# A vertical spring with a spring constant of 480 N/m is mounted on the floor. From directly above the spring, which is unstrained, a 0.30 kg block is dropped from rest. It collides with and sticks to the spring, which is compressed by 2.0 cm in bringing the block to a momentary halt. Assuming air resistance is negligible, from what height (in cm) above the compressed spring was the block dropped?

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A vertical spring with a spring constant of 480 N/m is mounted on the floor. From directly above the spring, which is unstrained, a 0.30 kg block is dropped from rest. It collides with and sticks to the spring, which is compressed by 2.0 cm in bringing the block to a momentary halt. Assuming air resistance is negligible, from what height (in cm) above the compressed spring was the block dropped?

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Step 1

The spring constant of the spring = 480 N/m.

The mass of the block =0.30 kg.

The compressed distance = 2 cm.

Consider the figure given. Initially block is at height h, when it is dropped towards the spring, the spring compressed to a distance of 2 cm.

Step 2

Hence at height h, block has a potential energy mgh as it dropped down it is completely converted to kinetic energy, which is responsible for a compression of x distance.

According to low of conservation of energy

Step 3

Rearrange equation (I) to obtain an expression fo...

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