Question

A 2 kg block is launched to the right by a spring with k=1000 N/m. The spring is initially compressed by 0.3 m and is not attached to the block. It slides across the table a distance of 0.2 m where is hits and sticks to a 4 kg block. The 4 kg block is right at the end of a second, initially uncompressed, 1000 N/m spring. Find the maximum compression of the second spring if the coefficient of friction is 0.5 everywhere along the table.

Answer 1

Hi,

Hope you are doing well.

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STEP 1: To find the final speed of 2 kg block.

Use law of conservation of energy.

Initial spring potential energy = kinetic energy of the mass + work done by friction.

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STEP 2: To find the final speed of 4 kg block.

Here an inelastic collision has happened.

Hence, The total momentum will be conserved.

Therefore, Final speed of the 4 kg block is given by:

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STEP 2: To find the compression of the second spring.

Use law of conservation of energy.

Kinetic energy of 4 kg block = spring potential energy.

Therefore, Maximum compression of the spring (X) is given by:

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Hope this helped for your studies. Keep learning. Have a good day.

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