Conservation of momentum with sprins

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SUMMARY

The discussion centers on a physics problem involving the conservation of momentum in a perfectly elastic collision between a projectile and a block attached to a spring. The projectile, with a mass of 20g and an initial velocity of 400m/s, collides with a stationary block of mass 5kg, which is connected to a spring with a spring constant of 500N/m. Key equations include the conservation of momentum and the potential energy stored in the spring, U(x)=1/2kx^2. The challenge lies in determining the velocities of both masses post-collision and the subsequent compression of the spring.

PREREQUISITES
  • Understanding of conservation of momentum principles
  • Knowledge of elastic collision equations
  • Familiarity with spring mechanics and Hooke's Law
  • Basic algebra for solving equations
NEXT STEPS
  • Study the principles of elastic collisions in detail
  • Learn how to apply conservation of momentum in multi-body systems
  • Explore the relationship between spring compression and force using Hooke's Law
  • Practice solving similar physics problems involving springs and collisions
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Students studying physics, particularly those focusing on mechanics and collision theory, as well as educators looking for examples of elastic collisions involving springs.

Matt_h
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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.
 
Physics news on Phys.org
The spring is there to confuse you. Immediately after impact, how far has the spring compressed? What, then, is the force in it?
 

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