Download KINETIC/POTENTIAL ENERGY #2

ENERGY & WORK (honors)
1)
When the temperature of a room is 68°F, it contains 120,000 J of heat energy. After the furnace brings the
temperature up to 70°F, the room contains 175,000 J of heat energy. How much work was done by the
furnace?
2)
How much kinetic energy is contained in a 3300-lb. car moving at 60. mph?
3)
How fast would a 950-lb. motorcycle have to travel (in mph) to contain the same amount of kinetic energy?
4)
The same 3300-lb. car is lifted 5.0 meters off the ground by a crane. Relative to the ground, how much
gravitational potential energy does the car now have?
5)
Relative to the top of a 2.5-meter pile of junk cars, how much gravitational potential energy does the car
have?
6)
How high above the ground would the car have to be lifted in order to have an amount of grav. potential
energy equal to the kinetic energy it has when moving at 60. mph?
7)
The spring from a ballpoint pen has a spring constant of 650.0 N/m. If it is compressed 1.00 cm, how much
elastic potential energy does the spring have?
8)
How far must a rubber band with a force constant of 955 N/m be stretched in order for it to have 29.8 J of
potential energy?
9)
How fast would a 200.-gram bullet have to move in order to have as much kinetic energy as a 1950.-kg
pickup truck moving at 10.0 m/s?
10)
An object moving at 7.50 m/s has 125 J of kinetic energy. What is the weight of the object?
11)
A 6.00-kg bowling ball rolls down the alley and off the end, falling 0.750 m. How much gravitational potential
energy does it have now (referenced to the alley)?
12)
It takes 7500. J of work to slide a crate a distance of 15.0 meters across a floor. A force of 650. N was
applied to the rope. What angle did the rope make with the ground?
13)
It took a horizontal force of 250. N to pull a crate weighing 765 N across the floor. The work done was 3500
J. How far was the crate moved?
14)
A mover applies a force of 1250 N to push a piano up a ramp 12.0 m long, whose top end is 1.50 m above
the ground. The piano weighs 7500. N.
a. How much work was done by the mover?
b. How much gravitational potential energy does the piano possess when it is at the top of the ramp?
c.
If the work done by the mover was transferring energy into the piano, why aren’t the answers to a. and
b. the same?
d. How much work was done by friction?
15)
A horizontal spring (k = 1200. N/m) is compressed 50.0 cm. A 15.0-kg mass is set against it. The spring is
released and pushes the mass along a level floor.
a. Assuming no nonconservative forces, what will be the speed of the mass when it leaves the spring?
b. The mass slides up a ramp and comes to rest at a height of 50.0 cm. Calculate the amount of heat
and sound generated.
16)
An acrobat (m = 75.0 kg) drops onto a trampoline from a certain height. The trampoline is 1.30 m above
the ground. Assuming the trampoline behaves like a spring (k = 12500 N/m), if the acrobat stops moving
when he is 0.500 m above the ground, from what height (above the ground) did he start?
17)
Going back to the last situation: If we assume a 25% loss of mechanical energy, to what height should the
acrobat bounce after hitting the trampoline?
18)
A vertical spring (k = 3500. N/m) is attached to the ground; its top end is 1.50 meters above the ground. A
20.0-kg mass, originally 3.50 meters above the ground, is dropped onto the spring.
19)
a.
What is the speed of the ball when it reaches the top of the spring?
b.
Calculate the compression distance of the spring at the instant the ball stops.
c.
If, under realistic conditions, the spring only compresses a maximum of 0.433 meter, calculate the
average retarding force that acted on the ball.
There is a toy that is basically a suction cup attached to a vertical spring. By compressing the spring, the
suction cup can be firmly attached to the base resting on the floor. Once the suction cup "loses its grip" the
toy (body, spring, and base) is catapulted straight into the air. This particular toy has a mass of 10.0 g, and
when set to launch, the spring is compressed 2.00 cm from its rest position. The spring constant of the
spring is 750. N/m
(at rest – before being ‘set’)
2.00 cm
(ready to go – spring is compressed)
a. What is the greatest height the toy will reach before falling back to the ground?
b. What is the velocity of the toy just as the base of it leaves the ground on its takeoff? (The spring is no
longer compressed – also assume the spring and base are of negligible mass)
c.
When dealing with roller coasters and conservation of mechanical energy, we see that the mass of the
coaster makes no difference to its speed at the various points on the track. Can the same be said for
this toy (will a heavier toy reach the same height)? Explain.
d. How much force is needed to compress the spring of this toy and attach the suction cup to the base?
20)
A 12-hp motor lifts an elevator of mass 3500. kg to a height of 9.50 meters at a constant speed. How long
does it take to accomplish this?
ANSWERS:
1) 55,000 J
2) 540,000 J
3) 110 mph
4) 74,000 J
5) 37,000 J
8) 0.250 m
9) 987 m/s
10) 43.6 N
11) -44.1 J
12) 40˚
14) a. 1.50 x 104 J b. 1.10 x 104 J d. -4.00 x 103 J
15) a. 4.47 m/s
b. 76.5 J
18) a. 6.26 m/s b. 0.533 m
c. 61.1 N
19) a. 1.53 m
b. 5.44 m/s
d. 7.40 N
6) 37 m
7) 0.0325 J
13) 14.0 m
16) 5.94 m
17) 4.46 m
20) 36 s
WORK & ENERGY concepts
1.
A string is used to pull a wooden block across the floor without accelerating the block. The string makes an
angle to the horizontal, as shown in the diagram.
θ
a. Does the force applied via the string do work on the block? Explain.
b. Is the total force involved in doing work, or just a portion of the force? Explain.
c.
Does the frictional force, which is obviously present, do work on the block? Explain.
d. Does the normal force of the floor pushing upward on the block do any work? Explain.
e. Does the block gain any energy during this interaction? (Hint: Take note of the underlined phrase at
the beginning of this question.) What does that tell you about the work done by the string and by
friction?
2.
Different net forces accelerate two blocks of the same mass. One block gains a speed twice that of the
other block in the process. Is the work done by the net force on the faster moving block twice that done on
the slower block? Explain.
3.
A mass attached to a spring, which in turn is attached to a wall, is free to move upon a frictionless,
horizontal surface. The mass is pulled back and then released.
a. What form of energy is added to the system prior to the release of the mass?
b. At what points in the motion of the mass is its potential energy the greatest?
c.
At what points is the kinetic energy the greatest?
4.
Suppose that a mass is hanging vertically at the end of a spring. The mass is pulled downward and
released to set it into oscillation. Is the potential energy of the system increased or decreased when the
mass is lowered? Explain.
5.
Two objects are dropped onto level ground, with object A falling four times the distance of object B. How
will their speeds compare just before they hit the ground?