Speed of object after collision related to spring

In summary, when object B with mass m and speed v collides with object A (also with mass m) resting on a smooth, horizontal surface and attached to a spring that compresses/stretch in the horizontal direction, the final speed of A when the spring is at maximum compression can be found using conservation of energy or conservation of momentum. The conditions for momentum conservation exist in this scenario, and the final speed of A will be equal to half of the initial speed of B.
  • #1
songoku
2,291
324

Homework Statement


As shown in the figure below, object A (mass: m) is at rest on a smooth, horizontal surface, and a lightweight spring that compress / stretches in the horizontal direction is attached to it. Object B, which has the same mass m, approaches A from the left side with speed v and collides with the spring. The spring compresses and A begins to move. A, B, and the spring travel in a straight line. What is the speed of A when the spring is at maximum compression?
qwe_zps299uruf2.png


Homework Equations


conservation of energy
momentum?

The Attempt at a Solution


I tried using conservation of energy:

Kinetic energy of B before hitting the spring = elastic potential energy of spring at maximum compression + kinetic energy of A

But then I stuck because I don't know how to change the spring constant and maximum compression to other variables
 
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  • #2
songoku said:
But then I stuck
so consider
songoku said:
momentum?
Do the conditions for momentum conservation exist here?
 
  • #3
haruspex said:
Do the conditions for momentum conservation exist here?

Yes, taking both boxes and spring as a closed system.

At maximum compression, object A and B will move with same speed?

Using conservation of momentum:
mAuA + mBuB = (mA+mB) V
V = 1/2 v

Is this correct?
 
  • #4
songoku said:
Yes, taking both boxes and spring as a closed system.

At maximum compression, object A and B will move with same speed?

Using conservation of momentum:
mAuA + mBuB = (mA+mB) V
V = 1/2 v

Is this correct?
That's it.
 
  • #5
Thanks a lot for the help
 

1. What is the formula for calculating the speed of an object after a collision with a spring?

The formula for calculating the speed of an object after a collision with a spring is v2 = (m1v1 + kx2)/(m1 + m2), where v2 is the final speed of the object, m1 is the mass of the object before the collision, v1 is the initial velocity of the object, k is the spring constant, x2 is the displacement of the spring, and m2 is the mass of the spring.

2. How does the spring constant affect the speed of the object after a collision?

The spring constant directly affects the speed of the object after a collision. A higher spring constant will result in a higher speed of the object after the collision, while a lower spring constant will result in a lower speed. This is because a higher spring constant means the spring is stiffer and will exert a greater force on the object during the collision.

3. Does the mass of the object have an impact on the speed after a collision with a spring?

Yes, the mass of the object does have an impact on the speed after a collision with a spring. A heavier object will have a lower speed after the collision compared to a lighter object, assuming all other variables remain constant. This is because a heavier object will require more force to accelerate, and the spring will not be able to exert as much force on the object.

4. Can the speed of the object after a collision with a spring be greater than the initial speed of the object?

Yes, it is possible for the speed of the object after a collision with a spring to be greater than the initial speed of the object. This can occur if the spring is very stiff and can exert a lot of force on the object during the collision, resulting in a higher final speed.

5. What other factors can affect the speed of an object after a collision with a spring?

Besides the mass and spring constant, other factors that can affect the speed of an object after a collision with a spring include the initial velocity of the object, the angle of collision, and any external forces acting on the object during the collision. Additionally, the type of spring (i.e. compression or extension) and the properties of the surface the collision occurs on can also impact the speed of the object after the collision.

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