Momentum and Energy

1. Momentum and Energy Chapter 4 ISCI 2002

2. Momentum and Inertia • (1). Momentum is inertia in motion • Momentum = mv • (2). A heavyobject in motion will have a great deal of momentum • (3). Mass is constant; momentumchanges • Change in velocity • Acceleration occurs

3. 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-MomentumRelationship • Ft = (mv) • Net force applied over a period of time changes momentum

4. Examples • (1). Why are cannons barrels so long? • Appliedforce on ball is extended • Increased impulse, increased momentum , • (2). YourChoice: 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.

5. Conservation of Momentum • (1). Mirrors Newton’sThirdLaw • As the cannonball gains momentum the cannon also gains momentum by recoiling • Net momentum = zero • (2). If an object has momentum • No change unless affected by unbalance force • Which Law?

6. Collisions and Momentum • (1). Oneobject in motion – with a specific momentum hits second object at rest • First object collides and stops • Second object moves with Vi of first ball • “elasticcollision” • Momentum is transferred from one ball to another. “rebound” • Conservation of momentum • (2). Objectonecollides with staticobjecttwo • 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)

7. 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)

8. Power • (1). Workdone/timeinterval • Measure or rate of how fast work is done • Rate at which energy is changed from one form to another • Unit: watt • One watt = used when one joule of work is done in one second.

9. 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

10. Work-Energy Theorem • (1). Work = ΔKE • Or (F)(d) = ΔKE • Work 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)

11. KE vs Momentum • (1). Properties of movingthings but: • Momentum is a vector – movement in a direction • KE 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

12. 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