1. Work done and KE

2. Work done Workdone by a force is defined as
Force Displacement = Fd Cosθ

3. A box rests on a horizontal, frictionless surface
A box rests on a horizontal, frictionless surface. A girl pushes on the box with a force of 18 N to the right and a boy pushes on the box with a force of 12 N to the left. The box moves 4.0 m to the right. Find the work done by (a) the girl, (b) the boy, and (c) the net force.

6. A box rests on an 30 deg inclined surface, with Static Coeff = 0
A box rests on an 30 deg inclined surface, with Static Coeff = 0.2 and Kinetic Coeff = 0.1 .
A girl pushes on the 10Kg box with a force of 100 N upwards. The box moves 1.0 m on the incline. Find the work done by (a) the girl, (b) the gravity, and (c) the friction (d) net Force.

7. What do you think?
If a Force increases velocity of an object , would you call the Wok done by this force as POSITIVE or NEGATIVE ? Why?

8. Work-Energy Theorem Prove using Vf2-Vo2 = 2ad
Work done by a Force = Change in Kinetic Energy
Prove using
Vf2-Vo2 = 2ad

9. If KE is lost where does it go?
If KE is gained where does it come from?

10. change in vertical height
Work done by gravity
end
dist
dist∥
start
change in vertical height
W=mg
Work = F x dist∥
= -mg x Change in height
= - Change in mg h

11. Gravitational Potential Energy
Workgrav = -Change in mgh
This is called:
“Gravitational Potential
Energy” (or PEgrav)
Change in PEgrav = -Workgrav
Workgrav = -change in PEgrav

12. If gravity is the only force doing work….
Work-Energy theorem:
- change in mgh = change in ½ mv2
0 = change in mgh + change in ½ mv2
change in (mgh + ½ mv2) = 0
mgh + ½ mv2 = constant

13. Conservation of energy
mgh + ½ mv2 = constant
Gravitational
Potential energy
Kinetic energy
If gravity is the only force that does work:
PE + KE = constant
Energy is conserved

14. Free fall height t = 0s 80m V0 = 0 75m t = 1s V1 = 10m/s 60m t = 2s

15. m=1kg free falls from 80m mgh ½ mv2 sum t = 0s V0 = 0 h0=80m 800J 0
750J J
V1 = 10m/s; h1=75m
800J
t = 2s
V2 = 20m/s; h2=60m J J J
t = 3s
V3 = 30m/s; h3=35m J J J
t = 4s
V4 = 40m/s; h4= J J

16. A 10-N force is applied to push a block across a frictional surface at constant speed for a displacement of 5.0 m
What is the net Work done on the block?
DO NOW

17. T is always ┴ to the motion
pendulum T
W=mg
Two forces: T and W
T is always ┴ to the motion
(& does no work)

18. Roller coaster

19. r Vector and dr vector
Work Done by a variable Force

20. Work Done by a variable Forcedr
Work Done by a variable Force dr

21. Spring - Hooke’s Law

22. Graphically
|Work done by the spring| = Area under the curve = ½ Kx2

23. Work done by spring = - change in ½ kx2
Work done by a spring
Relaxed
Position
F=0 x
When you compress
the spring
(+ work done;
spring does
-work)
Work done by spring = - change in ½ kx2

24. Spring Potential Energy
Workspring = -change in ½ kx2
This is the:
“Spring’s Potential
Energy” (or PEspring)
Workspring = -change in PEspring
change in PEspring = -Workspring

27. If spring is the only force doing work….
Work-energy theorem:
-change in ½ kx2 = change in ½ mv2
0 = change in ½ kx2 + change in ½ mv2
change in ( ½ kx2 + ½ mv2) = 0
½ kx2 + ½ mv2 = constant

28. Conservation of energy springs & gravity
mgh + ½ kx2 + ½ mv2 = constant
Gravitational
potential energy
spring
potential energy
Kinetic energy
If elastic force & gravity are the only force doing work:
PEgrav + PEspring + KE = constant
Energy is conserved

29. Summary Net Work Done on an object = KE final – KE initial
That it is + when the system gains KE energy
And it is - when it loses KE energy

30. An elevator cab of mass m = 500 kg is descending with speed vi = 4
An elevator cab of mass m = 500 kg is descending with speed vi = 4.0 m/s when its supporting cable begins to slip, allowing it to fall with constant acceleration a=g/5
(1) During the fall through a distance
d = 12 m, what is the work Wg done on the cab by the gravitational force ?
During the 12 m fall,
what is the work WT done on the cab by the upward pull of the elevator cable?

31. (3) What is the net work W done on the cab during the fall?
(4) What is the cab's kinetic energy at the end of the 12 m fall?

32. Conservative and
non- conservative forces

33. Path in-dependence of conservative forces

36. 1) If a coconut falls from a tree from a height of 20 m
1) If a coconut falls from a tree from a height of 20 m. It falls on a leaf that provides a constant resistance of 2N for a distance of 0.5 m before the coconut starts to fall freely. What is the total mechanical energy of the coconut before it starts to fall? What is the work done by the resistive force of the leaf?
2) In a second scenerio, a person climbs the tree and throws the coconut down from the same height of 20m. He pushes the coconut down with a force of 1N by moving his hand vertically through a distance of 0.25m. What is the total mechanical energy of the coconut when it starts to fall? What is the work done by the person’s applied force ?

37. 3) In a third scenerio, the person throws the coconut down from the same height of
20 m. But he pushes the coconut down with a force of 5N by moving his hand vertically through a distance of 0.25m. What is the total mechanical energy of the coconut when it starts to fall?
This time, the coconut falls on a sandy surface and the coconut makes a dent of 0.2 m on the surface before coming to stop.
What is the work done by the sand on the coconut ?
Draw the scenerio before solving.

38. What are the graphical models and the mathematical models that are used to represent the energy of a system?
Frictionless surface ( hypothetical)
Frictional Surface H