Download Chapter 5 HW – Conservation of Energy… and Springs

Chapter 5 HW – Conservation of Energy… and Springs
Conservation of Mechanical Energy (NO FRICTION) – page 173-178 ( Eo  E or K o  U g ,o  K  U g )
1. A 50.0 kg object is dropped from a height of 197 m. Calculate K, Ug and E for the object at: a) h = 197m b) at
50m, c) just before it strikes the ground.
2. A bowling ball is dropped from the top of the Leaning Tower of Pisa (h= 86 m). What is its velocity a) at the top
b) half way down c) What is its maximum velocity?
3. If the height in problem 2 is doubled, how does it affect the a) initial K, Ug and E b) final K, Ug and E c) velocity
just before it hits the ground.
4. A 10 kg fireworks shell is fired straight up with an initial velocity of 500 m/s. a) What is the its potential energy at
its highest point? b) If it had been fired at a 45° angle instead, what would be its potential energy at its highest
point?
5. A ball is attached to a 120 cm string as shown. When the ball is released,
it swings down the dotted arc. How fast will it be going when it reaches
the lowest point in its swing?
6. Two snow covered peaks are at elevations of 850 m and 750 m above the valley between them. A ski run
extends from the top of one peak to the top of the other. A skier starts from rest at the top of the taller peak
and goes as fast as possible down one and up the other. How fast will he be going at the top of the lower peak?
Conservation of Mechanical Energy (WITH FRICTION) : ( Eo  E  f k d or K o  U g ,o  K  U g  f k d )
7. A 120 kg object has an initial kinetic energy of 4300 J. It slows down on a horizontal surface due to friction and
comes to a stop in 9.2 m. a) What is the frictional force? b) What is the coefficient of friction? C) What was its
original velocity?
8. A roller coaster (m = 120 kg) starts at 90 m above the ground traveling at 2 m/s and goes through the course
ending 10 m above the ground going 20 m/s before brakes are applied. a) If the car traveled a distance of 0.65
km before braking, what is the average frictional force? b) If the average normal force for the roller coast is 1200
N, what is the coefficient of kinetic friction?
9. A 20 kg girl starts from rest and goes down a slide as shown at a 45° angle a distance of 3.0 m. a) What is her
velocity at the bottom ignoring friction? b) If she can only reach half that velocity due to friction, what would be
the coefficient of friction?
Problems with springs: pages 368-361 and 170,171( Fs  kx ; Ws   kx 2 ; U e 
1 2
kx )
2
10. A 2.0 kg mass hanging from the end of a spring has caused the spring to extend 6.5 cm from its equilibrium
position. a) What is the spring constant? b) Explain the meaning of this spring constant.
11. If a spring constant is 80 N/m and the spring is compressed 5.0 cm, what is the elastic potential energy of the
object?
12. A slinky has a constant of 138 N/m. What is the mass of an object that stretches the spring a) 1.0 cm b) 10 cm
c) 100 cm. d) How does changing the mass affect the distance a spring stretches (or compresses)?
13. A spring is 5.0 cm from its equilibrium position. A weight causes it to compress or stretch. How would the elastic
potential energy of the object change if the spring’s constant was a) doubled b) reduced three times? How
would the elastic potential energy of the spring change if it is c) stretched 15 cm d) compressed 1.0 cm?
14. A force of 18 N stretches a spring 0.25 m from its equilibrium position. a) How much work was done by the
spring? b) What is the spring constant? c) What force would be required to stretch the spring 0.50 m? d) What
force would it take to stretch it to 0.75 m? e) How much work is done on the spring when it is stretched 0.50 m?
Conservation of Mechanical Energy (With Elastic Potential): K o  U g ,o  U e ,o  K  U g  U e  f k d
15. A sling shot, which uses an elastic band to propel and object, has an elastic constant of 40 N/m. If a metal ball
with a mass of 200g is pulled back 10 cm, a) how fast will it be moving when it leaves the sling shot? b) If the
sling shot is held 1.5 m above the ground, what will its velocity be just before it hits the ground?
16. A 10 g Hotwheel car is put on a compressed spring launcher. The spring constant is 115 N/m and the spring has
been compressed 1.0 cm from its neutral position. Neglecting the mass of the spring and assuming the surface is
frictionless, if the object is released, a) how fast will it be moving as it passes the neutral position of the spring?
b) what is the coefficient of kinetic friction if the car comes to rest after traveling on a straight horizontal track
for 8.3 m?
17. A 2.0 g penny is pushed down on a vertical spring, compressing the spring by 1.0 cm. The force constant of
spring is 40 N/m. How far above this original position will the penny fly if it is released?
18. A 200 lbs man falls out a window into a fire net 30 ft below. The net stretches 6.0 ft before bringing him to rest
and tossing him back into the air. What is the potential energy of the stretched net if no energy is dissipated by
non-conservative forces (i.e, heat, sound, friction, etc))
19. A 1.0 kg block collides with a horizontal weightless spring (k = 2.0 N/m) as shown. If µk = 0.25 and the block
compresses the spring 4.0 cm, what was the speed of the block at the instant of the collision?
20. A 3.0 kg object is released from a compressed spring (k = 120 N/m) as shown. It travels over a horizontal surface
(µk = 0.20) for 8.0 m before it comes to rest. a) What is the maximum kinetic energy? b) How far was the spring
compressed?
Answers:
5. 4.8 m/s
13. a) doubles
1. a) K = 0
6. 44 m/s
b) one-third
Ug = 97,000 J
7. a) 470 N
c) nine times
E = 97,000 J
b) 0.40
d) one-twenty-fifth
b) K = 72,000 J
c) 8.5 m/s
14. a) -2.3 J
Ug = 25,000 J
8. a) 108 N
b) 72 N/m
E = 97,000 J
b) 0.90
c) 36 N
c) K = 97,000 J
9. a) 6.5 m/s
d) 54 J
Ug = 0 J
b) 0.53
e) 9.0 J
E = 97,000 J
10. a) 300 N/m
15. a) 1.4 m/s
2. a) 0
b) The spring will
b) 5.6 m/s
b) 29 m/s
stretch (if it could) 1
16. a) 1.1 m/s
c) 41 m/s
meter for every 300 N
b) 0.0074
3. a) K = 0
of force applied to it
17. 0.10 m
Ug = doubled
11. 0.10
18. 7200 ft lbs
E = doubled
12. a) 0.14 kg
19. 0.32 m/s
b) K = doubled
b) 1.4 kg
20. a) 47 J
Ug = 0
c) 14 kg
b) 0.89 m
E = doubled
d) when displacement
c) v = 1.41 times
increases 10 times,
4. a) 1,300,000 J
mass increases ten
b) 625,000 J
times