Download Work power and energy review answers

Work, Power, and Energy Review Answers
1. A box that weights 1000 N is lifted a distance of 20.0 m straight up by a rope and pulley system.
The work is done in 10.0 s. What is the power developed?
F = 1000 N
P = Fd/t
d = 20.0 m
P = 1000 N (20.0 m)/ 10.0 s
t = 10.0 s
P = 2000 W
2. A skier with a mass of M Is skating down a hill with a height of H and reaches the bottom with a
kinetic energy of KE. If the height is doubled and a new skier with half the mass, then what is
the kinetic energy the new skier will reach the bottom with?
KEf = PEi
the height is doubled = 2h, the mass is halved = ½ m
PE = mgh
PE = ½ m (g) 2h will equal the same as mgh, so the kinetic energy is KE
3. Gravitational potential energy is increased, and kinetic energy is decreased as an object
moves higher. Acceleration of an object going up or down is always the same (9.8 m/s2) due to
gravity.
4. How much work is done by holding a 20 kg object stationary above the ground?
m = 20 kg
W = mad
a = 9.8 m/s2
W = 20 kg ( 9.8 m/s2) 0 m = 0
d = 0 m (it’s stationary)
No work because it’s stationary
5. If the mass of a ball is doubled and the velocity is tripled, what is the kinetic energy increased
by?
KE = ½ mv2. KE = ½ (2m) (3v)2 2 x 32 = 18, It is increased by a factor of 18
6. In a pendulum, when is the kinetic energy equal to the potential energy?
When it’s halfway down the fall, the potential energy = the kinetic energy
7. Name the types of mechanical energies.
potential energy (both the gravitational and elastic kind) and kinetic energy
8. Name the types of non-mechanical energies.
chemical energy, electrical energy
9. What are all of the units for work?
J = N m = kg m2/ s2
10. What effect does a single fixed pulley have? What effect does a single moveable pulley have?
A fixed pulley changes direction of the force only.
A moveable pulley changes the amount of force needed.
11. What formula can be used to calculate the speed of an object with a mass of m and a height of h
when it hits the ground?
mgh = ½ m v2
m
m
gh = ½ v2
multiply both sides by 2
2gh = v2
v = √2𝑔ℎ
12. What is a book’s gravitational potential energy on a 2 m shelf compared to its potential energy
on a 1 m shelf?
It’s half as tall, so the potential energy is half.
13. What is the average power of a rock climber who weighs 150 kg and can climb 100 m in 120
seconds? Answer in kW and W
m = 150 kg
P = mad/t
d = 100 m
P = 150 kg (9.8 m/s2) 100 m / 120 s
a = 9.8 m/s2
P = 1225 W = 1.225 kW
t = 120 s
14. What is the definition of power?
The rate at which work or energy is transferred
15. What is the kinetic energy of a 5.44 kg object flying at 5.3 m/s?
KE = ½ m v2 = ½ (5.44 kg) (5.3 m/s)2 = 76.4 J
16. What type of energy is produced by friction? Thermal energy
17. A 1500 kg car is towed with a horizontal force of 3000 N a distance of 200 m in 450 seconds.
a. What is the work done on the car by the tow truck?
m = 1500 kg
W=Fd
F = 3000 N
W = 3000 N (200 d)
d = 200 m
W = 600,000 J
t = 450 s
b. How much power was used?
P = W/t
600,000 J / 450 s = 1333 W
c. What is the final velocity of the car?
W = ∆E, W = KE, KE = 600,000 J
KE = ½ m v2
600,000 J = ½ ( 1500 kg ) v2
v2 = 800 m2/s2
v = 28.3 m/s2
18. A 700 kg horse accelerates from rest to 10 m/s in 100 m.
a. How much work is performed to reach the final speed?
KE = ½ m v2
W = ∆E = 35,000 J – 0 J = 35,000 J
2
KE = ½ (700 kg ) (10m/s)
KE = 35,000 J at the end
KE = 0 when it started at rest
m = 700 kg
v = 10 m/s
d = 100 m
b. If the horse takes 47 s to reach the final speed, how much power is required?
P = W/t
P = 35,000 J / 47 s = 744.7 W
19. What is the velocity of a package the instant it hits the ground if it is dropped from a height of
25 m?
9.8𝑚
𝑣 = √2𝑔ℎ = √2 (
) 25𝑚 = 22.14 𝑚/𝑠
𝑠
20. Some children go tobogganing on an icy hill. They start from rest at the top of the hill as shown
in the diagram. The toboggan and the children have a combined mass of 90 kg. The kids have a
combined gravitational potential energy of 8.820 kJ at position A.
m = 90 kg
h (at A) = 10 m
h (at C) = 3 m
PE (at A) = 8.820 kJ = 8820 J  this is the total energy because the kids aren’t moving yet
g = 9.8 m/s2
a. What is the gravitational potential energy at point C?
PE = mgh = 90kg (9.8 m/s2) 3 m = 2646J
b. What is the kinetic energy at C?
KE + PE = total energy
KE + 2646 J = 8820 J
KE = 6174 J
c. What is the velocity of C?
KE = ½ m v2
6174 J = ½ (90 kg) v2
6174 J = 45 kg v2
137.2 m2/s2= v2
v = 11.7 m/s