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 = 180 Rim 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 0.095 m? (b) What is the kinetic energy of the hanging block when it has fallen that 0.095 m? (c) What maximum distance does the hanging block fall before momentarily stopping? (a) Number 0.66735 Units j (b) Number 0.4449 j (c) Number 0.174 Units m

Explanation / Answer

A.

Work done by gravity = 2MgS.
Energy given to the spring = 1/2kS^2 where Sis the displacement of the spring.
Kinetic energy gained by the both masses
= 2MgS - 1/2kS2
= (2*1.6*9.8*0.095) - (0.5*180*0.0952 )
=2.16 J

B.

Since both the masses have the same velocity, their energy will be in the raio of their masses
1/2(2M)u^2 / 1/2(M)u^2 = 2/1
Kinetic energy of M is (1/3) of 2.16 = 0.722 J
Kinetic energy of 2M is (2/3) of 2.16 = 1.44 J

C.

S(m) is the maximum displacemet, both masses will loose their kinetic energies.
The gravitataional work 2Mg* S (m) = 1/2* k*S (m) ^2
S(m) = 4Mg / k =4*1.6*9.8/ 180 = 0.348 m

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