Please show the steps, Thanks you A cart m = 0.500 kg has been moving with a con

Question

Please show the steps,

Thanks you

A cart m = 0.500 kg has been moving with a constant velocity of 1.60 m/s along a horizontal surface before it hits a horizontal spring with a spring constant of 100 N/m and compresses it. How will the spring have compressed when the cart's velocity is down to V = 0.400 m/s? A mass m = 0.500 kg is dropped from a height of 1.50 m above the end of an uncompressed vertical spring of spring constant k = 100 N/m. What is the maximum compression of the spring? How far is the spring compressed at the instant when the mass reaches its maximum velocity?

Explanation / Answer

7.2.1)   Here, loss in kinetic energy = work done by spring

=>    1/2 * 0.5 * (1.62 - 0.42) = 1/2 * 100 * x2

=>   x = 0.1095 m

=> spring has compressed =   0.1095 m

7.2.2) a) Here, 1/2 * 100 * x2 = 1/2 * 0.5 * (2 * 9.8 * 1.50)

           => x = 0.3834 m

=> maximum compression of spring =    0.3834 m

b) When mass reaches its maximum velocity , spring is compressed by 0 m . (no compression)

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