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 3 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?
6 m/sec
0.24 m/sec
4.2 m/sec
1.5 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?
3.2 m/sec
1.5 m/sec
2.1 m/sec
4.9 m/sec
omit
Question 3
A spring is attached to a 1.5-kg block. The other end of the spring is pulled by a motorized toy train that moves forward at 8 cm/s. The spring constant is 85.9 N/m, and the coefficent of static friction between the block and the surface is µ
_{s}
= 0.40. 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?
5.48 x 10
^{-3}
seconds
6.85 x 10
^{-2}
seconds
8.56 x 10
^{-1}
seconds
5.88 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 85.9 N/m and is compressed 8 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 300 grams and cart B has a mass of 150 grams, what would be the speed of cart B after the string is burned?
3.86 m/sec
3.08 m/sec
0.78 m/sec
the correct answer is not provided
1.56 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 3 cm. The block is released and is launched off the table, striking the ground 85.9 cm away from the table. Air resistance is negligible. What is the spring's force constant?
4.53 x 10
^{4}
N/m
1.85 x 10
^{4}
N/m
9.24 x 10
^{3}
N/m
4.62 x 10
^{3}
N/m
omit
Question 6
What was the initial acceleration of the block in
Question #5
?
1.21 x 10
^{2}
m/sec
^{2}
1.21 x 10
^{4}
m/sec
^{2}
7.08 x 10
^{3}
m/sec
^{2}
7.08 x 10
^{5}
m/sec
^{2}
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