A block of mass m 1 moving with speed v 1 undergoes a completely inelastic colli

Question

A block of mass m1 moving with speed v1 undergoes a completely inelastic collision with a stationary block of mass m2. The blocks then move, stuck together, at speed v2. After a short time, the two-block system collides inelastically with a third block, of mass m3, which is initially stationary. The three blocks then move, stuck together, with speed v3 (Figure 1) . All three blocks have nonzero mass. Assume that the blocks slide without friction.

Part A

Find v2/v1, the ratio of the speed v2 of the two-block system after the first collision to the speed v1 of the block of mass m1 before the collision.

Express your answer in terms of m1, m2, and/or m3.

Part B

Find K2/K1, the ratio of the kinetic energy K2 of the two-block system after the first collision to the kinetic energyK1 of the block of mass m1 before the collision.

Express your answer in terms of m1, m2, and/or m3.

Part C

Find v3/v1, the ratio of the speed v3 of the three-block system after the second collision to the speed v1 of the block of mass m1 before the collisions.

Express your answer in terms of m1, m2, and/or m3.

Part D

Find K3/K1, the ratio of the kinetic energy K3 of the three-block system after the second collision to the initial kinetic energy K1 of the block of mass m1 before the collisions.

Express your answer in terms of m1, m2, and/or m3.

Part E

Suppose a fourth block, of mass m4, is included in the series, so that the three-block system with speed v3collides with the fourth, stationary, block. Find K4/K1, the ratio of the kinetic energy K4 of all the blocks after the final collision to the initial kinetic energy K1 of the block of mass m1 before any of the collisions.

Express your answer in terms of m1, m2, m3, and/or m4.

- Item 13 Part A A block of mass m1 moving with speed vi undergoes a completely inelastic collision with a stationary block of mass m2. The blocks then move, stuck together, at speed v2. After a short time, the two-block system collides inelastically with a third block, of mass m3, which is initially stationary. The three blocks then move, stuck together, with speed v3 (Figure 1). All three blocks have nonzero mass. Assume that the blocks slide without friction Find the ratio of the speed v2 of the two-block system after the first collision to the speed vi of the block of mass m1 before the collision Express your answer in terms of m1, m2, and/or m3 Hints My Answers Give Up Review Part Part B Find , the ratio of the kinetic energy K2 of the two-block system after the first collision to the kinetic energy K1 of the block of mass m1 before the collision. Express your answer in terms of m1, m2, and/or m3 K2 Hints My Answers Give Up Review Part Part C ind ratio of the speed vs of the three-block system after the second collision to the speed vi of the block of mass mi before the collisions Express your answer in terms of m1, m2, and/or m3 r1 of 1 Hints My Answers Give Up Review Part Part D v2 Im Find , the ratio of the kinetic energy K3 of the three-block system after the second collision to the initial kinetic energy K1 of the block of mass mi before the collisions Express your answer in terms of m1, m2, and/or m3 in K3 My Answers Give Up

Explanation / Answer

a) by conservation of momentum we have

M1*V1=(M1+M2)*V2...............................................eqn1

hence V2/V1 =M1/(M1+M2)

b)K2/K1 = (M1+M2)*V22/M1*V12

and V2/V1 = M1/(M1+M2)

hence K2/K1 = M1/(M1+M2)

c)(M1+M2)*V2 = (M1+M2+M3)*V3

V3/V2 = (M1+M2)/(M1+M2+M3)

and V2/V1 =M1/(M1+M2)

hence V3/V1 = M1/(M1+M2+M3)

d)K3/K1 =  M1/(M1+M2+M3)

e)

(M1+M2+M3)*V3 = (M1+M2+M3+M4)*V4

K4/K1 = (M1+M2+M3+M4)/M1

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