Two blocks, of masses M = 1.6 kg and 2M, are connected to a spring of spring con

Question

Two blocks, of masses M = 1.6 kg and 2M, are connected to a spring of spring constant k = 250 N/m that has one end fixed, as shown in the figure. The horizontal surface and the pulley are frictionless, and the pulley has negligible mass. The blocks are released from rest with the spring relaxed. (a) What is the combined kinetic energy of the two blocks when the hanging block has fallen 0.086 m? (b) What is the kinetic energy of the hanging block when it has fallen that 0.086 m? (c) What maximum distance does the hanging block fall before momentarily stopping?

Explanation / Answer

Here ,

x = 0.086 m

a)here ,

0.5 kx^2 = KE + 2mgh

0.5*250*.086^2 = KE + 2*1.6*9.8*.086

KE = 1.772 J

the combined KE is 1.772 J

b)

the KE of hanging mass = 2/3 * KE

the KE of hanging mass = 2*1.772/3

the KE of hanging mass = 1.182 J

the kinetic energy of hanging mass is 1.182 J

c)

Here , for force equal

k*A = 2Mg

250*A = 2*1.6*9.8

A =0.125 m

therefore ,

maximum distance =2*0.125

maximum distance = 0.251 m

the maximum distance is 0.251 m

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