An ingenious brick layer 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 = 546 N/m and negligible mass. When the spring is released, the brick is propelled upward. If the brick has mass 3.62 kg and is to reach a maximum height of 3.8 m above its initial position on the compressed spring, what distance must the bricklayer compress the spring initially? (Note: The brick loses contact with the spring when the spring returns to its uncompressed length.)
Explanation / Answer
Given: -- k = spring constant = 546 N/m m = mass of brick = 3.62 kg h = height = 3.8 m -- Now, the spring provides enough energy to propel the brick toa height h, and with conservation of energy: -- 1/2kx^2 = mgh x = (2mgh/k) x = 0.703 m -- -- Hope this helps.