Download KINETIC/POTENTIAL ENERGY #2

ENERGY & WORK
#2
1)
A car of mass 1200. kg moves with a speed of 25.0 m/s. Calculate its kinetic energy.
2)
If the car from #1 was parked on a hill, how high must the car be above the bottom of the hill in order to
have a gravitational potential energy equal to its kinetic energy in #1?
3)
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?
4)
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?
5)
An object moving at 7.50 m/s has 125 J of kinetic energy. What is the weight of the object?
6)
How far must a rubber band with an effective spring constant of 955 N/m be stretched in order for it to have
29.8 J of potential energy?
7)
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)?
8)
A 4.00-gram rubber band is held 1.30 m above the ground and is stretched 10.0 cm from its rest position. If
the spring constant of the rubber band is 365 N/m, how much total mechanical energy does the rubber band
have?
9)
If the rubber band from #8 would change all of the energy into the kinetic state, how fast would it be
moving?
10)
A spring of spring constant 550. N/m is compressed 20.0 cm. How much elastic potential energy is stored
in the spring?
11)
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 non-conservative 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 gravitational
potential NRG of the mass.
c.
12)
How much NRG was lost during this process? Where do you think this NRG went?
A 15.0-kg ball is sitting on top of a vertical spring (k = 1500.N/m) that is attached to the floor. The spring
has been pre-compressed 35.0 cm so that the ball is 45.0 cm above the floor. The spring is released,
sending the ball into the air. What should the speed of the ball be when the spring reaches its 'at-rest'
position?
13)
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?
14)
Going back to the last situation: If we assume a 25% loss of mechanical energy during one bounce, to what
height should the acrobat bounce after hitting the trampoline?
15)
Suppose that two horizontal forces are acting on a 5.00-kg wooden block as it moves across a laboratory
table: an 8.00-N force pulling the block and a 3.00-N frictional force opposing the motion. The block moves
a distance of 2.00 meters across the table.
a. What is the work done by the 8.00-N force?
b. What is the block's change in kinetic energy as a result of the application of the forces?
c.
16)
Did all of the work done by the 8.00-N force go into increasing the speed of the block? Explain.
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 NRG, 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?
ANSWERS:
1) 375000 J
7) -44.1 J
12) 2.32 m/s
16) a. 1.53 m
2) 31.9 m
8) 1.88 J
13) 5.94 m
b. 5.44 m/s
3) 0.0325 J
9) 30.7 m/s
14) 4.46 m
d. 7.40 N
4) 987 m/s
10) 11.0 J
15) a. 16.0 J
5) 43.6 N
11) a. 4.47 m/s
b. 10.0 J
6) 0.250 m
b. 73.5 J
c. 76.5 J