A certain spring hanging from the ceiling has a force
constant
k
= 50 N/m and a natural length
l
o
= 20 cm.
A
0.5-kg mass is attached to the spring, and the mass is
lifted so that the spring is 10 cm long.
The mass is then
released from rest.
1)
How much potential energy is stored in the spring
before the mass is released?
Answer:
0.250 J
2)
What force does the spring exert on the mass before
it is released?
Answer:
5.00 N [down]
3)
What is the acceleration of the mass at the instant it is released?
Answer:
19.8 m/s
2
[down]
4)
How much has the spring stretched when the net force on the mass is zero?
(This is when the mass is
“in equilibrium.”)
How long is the spring at that instant?
Answer:
9.80 cm
5)
What is the speed of the mass when it is in equilibrium?
(The answer is
not
zero.)
Answer:
1.98 m/s
6)
What is the speed of the mass when the spring is again 20-cm long?
Answer:
1.72 m/s
7)
What is the maximum stretch of the spring?
What is the maximum length of the spring?
Answer:
29.6 cm, 49.6 cm
8)
If the maximum length of the spring is 40 cm, what average friction force opposes the motion of
the mass?
Answer:
2.40 N [up]
A 50-kg mass on a smooth surface is released
from rest from the position shown.
It is pulled
up and to the right by force
F
= 50 N and
horizontally to the left by a spring.
The spring
has force constant
k
= 50 N/m and unstretched
length
l
o
= 0.10 m.
9)
What is the potential energy initially stored in the spring?
Answer:
4.00 J
10)
If the mass moves forward 0.5 m, how much work is done by force
F
?
Answer:
20.5 J
11)
If the mass moves forward 0.5 m, how much work is done on the spring?
Answer:

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