Question

A 2 300-kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 3.00 m before coming into contact with the top of the beam, and it drives the beam 15.6 cm farther into the ground before coming to rest. Using energy considerations, calculate the average force the beam exerts on the pile driver while the pile driver is brought to rest.

Answer 1

Answer:

433903.8 N

Explanation:

From work energy theorem, the total work done is equivalent to change in kinetic energy. Kinetic energy is depedant on speed and since pile drive finally comes to rest, then final velocity is zero. Also, its initial velocity is not given. Therefore, the sum of work due to gravity and beam equals to zero. Work due to gravity is product of mass of pile driver, acceleration due to gravity and height while work due to beam is a product of force and distance. Substituting the given values then

2300*9.81*3+(F*0.156)=0

F=-433903.84615384615384615384615384615384615 N

Approximately, the magnitude of force is 433903.8 N and it acts upwards