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 6 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?
8.5 m/sec
3 m/sec
12 m/sec
0.12 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 1.5 times the original spring's compression.
If the same block is launched, what is its new speed as it passes through equilibrium?
5.2 m/sec
3.0 m/sec
4.2 m/sec
6.4 m/sec
omit
Question 3
A spring is attached to a 3-kg block. The other end of the spring is pulled by a motorized toy train that moves forward at 10 cm/s. The spring constant is 80.3 N/m, and the coefficent of static friction between the block and the surface is µ
_{s}
= 0.70. 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?
2.56 x 10
^{-1}
seconds
2.06 x 10
^{1}
seconds
2.56 x 10
^{0}
seconds
2.56 x 10
^{-2}
seconds
omit
Question 4
The air-track carts in the diagram shown above are sliding to the right at 1.5 m/sec. The spring between them has a spring constant of 80.3 N/m and is compressed 10 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 600 grams and cart B has a mass of 300 grams, what would be the speed of cart B after the string is burned?
2.84 m/sec
1.34 m/sec
the correct answer is not provided
0.67 m/sec
2.17 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 1.5 kg is pushed against the spring until it is compressed a distance of 6 cm. The block is released and is launched off the table, striking the ground 80.3 cm away from the table. Air resistance is negligible. What is the spring's force constant?
1.32 x 10
^{3}
N/m
6.58 x 10
^{2}
N/m
6.45 x 10
^{3}
N/m
2.63 x 10
^{3}
N/m
omit
Question 6
What was the initial acceleration of the block in
Question #5
?
3.29 x 10
^{4}
m/sec
^{2}
3.29 x 10
^{2}
m/sec
^{2}
5.27 x 10
^{1}
m/sec
^{2}
5.27 x 10
^{3}
m/sec
^{2}
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