1. Energy m m
Physics 2053
Lecture Notes
Energy

2. Energy Topics 5-01 Work 5-02 Kinetic Energy & the Work Energy Theorem
5-03 Gravitational Potential Energy
5-04 Spring Potential Energy
5-05 Systems and Energy Conservation
5-06 Power
Energy

3. Work
The work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement:
Energy

4. What is the correct unit of work expressed in SI units? A) kg m2/s2
B) kg m2/s
C) kg m/s2
D) kg2 m/s2
Energy

5. Work
How much work did the movers do (horizontally) pushing a 160 kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0.50?
Energy

6. Can work be done on a system if there is no motion?
A) Yes, if an outside force is provided.
B) Yes, since motion is only relative.
C) No, since a system which is not moving has no energy.
D) No, because of the way work is defined.
Energy

7. Work
Object falls in a gravitational field m mg h m
Wg = mgh
Energy

8. A 50 N object was lifted 2.0 m vertically and is being held
Work
A 50 N object was lifted 2.0 m vertically and is being held
there. How much work is being done in holding the box
in this position?
A) more than 100 J
B) 100 J
C) less than 100 J, but more than 0 J
D) 0 J
Energy

9. Work
Work done by forces that oppose the direction of motion, such as friction, will be negative. f v d v Fc
Centripetal forces do no work, they are always perpendicular to the direction of motion.
Energy

10. Does a centripetal force acting on an object do work on the object?
A) Yes, since a force acts and the object moves, and work
is force times distance.
B) No, because the force and the displacement of the
object are perpendicular.
C) Yes, since it takes energy to turn an object.
D) No, because the object has constant speed.
Energy

11. Friction acts on moving object
Work
Friction acts on moving object m m f d
Energy

12. The area under the curve, on a Force versus position
Work
The area under the curve, on a Force versus position
(F vs. x) graph, represents
A) work.
B) kinetic energy.
C) power.
D) potential energy.
Energy

13. On a plot of Force versus position (F vs. x), what
Work
On a plot of Force versus position (F vs. x), what
represents the work done by the force F?
A) the slope of the curve
B) the length of the curve
C) the area under the curve
D) the product of the maximum force times the maximum x
Energy

14. Kinetic Energy and the Work Energy Theorem
Force acts on a moving object vf vi
Kinetic
Energy F m x
Energy

15. Kinetic Energy and the Work Energy Theorem (Problem)
A baseball (m = 140 g) traveling 32 m/s moves a fielder’s glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove? .
Energy

16. A) the kinetic energy of the object.
Work
The quantity is
A) the kinetic energy of the object.
B) the potential energy of the object.
C) the work done on the object by the force.
D) the power supplied to the object by the force.
Energy

17. Kinetic Energy and the Work Energy Theorem (Problem)
(a) If the KE of an arrow is doubled, by what factor has its speed increased?
Energy

18. Kinetic Energy and the Work Energy Theorem (Problem)
(b) If the speed of an arrow is doubled, by what factor does its KE increase?
Energy

19. Kinetic Energy and the Work Energy Theorem
Work done is equal to the change in the kinetic energy:
If the net work is positive, the kinetic energy increases.
If the net work is negative, the kinetic energy decreases.
Energy

20. Gravitational Potential Energy
When an object is thrown upward.
Positive work
done by the
gravitational
force
Negative work
done by the
gravitational
force
Earth
Energy

21. Gravitational Potential Energy
An object can have potential energy by virtue of its position.
Familiar examples of potential energy:
A wound-up spring
A stretched elastic band
An object at some height above the ground
Energy

22. Gravitational Potential Energy
In raising a mass m to a height h, the work done by the external force is y2
Fext m h mg
We therefore define the gravitational potential energy: y1
Energy

23. A) the kinetic energy of the object.
Work
The quantity mgh is
A) the kinetic energy of the object.
B) the gravitational potential energy of the object.
C) the work done on the object by the force.
D) the power supplied to the object by the force.
Energy

24. Gravitational Potential Energy (Problem)
How high will a 1.85 kg rock go if thrown straight up by someone who does 80.0 J of work on it? Neglect air resistance.
Energy

25. Spring Potential Energyx
F = kx F x kx
Work
Energy

26. Spring Potential Energy
The restoring force of a spring is
where k is called the spring constant, and needs to be measured for each spring.
The force required to compress or stretch a spring is:
Energy

27. Spring Potential Energy
The force increases as the spring is stretched or compressed further. We find that the potential energy of the compressed or stretched spring, measured from its equilibrium position, can be written: F x
Work kx
Energy

28. A) the kinetic energy of the object.
Work
The quantity is
A) the kinetic energy of the object.
B) the elastic potential energy of the object.
C) the work done on the object by the force.
D) the power supplied to the object by the force.
Energy

29. Spring Potential Energy (Problem)
A spring (with k = 53 N/m) hangs vertically next to a ruler. The end of the spring is next to the 15 cm mark on the ruler. If a 2.5 kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler marks?
Energy

30. Systems and Energy Conservation
Conservative
Forces
Non-conservative
Forces
Gravitational
Friction
Elastic
Air Resistance
Electric
Potential energy can only be defined for conservative forces.
Energy

31. Systems and Energy Conservation
We distinguish between the work done by conservative forces and the work done by nonconservative forces.
We find that the work done by nonconservative forces is equal to the total change in kinetic and potential energies:
Energy

32. Systems and Energy Conservation
If there are no nonconservative forces, the sum of the changes in the kinetic energy and in the potential energy is zero – the kinetic and potential energy changes are equal but opposite in sign.
This allows us to define the total mechanical energy:
And its conservation:
Energy

33. Systems and Energy Conservation
If there is no friction, the speed of a roller coaster will depend only on its height compared to its starting height. y
Energy

34. Systems and Energy Conservation
Ball dropped from rest falls freely from a height h.
Find its final speed. h v
Energy

35. Systems and Energy Conservation
A block of mass m compresses a spring (force constant k) a distance x. When the block is released, find its final speed. v m m x
Energy

36. Systems and Energy Conservation
When released from rest, the block slides to a stop.
Find the distance the block slides.
v = 0
Friction (m) m m k x d
Energy

37. Systems and Energy Conservation
A block released from rest slides
freely for a distance d.
vo = 0 m d h q m
V = ?
Find the final speed of the block
h = d sin(q)
Energy

38. Power is the rate at which work is done –
In the SI system, the units of power are watts:
The difference between walking and running up these stairs is power – the change in gravitational potential energy is the same.
Energy

39. Power
Power is also needed for acceleration and for moving against the force of gravity.
The average power can be written in terms of the force and the average velocity: v F FR d
Energy

40. Power (Problem)
A 1000 kg sports car accelerates from rest to 20 m/s in 5.0 s. What is the average power delivered by the engine?
Energy

41. END