Question Details: I only need help with part c. Thanks. I only need help with pa

Question

Question Details: I only need help with part c. Thanks. I only need help with part c. Thanks. A block of mass m1 = 1.0 kg slides along a frictionless table with avelocity of +10 m/s. Directly in front of it, and moving with avelocity of +3.0 m/s, is a block of mass m2 =7.0 kg. A massless spring with springconstant k = 1120 N/m is attached to the second block asin the figure below. (a) Before m1 runs into the spring, whatis the velocity of the center of mass of the system? 3.875m/s (b) After the collision, the spring is compressed by a maximumamount x. What is the value ofx? .1957m (c) The blocks will eventually separate again. What is thefinal velocity of each block measured in the reference frame of thetable? vb1=? vb2=? vb2=?

Explanation / Answer

The idea is that this is an elastic collision, so momentum andKE are each conserved. This means: .    initial momentum = finalmomentum . or:      1 * 10 + 7 * 3   =   1 * u + 7* v          (uand v are the two things you're looking for now) . Simplify:             31   =  u + 7 v . Also     initial KE =  final KE .          (1/2) * 1 *102   +   (1/2) * 7 *32   = (1/2) * 1 *u2    + (1/2) * 7 *v2 . Simplify:       163 = u2   +  7v2 . Now solve for v, thenu:           u =   31 - 7v .               163 = ( 31 - 7v)2 +  7v2 .             163 =   961   - 434 v  + 56 v2 . Use quadratic formula... .                    v = 3    or    4.75 . We know that v must be greater than 3, theinitial speed of the second block, so .     v =  4.75      and    u =   31 - 7*4.75   = -2.25 . And the two answers must be     -2.25    and    4.75   (inthat order... the smaller block gets bounced back to theleft) . Use quadratic formula... .                    v = 3    or    4.75 . We know that v must be greater than 3, theinitial speed of the second block, so .     v =  4.75      and    u =   31 - 7*4.75   = -2.25 . And the two answers must be     -2.25    and    4.75   (inthat order... the smaller block gets bounced back to theleft)

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