1. WORK, 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 = (Fcosq)d
W = 0

3. WORK & KINETIC ENERGY Work done by any force: W = Fdcosq
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 J/s = 1 Nm/s)
english unit: horsepower, hp (1.00 hp = 746 W)
P = Fv
Lift
Thrust
Drag
Weight

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
can only be zero or positive – never negative

6. WORK & KINETIC ENERGY

7. WORK & KINETIC ENERGY
Work/Energy Theorem: net work done on an object is equal to the total change in kinetic energy of the object
Wnet = Kf – Ki
Fnetdcosq = 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. UNIT 4: ENERGY & MOMENTUM
PHYSICS
UNIT 4: ENERGY & MOMENTUM

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

11. POTENTIAL ENERGY & CONSERVATION
pendulum:
U   K
K   U
the amount stays the same

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
However, if there is friction, some K will be turned into other energy forms - heat, sound, etc.
Ki + Ui = Kf + Uf + Wlost
mechanical energy is not conserved
total energy is still conserved

13. Cons. Of Energy Example: a Mass in Free Fall Ki + Ui = Kf + Uf
½mvi2 + mghi = ½mvf2 + mghf

14. POTENTIAL ENERGY & CONSERVATION
Example: a Mass on a Horizontal Spring
Ki + Ui = Kf + Uf
½mvi2 + ½kxi2 = ½mvf2 + ½kxf2

15. POTENTIAL ENERGY & CONSERVATION

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

17. QUIZ 4.1
Joe throws a ball straight up into the air, and catches it on the way back down. (a) Draw a graph showing the kinetic energy of the ball throughout its flight. (b) Draw a graph showing the gravitational potential energy of the ball throughout its flight. (c) Draw a graph showing the total energy of the ball throughout its flight.

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

19. QUIZ 4.2
(a) Tell what kinds of energy a pole vaulter has at each of the four points labeled on the picture above (point 4 is just before hitting the mat)
(b) After the pole vaulter hits the mat, his total energy is zero. Where did all his energy go?

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

21. QUIZ 4.3
A roller coaster car, mass 500 kg, starts from rest at the top of a hill 30 m above ground level. Ignore friction. (a) What is the car’s potential energy at the top of the hill? (b) What is the car’s kinetic energy at the bottom of the hill? (c) How fast will the car be going at the bottom of the hill? (d) What is the car’s kinetic energy at the top of the next hill, 10 m above ground level?
147,000 J
147,000 J
24.2 m/s
98,000 J

22. PHYSICS
MOMENTUM

23. MOMENTUM & IMPULSE
Momentum, p: amount of “umph" an object has (Inertia in Motion)
= mv
unit p : kg m/s
vector quantity - includes direction
+2 kgm/s
–2 kgm/s

24. MOMENTUM & IMPULSE
Impulse, J: A force that acts over a duration of time.
J = Ft
unit: kg m/s or N s

25. MOMENTUM & IMPULSE Impulses cause a change in momentum.
This is known as the Impulse-Momentum Theorem.
It is analogous to the Work-Energy Theorem.
FΔT = Δp = pf – pi = mvf -mvi
unit: kg m/s or N s
force of impact, F = -pi/t
to decrease force of impact, decrease pi (decrease v before impact) or increase t (catching an egg; stunt falling; air bags)

26. Practice
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 kg m/s
0 kg m/s
-60,000 kg m/s
-120,000 N

27. 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

28. 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)

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

30. COLLISIONS
propulsion or explosion: total initial momentum is zero; separated pieces receive equal & opposite momentums, so total final momentum is zero
0 = m1v1f + m2v2f or m1v1f = –m2v2f
ex: rocket propulsion, gun recoil

31. 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?

32. COLLISIONS
elastic collision: objects collide and bounce off with no loss of energy
both momentum and kinetic energy are conserved
BEFORE = AFTER
m1v1o + m2v2o = m1v1f + m2v2f
½m1v1o2 + ½m2v2o2 = ½m1v1f2 + ½m2v2f2

33. Useful Equations p = mv J = pf – pi = Ft m1v3 = –m2v4
m1v1 + m2v2 = Mv3
m1v1 + m2v2 = m1v3 + m2v4