3) A linear spring having spring constant K is positioned horizontally along a friction-less horizontal surfac One end of the spring is attached to a vertical wall and the other end is attached to a block having mass M. horizontal x-axis is defined for the position of the block, such that the block is at the origin when the spring is at its “natural" length, ie. not stretched or compressed. Furthermore, stretching the spring results in the block having a positive value of x. a) During a 1s* process, an external agent grasps the block and slowly stretches the spring so that the block comes to rest at x = XA. Determine an expression {K, M, XA} for the work done by the agent onto the bloc system during this 1sª process. b) During a 2nd process, the agent continues to slowly stretch the spring so that block comes to rest at x = X Determine an expression {K, M, XA, XB} for the work done by the agent onto the block system during this 2nd process. c) During a 3rd process, the agent releases the block from rest at x = XB, which causes the block to speed up and travel back to x = 0 as the spring returns to its natural length. Determine an expression {K, M, XẠ, XB} for the final speed of the block at the end of this 3rd process.
3) A linear spring having spring constant K is positioned horizontally along a friction-less horizontal surfac One end of the spring is attached to a vertical wall and the other end is attached to a block having mass M. horizontal x-axis is defined for the position of the block, such that the block is at the origin when the spring is at its “natural" length, ie. not stretched or compressed. Furthermore, stretching the spring results in the block having a positive value of x. a) During a 1s* process, an external agent grasps the block and slowly stretches the spring so that the block comes to rest at x = XA. Determine an expression {K, M, XA} for the work done by the agent onto the bloc system during this 1sª process. b) During a 2nd process, the agent continues to slowly stretch the spring so that block comes to rest at x = X Determine an expression {K, M, XA, XB} for the work done by the agent onto the block system during this 2nd process. c) During a 3rd process, the agent releases the block from rest at x = XB, which causes the block to speed up and travel back to x = 0 as the spring returns to its natural length. Determine an expression {K, M, XẠ, XB} for the final speed of the block at the end of this 3rd process.
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Transcribed Image Text:3) A linear spring having spring constant K is positioned horizontally along a friction-less horizontal surface
One end of the spring is attached to a vertical wall and the other end is attached to a block having mass M. A
horizontal x-axis is defined for the position of the block, such that the block is at the origin when the spring
is at its “natural" length, ie. not stretched or compressed. Furthermore, stretching the spring results in the
block having a positive value of x.
a) During a 1s* process, an external agent grasps the block and slowly stretches the spring so that the block
comes to rest at x = Xa. Determine an expression {K, M, XA} for the work done by the agent onto the block
system during this 1* process.
b) During a 2nd process, the agent continues to slowly stretch the spring so that block comes to rest at x = XB
Determine an expression {K, M, XA, XB} for the work done by the agent onto the block system during this
2nd process.
c) During a 3rd process, the agent releases the block from rest at x = XB, which causes the block to speed up
and travel back to x = 0 as the spring returns to its natural length. Determine an expression {K, M, XẠ, XB}
for the final speed of the block at the end of this 3rd process.
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