Unit 1. Newtonian Mechanics
III. Work, energy, and power
1.
A 6.0 kg cart undergoes a constant acceleration of 2.0 m/s
2
for 3.0 s. What is the net work done on the cart?
108 J
216 J
36 J
54 J
The net work cannot be determined unless the initial speed of the cart is known.
2.
A 10 kg cart is pulled along the ground by a pulling force
P
, applied at a 60° angle (measured from the horizontal). If
P
is equal to 100 N, how much work is done by
P
over a 50 cm displacement?
10 J
100 J
250 J
25 J
50 J
3.
Consider a simple pendulum. Let θ represent the bob's angular displacement, where the lowest point is θ = 0. Let U represent the bob's potential energy. Which of the following is a correct U vs. θ graph for values of ranging from -90° to +90°?
A
B
C
D
4.
A block of mass
m
is released from rest at the top of the inclined plane shown above. The force of friction on the block is
f
. The block moves from the top of the plane to the bottom of the plane. Which of the following equations allows for a correct solution for
v
, the speed of the block at the bottom of the plane?
mgx
2
= ½
mv
2
+
fx
2
mgx
2
= ½
mv
2
+
fx
3
mgx
3
= ½
mv
2
+
fx
2
mgx
3
= ½
mv
2
+
fx
3
mgx
3
= ½
mv
2
+
fx
5.
A motor is capable of producing up to 40 W of mechanical power. The motor is used to lift a mass straight up at a constant speed of 2.0 m/s. What is the heaviest mass that the motor could lift at this speed?
0.3 kg
0.5 kg
1.0 kg
2.0 kg
4.0 kg
6.
An object experiences a potential energy described by the function
U
(
x
) = 2
x
+ 3
x
2
, where
x
represents the distance from the origin in meters, and
U
represents the potential energy in joules. Consider the positive
x
direction to be to the right. If this object is released at the origin with an initial velocity to the left, which of the following describes its motion just after release?
It will continue to move left, speeding up.
It will continue to move left, slowing down.
It will continue to move left, maintaining a constant speed.
It will immediately come to rest and remain at rest.
It will return to the origin and remain at rest.
7.
A horizontal spring is attached to a cart of mass
m
on an air track. The cart is released from rest a distance
A
from the spring's unstretched position, giving the cart some initial potential energy. How would the cart's initial potential energy change if its mass were doubled, but it were released from rest at a distance ½
A
from the spring's unstretched position?
The potential energy would be unchanged.
The potential energy would be ½ of its previous value.
The potential energy would be ¼ of its previous value.
The potential energy would be twice its previous value.
The potential energy would be four times its previous value.
8.
When a spring supports a 100 g mass in the setup shown above, the top of the mass hangs 25 cm below the spot where the spring attaches to the stand. However, when instead the spring supports a 150 g mass, the top of the mass hangs 30 cm below the stand. What is the spring constant of the spring?
0.020 N/m
2.0 N/m
10 N/m
1.7 N/m
1000 N/m
9.
A 2000 kg helicopter, initially at rest, lifts off the ground. When it reaches a height of 20 m above the ground, it is moving upwards at 8.0 m/s. In order to achieve this speed, how much work was done on the helicopter by its blades?
400 kJ
64 kJ
464 kJ
336 kJ
528 kJ
10.
A 100 kg skater is traveling 6.0 m/s as he flies horizontally off of a 2 m high platform. How much kinetic energy does he have upon hitting the ground?
200 J
1800 J
2000 J
3800 J
2700 J
