Two gliders are set in motion on an air track. A spring of force constant k is a

Question

Two gliders are set in motion on an air track. A spring of force constant k is attached to the back of the second glider. The first glider moves right with a speed v1, and the second glider, of mass m2, moves more slowly to the right with a speed, v2. When m1 collides with the spring attached to m2, the spring compresses by a distance xmax, and the gliders then move apart again. In terms of v1, v2, m1, m2, and k. (a) Find speed v at maximum compression. (b) Find the maximum compression xmax. (c) Find the speed of each glider after m1 has lost contact with the spring.

Please include steps

Explanation / Answer

A. We know that the speed of the two objects is = when the compression is at a max. Use conservation of linear momentum to solve for V (it is the only unknown variable because V1=V2 at this instant.) Pinital=Pfinal m1v1+m2v2=m1v2f+m2v2f f=final m1v1+m2v2=V(m1+m2) solve for V B. Then to get the compression of the spring use (.5)(k)(xmax^2) + (.5)(m1f+m2f)(V^2) solve for xmax c. Now use your final speed from part A as your initial speed for this. Pi=PF v(m1+m2)= m1v1f + m2v2f solve for v1f and v2f. This can be done using linear algebra i am going to assume you know how to solve this. Hope this helps

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