Conservation of momentum with sprins

In summary, this problem involves a projectile of mass 20g colliding with a block of mass 5kg attached to a horizontal massless spring with a spring constant of 500N/m. The collision is perfectly elastic and the velocities of the two masses after the collision are unknown. The conservation of momentum and the equations for potential energy and force are used to solve for the velocities and the compression of the spring. The presence of the spring makes the problem more challenging.
  • #1
Matt_h
7
0

Homework Statement


Problem 2 (35 points): A projectile of mass mA=20g is shot towards a block of mass
MB= 5kg with a velocity of vA=400m/s. The block is at rest, attached to a horizontal
massless spring (at equilibrium) with k=500N/m.

a. If the collision between the projectile and the mass is perfectly elastic,
what are the velocities of the two masses immediately following the collision?


Homework Equations



U(x)=1/2kx^2
F=ma
Conservation of momentum
M1U1 + M2U2 = M1V1 + M2V2
When U is equal to the velocity before the impact.


The Attempt at a Solution



I would have a good idea on how to do this problem without the spring being there but with it there i can not figure out how to do it.

I know that the total velocities after the collision needs to combine to make 400 but other than that i am pretty lost on this one.
 
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  • #2
The spring is there to confuse you. Immediately after impact, how far has the spring compressed? What, then, is the force in it?
 

What is conservation of momentum with springs?

Conservation of momentum with springs is a physical law that states that the total momentum of a system remains constant as long as there are no external forces acting on it. This means that the initial momentum of a system before a spring is released must be equal to the final momentum after the spring has been released.

How does conservation of momentum apply to springs?

In the case of springs, momentum is conserved because the energy stored in the spring as potential energy is converted into kinetic energy as the spring is released. This transfer of energy results in the same total momentum before and after the spring is released.

What factors affect the conservation of momentum with springs?

The conservation of momentum with springs is affected by the mass of the object attached to the spring, the initial velocity of the object, the spring constant, and the distance the spring is compressed or stretched.

What are some real-life examples of conservation of momentum with springs?

One example is a pogo stick, where the potential energy stored in the compressed spring is converted into kinetic energy as the person jumps. Another example is a car suspension system, where the springs absorb the momentum of the car as it hits a bump on the road.

What happens if there are external forces acting on a system with springs?

If there are external forces acting on a system with springs, the momentum will no longer be conserved. This is because the external forces will add or subtract from the total momentum, causing it to change. This is why it is important to consider all external forces when analyzing the conservation of momentum with springs.

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