A 1,800-kg pile driver is used to drive a steel I-beam into the ground. The pile
ID: 1331783 • Letter: A
Question
A 1,800-kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 4.60 m before coming into contact with the top of the beam, and it drives the beam 15.4 cm farther into the ground as it comes to rest. Using energy considerations, calculate the average force the beam exerts on the pile driver while the pile driver is brought to rest. magnitude Make sure you are also correctly accounting for the change in gravitational potential energy when the beam is pushed the extra distance into the ground. NExplanation / Answer
Two forces do work on the driver:
mg, the force of gravity
F, the resistive force of the ground
mg acts over a distance h+d, where h is the initial height of the driver above the ground and d is the distance it sinks into the ground
if 0 is driver's final height, then its initial height should be h+d
F acts only over the distance d
Using the definition of work:
mg does work equal to mg(h+d)
F does work equal to -Fd
"-F" because F is a resistive force, acting in the direction opposite to the motion of the object
Using Conservation of Energy:
Work = Change in Kinetic Energy
mg(h+d) - Fd = 0, since object begins at rest and ends at rest
mg(h+d) = Fd
F = mg(h+d)/d
F = 1800 * 9.8 * (4.6 + 0.154) / 0.154
F = 544549 N
F is clearly greater than the driver's weight because it only takes the ground 0.118 m to "undone" the positive work done by gravity over 7.64 m - while opposing gravity.
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