Determine the compression in the spring

In summary, two gliders of equal mass, initially moving at 3.0 m/s in opposite directions, undergo an elastic head-on collision cushioned by a spring with k=6.0*10^4 N/m. The question asks for the compression in the spring when one glider is moving at 1.5 m/s. The answer is 1.6 cm. The initial velocities of the gliders do not change instantaneously during the collision process, but rather over a period of time. This allows for conservation of energy and momentum.
  • #1
rrosa522
48
0

Homework Statement


A 1.2 kg glider moving at 3.0 m/s right
undergoes an elastic head-on collision with a glider of equal mass moving at 3.0 m/s left . T​
he collision is cushioned by a spring with k=6.0*10^4 N/m. Determine the compression in the spring when the second glider is moving at 1.5m/s. Ans =1.6cm

Homework Equations


same mass therefore..
vf1= Vi2
vf2= Vi1

The Attempt at a Solution


I think I would be able to do this question if could understand it. Is the initial velocity of the second glider 3m/s or 1.5m/s?. I would really appreciate if someone can explain this question to me because I really don't know where to start.​
 
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  • #2
Initially, before the collision, each mass is moving at 3.0 m/s.
 
  • #3
The equations given refer to the exchanged velocities after the collision wen they are not again in contact with each other. The question has been asked about the state when they are still existing force on each other through the spring. At that instant apply energy and momentum conservation.
 
  • #4
TSny said:
Initially, before the collision, each mass is moving at 3.0 m/s.
My teacher told me that when the masses are identical then vf1= Vi2 and vf2= Vi1, so how is it even possible that vf2=1.5m/s ?
 
  • #5
Your teacher is right but does that happen in zero time just try to visualize the situation. Both change their momentum over a period of time called collision time. This time cannot be zero why. Why think it over. Suppose collision time is zero what will be the rate of change of momentum?
 
  • #6
Let'sthink said:
Your teacher is right but does that happen in zero time just try to visualize the situation. Both change their momentum over a period of time called collision time. This time cannot be zero why. Why think it over. Suppose collision time is zero what will be the rate of change of momentum?
the momentum of both bodies wouldn't change if collision time was zero
 
  • #7
It is given in the problem that the velocity of one has changed from 3.0 to 1.5. So what will be the velocity of the other as per conservation of momentum? Where has the KE of both gone?
 
  • #8
rrosa522 said:
My teacher told me that when the masses are identical then vf1= Vi2 and vf2= Vi1, so how is it even possible that vf2=1.5m/s ?
That applies when 'final' refers to the completion of the collision process. It is clearly not true during the process. E.g., at some point they must both be instantaneously stationary.
 

Related to Determine the compression in the spring

1. What is the definition of compression in a spring?

Compression in a spring refers to the decrease in length or volume of the spring when a force is applied to it.

2. How is the compression of a spring measured?

The compression of a spring is typically measured using a ruler or a caliper to measure the change in length of the spring when a force is applied.

3. What factors affect the compression of a spring?

The compression of a spring is affected by the material, size, and shape of the spring, as well as the amount of force applied to it.

4. How does the compression of a spring relate to its stiffness?

The compression of a spring is directly proportional to its stiffness, meaning that a stiffer spring will compress less than a less stiff spring when the same amount of force is applied.

5. How is the compression of a spring used in scientific experiments?

The compression of a spring is often used in experiments to study the relationship between force and displacement, as well as to determine the spring constant and other properties of the spring.

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