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Homework Statement
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 verticle compressed spring with force constant k=450N/m and negligible mass. When the spring is released, the brick is propelled upward. If the brick has mass 1.80kg and is to reach a maximum height of 3.6m above the initial position on the compressed spring, what distance must the spring be compressed initially?
Homework Equations
W=Fs
Wtotal=Kf-Ki
F=kx (Hooke's law)
The Attempt at a Solution
Someone else has already solved this problem (but with k=350 instead of 450) https://www.physicsforums.com/showthread.php?t=254633&highlight=bricklayer", though I can't really understand much of it. They said that the total work done on the brick is 0, but I'm not really sure why. Is it because the velocity of the block is 0 when the spring begins to decompress and when the block reaches its maximum height (so the initial and final kinetic energy would both be 0)? For some reason, I can't seem to understand this on a conceptual level.
I'm also not very sure about the rest of the solution. So the work done to compress the spring is W=0.5kd2, where d is how much the spring was compressed. Does that mean when the spring decompresses, an equal amount of work is done?
The work done by gravity from the time when the brick leaves the spring to the time when the brick reaches its maximum height is W=-mgh, where h is the maximum height (3.6m).
Then I'm supposed to relate W=0.5kd2 and W=mgh to get 0.5kd2=mgh, but I don't really understand how this can be done...
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