An ingenious bricklayer builds a device for shooting bricks up to the top of the wall where he is working. He places a brick on a vertical compressed spring with force constant k = 450 N/m and negligible mass. When the spring is released, the brick is propelled upward. If the brick has mass 1.80 kg and is to reach a maximum height of 3.6 m above its initial position on the compressed spring, what distance must the bricklayer compress the spring initially? (The brick loses contact with the spring when the spring returns to its uncompressed length. Why?)

(b) The brick loses contact with the spring when the spring returns to its uncompressed length because the elastic potential energy of the spring has been converted into kinetic energy of flying brick.

Conservation of energy

When the brick reaches the maximum height, the elastic potential energy of the spring will be converted into potential energy of the brick due to law of conservation of energy.

Ux = P.E

¹/₂kx² = mgh

kx² = 2mgh

x² = 2mgh/k

x = √(2mgh/k)

x = √(2 x 1.8 x 9.8 x 3.6 / 450)

x = 0.53 m

Thus, the distance the bricklayer must compress the spring initially is 0.53 m.

The brick loses contact with the spring when the spring returns to its uncompressed length because the elastic potential energy of the spring has been converted into kinetic energy of flying brick.

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