Block collidining with a spring

In summary, a 2.40 kg block collides with a horizontal spring with a spring constant of 400 N/m, compressing it 5.00 cm from its rest position. The coefficient of kinetic friction between the block and the surface is 0.450. The question asks for the work done by the spring in bringing the block to rest. The key is to understand that the work done by a conservative force, such as a spring force, is equal to the change in potential energy. Integrating kx from 0 to 0.05 should work, but it's important to show how you did the integration.
  • #1
zhenyazh
56
0
hi,
i am preparing for an exam and have a problem with the following question.
an image is attached.

A moving 2.40 kg block collides with a horizontal spring whose spring constant is 400 N/m.
The block compresses the spring a maximum distance of 5.00 cm from its rest position. The coefficient of kinetic friction between the block and the horizontal surface is 0.450. What is the work done by the spring in bringing the block to rest?

i am confused. tried to integrate kx on the 0 until 0.05 didn't work.
tried the same minus the friction force on that area. didn't work.

could some one explain in detail how it is done here?

thanks
 

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  • #2
you can start from the fact that the work done by a conservative force which in your case is a spring force equals to the change in potential energy ..


I hope now it is clear enough for you to start ..
 
  • #3
zhenyazh said:
i am confused. tried to integrate kx on the 0 until 0.05 didn't work.
That should work just fine--show how you did the integration.
 

1. How does a block colliding with a spring affect the spring's motion?

When a block collides with a spring, the spring's motion is affected by the transfer of energy from the block. The spring compresses as the block collides with it, storing potential energy. As the block moves away, the spring releases this potential energy, causing it to oscillate back and forth.

2. What factors affect the magnitude of the spring's compression when a block collides with it?

The magnitude of the spring's compression 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. A heavier block or a faster collision will result in a greater compression of the spring.

3. How does the spring's stiffness affect the block's motion after collision?

The stiffness of the spring plays a crucial role in determining the block's motion after collision. A stiffer spring will transfer more energy to the block, causing it to bounce back with a higher velocity. On the other hand, a less stiff spring will absorb more of the block's energy, resulting in a slower rebound.

4. What happens to the energy of the system when a block collides with a spring?

When a block collides with a spring, the energy of the system is conserved. The kinetic energy of the block is transferred to the spring, causing it to compress and store potential energy. As the spring releases this potential energy, it converts back to kinetic energy, propelling the block back in the opposite direction.

5. Can a block colliding with a spring result in a different outcome if the collision is elastic or inelastic?

Yes, the outcome of a block colliding with a spring can vary depending on whether the collision is elastic or inelastic. In an elastic collision, both the block and the spring will rebound with the same velocity as before the collision. In an inelastic collision, some of the energy will be lost to heat and sound, resulting in a lower rebound velocity for both the block and the spring.

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