mental asked in Science & MathematicsPhysics · 2 months ago

A 2710 kg pile driver is used to drive a steel I-beam into the ground.?

A 2710 kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 7.01 m before contacting the beam, and it drives the beam 16.2 cm into the ground before coming to rest. Find the magnitude of the average force the beam exerts on the pile driver while the pile driver is brought to rest. The acceleration of gravity is 9.8 m/s 2.

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• 2 months ago

m = mass of the pile driver = 2710 kg

h = distance fallen to contact = 7.01m

d = distance into the ground = 0.162 m

g = acceleration by gravity = 9.81 m/s²

F = force exerted by I-beam on the pile driver = ?

The TOTAL distance the pile driver falls is

D = h + d

D = (7.01 m) + (0.162 m)

D = 7.172 m

The difference in potential energy of the pile driver between initial and final position is:

PE = m*g*D

PE = (2710 kg)*(9.81 m/s²)*(7.172 m)

PE = 190668.34 J

That is also how much work that has to be done by the force exerted by the beam on the pile driver, so

PE = F*d

m * g*(h + d) = F*d

(190668.34 J) = F×(0.162 m)

F = 1176965.044 N

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