Block Collides With Horizontal Spring

In summary, a 2.40 kg block collides with a spring with a spring constant of 478 N/m, compressing it 13.00 cm. The coefficient of kinetic friction between the block and surface is 0.360. The work done by the spring can be calculated by finding the energy stored in the compressed spring.
  • #1
Becca93
84
1
Homework Statement

A moving 2.40 kg block collides with a horizontal spring whose spring constant is 478 N/m.

The block compresses the spring a maximum distance of 13.00 cm from its rest position. The coefficient of kinetic friction between the block and the horizontal surface is 0.360. What is the work done by the spring in bringing the block to rest?


The attempt at a solution

I calculated the energy dissipated by the friction (which was 1.10 J, it was the second part of the question), but I'm at a loss as to how to solve for work.

Any help would be very much appreciated!
 
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  • #2
Hint: What's the energy stored in the compressed spring?
 

1. How does a block colliding with a horizontal spring affect the motion of the block?

When a block collides with a horizontal spring, the spring exerts a force on the block in the opposite direction of the block's motion. This force causes the block to compress the spring, storing potential energy. As the spring expands back to its original length, it exerts a force on the block in the direction of the block's motion. This back-and-forth motion continues until all of the potential energy is dissipated.

2. What factors affect the amount of energy transferred from the block to the spring during a collision?

The amount of energy transferred from the block to the spring during a collision depends on several factors, including the mass and velocity of the block, the stiffness of the spring, and the angle at which the block collides with the spring. The greater the mass and velocity of the block, the more energy will be transferred to the spring. A stiffer spring will also absorb more energy, and a head-on collision will result in more energy transfer than a glancing one.

3. How does the spring constant affect the behavior of a block colliding with a horizontal spring?

The spring constant, or stiffness, of a spring affects the behavior of a block colliding with a horizontal spring in several ways. A higher spring constant means that the spring will exert a greater force on the block during compression and expansion, resulting in a larger transfer of energy. It also means that the spring will return to its original length more quickly, resulting in a shorter period of back-and-forth motion for the block.

4. Is the motion of the block-spring system affected by the surface on which it is placed?

Yes, the surface on which the block-spring system is placed can affect its motion. A smooth, frictionless surface will result in a more idealized motion, with no loss of energy due to friction. However, a rough or sticky surface will cause some energy to be lost due to friction, resulting in a slightly different motion for the block-spring system.

5. Can a block colliding with a horizontal spring exhibit harmonic motion?

Yes, a block colliding with a horizontal spring can exhibit harmonic motion under certain conditions. For the block-spring system to exhibit harmonic motion, the spring must have a high enough spring constant and the block must have a low enough mass. This will result in a short period of back-and-forth motion with a constant amplitude, similar to the motion of a simple pendulum.

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