AP Physics 1 Notes Work, Energy, and Power
1. Work: W = F Δr cosΘ (Unit: J, joules)
2. Applications:
a. A football player lifts a 110 kg QB 2 meters in the air. How much work does he do on the quarterback?
b. A lineman pushes a running back with a force of 85 N while pushing him backwards 2.5 meters. Determine the work done on the running back. Why is this work positive? What would make it negative?
3. Examples:
a. A box slides across a floor 12 meters while 3 N of force is applied horizontally. How much work is done on the box?
3 N
b. A box slides across a floor 12 meters while 3 N of force is applied at an angle of 30° above the horizontal. How much work is done on the box?
3 N
4. Practice: A 20 N force is applied horizontally on a 3 kg box to slide it 8 meters. The coefficient of friction between the box and the floor is 0.33.
a. How much work was done to the box by the 20 N force?
b. How much work does the friction do on the box? Is this work negative or positive? Justify your answer.
c. How much work is required to lift the box 5 meters above the floor? ? Is this work negative or positive? Justify your answer.
5. Potential Energy (Unit: J, joules): a. Gravitational Potential Energy
i. We consider U=0 at infinity.
ii. UG = -Gm1m2/
R
iii. ΔU = mgh
iv. The position for U=0 is arbitrary since we are using ΔU. We generally use (and assume unless otherwise noted) the floor or the ground as U=0.
b. Spring Potential Energy
6. Application:
a. A 2000 kg object is 1.55 x 107 m from earth. What is this object’s potential energy and why is this value negative?
b. A 300 kg box is on the top of a 2 meter tall shelf. What is the box’s potential energy?
c. A .024 kg arrow is shot to a certain height such that it has 2.4 J of potential energy. How high does the arrow go?
d. A spring is compressed 35 meters. How much potential energy is stored in the spring if its spring constant is 40 N/m?
e. A spring is compressed 3.5 meters until is has a potential energy level of 45 J. What is the spring constant?
7. Kinetic Energy: K = ½ m v2 (Unit: J, joules):
8. How much kinetic energy does a proton have as it travels 3000 m/s?
Conservation of Energy:
10. A 0.050 kg ball rolls down a track having a loop in it. It starts from rest at position A. Position A is 0.45 m above B and Position C is 0.14 m above position B.
A
C
.45 m .14 m
B
a. Fill in the data chart below:
Position Total Mechanical Energy Potential Energy Kinetic Energy
A
B
C
b. How fast is the ball traveling at position: a. B
b. C
Law of Conservation of Energy: The total energy of a system remains constant, if no work is done to or by the system.
Total Mechanical Energy = U + K
11. A 1.5 kg box is placed on a spring with a spring constant, k = 750 N/m. The spring is then compressed 0.5 meters by pushing down on the box. The box is then releases such that the spring pushes the box up. The spring releases the box at B and position C is the highest point that the box reaches.
C (highest point)
Let this be h = 0. B (spring releases box)
k = 750 N/m
A (lowest point)
a. Fill in the data chart below:
Position Total Mechanical Energy Potential Energy Kinetic Energy
A
B
C
b. Determine the speed of the box at B.
c. How far is position B from C? 1.5 kg
1.5 kg
12. Work-Energy Theorem: The work done on a system is equal to the amount of energy the system gains. The work done by a system is equal to amount of energy the system loses. (Discuss in terms of a mouse trap racer.)
13. Where does energy generally go when a system loses energy?
14. A 10 kg box traveling 25 m/s on a rough horizontal surface slides to a stop. a. How much mechanical energy does the box have initially?
b. How much work does friction do on the box to bring it to a stop?
c. How much heat is generated by this process?
15. A spring is compressed such that it gains 200 J of energy. The spring is then released such that it pushes on a 0.5 kg box on a frictionless surface.
a. How much work was done to pull the spring back?
b. How fast does the box move when released from the spring?
16. Power: (Unit: W, watts)
a. Pavg = W / Δt
b. P = F v cosΘ
17. How much power is dissipated as a 35 kg mass is pulled up 10 meters in 16 seconds?
18. How much energy can a 60 W bulb give off in one day?
Power is the rate at which work is done, or the rate at which energy is used.
Pre-Lab: Power
We want to find the power rating of this person as she runs up the stairs.
a. What variables should we measure?
b. What devices should we employ to measure these variables?
c. Use hypothetical values for your measurements and calculate her power rating.
