1. PHYSICS UNIT 4: ENERGY & MOMENTUM

2. WORK & KINETIC ENERGY
Work, W: using a force, F, to displace an object a distance, d
unit: Joule (1 J = 1 Nm)
W = Fd
W = 0
W < Fd

3. WORK & KINETIC ENERGY Work done by any force: W = Fd
can be positive, negative, or zero d
Ex: sled sliding down a hill
gravity does positive work
friction does negative work
normal force does no work

4. WORK & KINETIC ENERGY Power, P: the time rate at which work is done
P = W/t
unit: Watt, W (1 W = 1 J/s = 1 Nm/s)
english unit: horsepower, hp (1.00 hp = 746 W)
What happens to power with twice work?
What happens to power with ½ the time?

5. WORK & KINETIC ENERGY Kinetic Energy, K: energy of motion
energy: the ability to do work
K = ½mv2
unit: Joule
scalar quantity – amount only – direction doesn’t matter
If velocity doubles what happens to K?

6. WORK & KINETIC ENERGY

7. WORK & KINETIC ENERGY
Work – Kinetic Energy Theorem: Work done on an object is equal to the total change in kinetic energy of the object
Wnet = Kf – Ki
Fnetd = ½mvf2 – ½mvi2

8. WORK & KINETIC ENERGY
net work determines the change in an object’s motion
positive work = increase in kinetic energy (speed up)
Ex: throwing a ball
negative work = decrease in kinetic energy (slow down)
Ex: catching a ball
zero work = no change in kinetic energy
Ex: weightlifting

9. POTENTIAL ENERGY & CONSERVATION
Potential Energy, PE: stored energy
gravitational: energy of position due to gravity force
Grav. PE = mgh
h: height - measured from origin (reference point)
unit: Joule, J
can be positive, zero, or negative depending on choice of origin

10. POTENTIAL ENERGY & CONSERVATION
Potential Energy, PEspring: energy of position
elastic: energy of position due to elastic force
PEspring = ½kx2
k: spring constant, x: stretch/compress distance
unit: Joule
can only be positive or zero

11. Energy 101

12. POTENTIAL ENERGY & CONSERVATION
Conservation of Mechanical Energy: a system's total mechanical energy (K+U) stays constant if there is no friction
Ki + Ui = Kf + Uf
if there is friction, some K will be turned into other energy forms - heat, sound, etc.
mechanical energy is not conserved
total energy is still conserved

13. UNIT 4: ENERGY & MOMENTUM
PHYSICS
UNIT 4: ENERGY & MOMENTUM

14. MOMENTUM & IMPULSE Impulse, J: change in momentum produced by a force
J = change in P, = Ft
unit: kg m/s

15. MOMENTUM & IMPULSE Bouncing vs. Sticking in an impact
ex: a 1000 kg car going +10 m/s hits a wall
J = pf-pi
sticking: pi = +10,000 kgm/s, pf = 0
J = –10,000 kgm/s
bouncing: pi = +10,000 kgm/s, pf = – 10,000 kgm/s
J = –20,000 kgm/s
bouncing off at impact has up to twice the force of sticking

16. MOMENTUM & IMPULSE
angular momentum, L: amount of “rotation” an object has
L = Iw
w: angular velocity, rad/s
I: rotational inertia, resistance to rotation (due to mass and its distribution - same mass further from center has more I), kgm2
unit: kgm2/s

17. MOMENTUM & IMPULSE
Law of Conservation of Momentum: total momentum of a system of objects is constant if no outside forces act
mivi = mfvf
if mass increases, velocity decreases (and vice versa)

18. MOMENTUM & IMPULSE
Law Conservation of Angular Momentum: total angular momentum of a system of objects is constant if no outside torques act
Iiwi = Ifwf

19. MOMENTUM & IMPULSE
if rotational inertia increases, angular velocity decreases (and vice versa)

20. UNIT 4: ENERGY & MOMENTUM
PHYSICS
UNIT 4: ENERGY & MOMENTUM

21. QUIZ 4.4
A 2000 kg car going 30 m/s hits a brick wall and comes to rest. (a) What is the car’s initial momentum? (b) What is the car’s final momentum? (c) What impulse does the wall give to the car? (d) If the impact takes 0.5 seconds, what force is exerted on the car?
60,000 kgm/s
0 kgm/s
-60,000 kgm/s
-120,000 N

22. UNIT 4: ENERGY & MOMENTUM
PHYSICS
UNIT 4: ENERGY & MOMENTUM

23. COLLISIONS
inelastic collision: objects collide and stick (or collide and deform)
momentum is conserved, kinetic energy is not
m1v1 + m2v2 = Mv (M = m1 + m2)
be sure to include + or – for velocity’s direction

24. COLLISIONS
Ex: An 8000 kg truck going 10 m/s N collides with a 1000 kg car going 5 m/s S and their bumpers lock. How fast are the truck & car going after the collision?

25. COLLISIONS
propulsion or explosion: total initial momentum is zero; separated pieces receive equal & opposite momentums, so total final momentum is zero
0 = m1v3 + m2v4 or m1v3 = –m2v4
ex: rocket propulsion, gun recoil

26. COLLISIONS
Ex: A 4 kg rifle fires a kg bullet, giving the bullet a final velocity of 300 m/s east. What is the recoil velocity of the rifle?

27. COLLISIONS
elastic collision: objects collide and bounce off with no loss of energy
both momentum and kinetic energy are conserved
m1v1 + m2v2 = m1v3 + m2v4
½m1v12 + ½m2v22 = ½m1v32 + ½m2v42

28. QUIZ 4.4
A 1 kg soccer ball going 8 m/s hits a player’s 4 kg head (which is not moving before the hit). The soccer ball bounces back in the opposite direction (-) at 8 m/s. There is no loss of energy. (a) What kind of collision is this? (b) What conservation of momentum equation applies? (c) What is the velocity of the player’s head after the collision?

29. UNIT 4: ENERGY & MOMENTUM
PHYSICS
UNIT 4: ENERGY & MOMENTUM

30. UNIT 4 REVIEW Ki + Ui = Kf + Uf Ug = mgh Ue = ½kx2 K = ½mv2 W = Fdcosq
Wnet = Kf – Ki
P = W/t
1.00 hp = 746 W
p = mv
J = pf – pi = Ft
L = Iw Iiwi = Ifwf
m1v3 = –m2v4
m1v1 + m2v2 = Mv3
m1v1 + m2v2 = m1v3 + m2v4