Practice Problems
Basic Spring Systems
Directions:
On this worksheet you will work with the basic relationships for spring systems.
omit
Question 1
The spring shown above is compressed by
D
x from its equilibrium position. When released it launches a block across a frictionless surface with speed of 4 m/sec. The two springs in the following figure are identical to the spring shown above and are also compressed
D
x to launch an identical block.
What is the block’s new speed as it passes through equilibrium?
0.18 m/sec
5.7 m/sec
2 m/sec
8 m/sec
omit
Question 2
The two springs in the following figure are also identical to the initial spring in
Question #1
but are compressed
D
x equal to 2.3 times the original spring's compression.
If the same block is launched, what is its new speed as it passes through equilibrium?
6.5 m/sec
4.3 m/sec
2.8 m/sec
2.0 m/sec
omit
Question 3
A spring is attached to a 2-kg block. The other end of the spring is pulled by a motorized toy train that moves forward at 5 cm/s. The spring constant is 94 N/m, and the coefficent of static friction between the block and the surface is µ
s
= 0.50. The spring is at its equilibrium length at t = 0 seconds when the train starts to move. At what time does the block initially begin slipping?
1.04 x 10
-1
seconds
5.21 x 10
-3
seconds
2.09 x 10
0
seconds
9.8 x 10
0
seconds
omit
Question 4
The air-track carts in the diagram shown above are sliding to the right at 2.3 m/sec. The spring between them has a spring constant of 94 N/m and is compressed 5 cm. At some point, the carts will slide past a flame that will burn through the string holding them together. If cart A has a mass of 400 grams and cart B has a mass of 200 grams, what would be the speed of cart B after the string is burned?
2.74 m/sec
3.19 m/sec
0.44 m/sec
the correct answer is not provided
0.89 m/sec
omit
Question 5
One end of a spring is attached to a wall while the other end reaches exactly to the edge of a frictionless table 1 meters tall. A block of mass 2.3 kg is pushed against the spring until it is compressed a distance of 4 cm. The block is released and is launched off the table, striking the ground 94 cm away from the table. Air resistance is negligible. What is the spring's force constant?
1.24 x 10
4
N/m
3.05 x 10
4
N/m
3.11 x 10
3
N/m
6.22 x 10
3
N/m
omit
Question 6
What was the initial acceleration of the block in
Question #5
?
1.08 x 10
4
m/sec
2
3.58 x 10
3
m/sec
2
1.08 x 10
2
m/sec
2
3.58 x 10
5
m/sec
2
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