Two spheres having masses M and 2M and radii R and 3R, respectively, are simultaneously released from rest when the distance between their centers is 12R. Assume the two spheres interact only with each other and we wish to find the speeds with which they collide. (a) What two isolated system models are appropriate for this system? (b) Write an equation from one of the models and solve it for v1→, the velocity of the sphere of mass M at any time after release in terms of v2→, the velocity of 2M. (c) Write an equation from the other model and solve it for speed υ1 in terms of speed υ2 when the spheres collide. (d) Combine the two equations to find the two speeds υ1 and υ2 when the spheres collide.

Two spheres having masses M and 2M and radii R and 3R, respectively, are simultaneously released from rest when the distance between their centers is 12R. Assume the two spheres interact only with each other and we wish to find the speeds with which they collide. (a) What two isolated system models are appropriate for this system? (b) Write an equation from one of the models and solve it for v1→, the velocity of the sphere of mass M at any time after release in terms of v2→, the velocity of 2M. (c) Write an equation from the other model and solve it for speed υ1 in terms of speed υ2 when the spheres collide. (d) Combine the two equations to find the two speeds υ1 and υ2 when the spheres collide.

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Question

Two spheres having masses M and 2M and radii R and 3R, respectively, are simultaneously released from rest when the distance between their centers is 12R. Assume the two spheres interact only with each other and we wish to find the speeds with which they collide. (a) What two isolated system models are appropriate for this system? (b) Write an equation from one of the models and solve it for v₁→, the velocity of the sphere of mass M at any time after release in terms of v₂→, the velocity of 2M. (c) Write an equation from the other model and solve it for speed υ₁ in terms of speed υ₂ when the spheres collide. (d) Combine the two equations to find the two speeds υ₁ and υ₂ when the spheres collide.