98% efficiency