An object of mass m1 approaches with velocity v1 another object of mass m2, which is...

An object of mass m₁ approaches with velocity v₁ another object of mass m₂, which is at rest, next to a spring having force constant k. The spring is fixed to a wall and m₂ can compress the spring. This is one-dim horizontal collision without friction. We consider two collision scenarios, one which is perfectly inelastic, and the other which is elastic.

(a) In the first collision case the object m₁ strikes m₂ and sticks. Moving together, they compress the spring. Find the velocity u of both m₁and m₂just after the collision.

(b) Find the distance A₁ through which the spring is compressed.

(c) In the second collision case, object m₁ bounces off m₂elastically: the total kinetic energy is conserved. Find the velocities u₁ and u₂of both objects just after the collision.

(d) Find the distance A₂ to which the object m₂ compresses the spring.

(e) Under what condition imposed on the masses m₁ and m₂ will A₁=A₂?

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Expert Solution

genius_generous answered 1 year ago

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