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 end of the second glider. As shown in the figure below, The first glider, of mass m1, moves to the 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. Find the the following.
(a) speed v at maximum compression (Use any variable or symbol stated above as necessary.)


(b) the maximum compression xmax (Use any variable or symbol stated above as necessary.)


(c) the speed of each glider after m1 has lost contact with the spring (Use any variable or symbol stated above as necessary.)

Explanation / Answer

a) conserving momentum, m1*v1 + m2*v2 = (m1+m2)*v so, v = (m1*v1+m2*v2)/(m1+m2) b)conserving energy, .5*m1*v1^2 + .5*m2*v2^2 = .5*(m1+m2)*v^2 + .5*k*x^2 so, x = sqrt((m1*m2/k)*(v1-v2)^2/(m1+m2)) 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. I am going to assume you know how to solve this. Hope this helps

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