A 140 g block on a frictionless table is firmly attached to one end of a spring

Question

A 140 g block on a frictionless table is firmly attached to one end of a spring with k = 24 N/m . The other end of the spring is anchored to the wall. A 30 g ball is thrown horizontally toward the block with a speed of 5.4 m/s . Part A If the collision is perfectly elastic, what is the ball's speed immediately after the collision? Express your answer to two significant figures and include the appropriate units. Part B What is the maximum compression of the spring? Express your answer to two significant figures and include the appropriate units. Part C Repeat part A for the case of a perfectly inelastic collision. Express your answer to two significant figures and include the appropriate units. Part D Repeat part B for the case of a perfectly inelastic collision. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

A)
Vcm = m1*v1/(m1+m2)

Vcm = 0.03 * 5.4 / ( 0.03 + 0.14) = 0.953 m/s; u1 = 5.4 - 0.953 = 4.447 m/s
V1 = Vcm - u1

V1 = 4.447 - 0.953 = 3.494 m/s

B)
V2 = 2*Vcm = 1.906 m/s; 0.5*m2*V2^2 = 0.5*k*x^2 x = V2 * sqrt[m2/k]

x = = 1.906 * sqrt( 0.14 / 24)

x = 0.145 m

C)
V2 = m1 * v1/(m1+m2)

V2 = 0.03 * 5.4 / ( 0.03 + 0.14) = 0.953 m/s

D)
x = V2 * sqrt[(m1+m2)/k]

x = 0.953 * sqrt( (0.14+0.03)/24)

x = 0.08 m

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