A 1 900-kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 4.00 m before coming into contact with the top of the beam, and it drives the beam 15.8 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.

Question

Abigayle Bass

Physics

17 August, 19:06

A 1 900-kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 4.00 m before coming into contact with the top of the beam, and it drives the beam 15.8 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.

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Answers (1)

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Mason · Answer 1

471392.4 N

Explanation:

From the question,

Just before contact with the beam,

mgh = Fd ... Equation 1

Where m = mass of the beam, g = acceleration due to gravity, h = height. F = average Force on the beam, d = distance.

make f the subject of the equation

F = mgh/d ... Equation 2

Given: m = 1900 kg, h = 4 m, d = 15.8 = 0.158 m

Constant: g = 9.8 m/s²

Substitute into equation 2

F = 1900 (4) (9.8) / 0.158

F = 471392.4 N