Question

A 1230 kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 7.07 m before contacting the beam, and it drives the beam 15.9 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. Answer in units of N.

Answer 1

`F_(avg) = 5.48 * 10^5 N`

Step-by-step explanation:

As we know that initial and final speed of the beam is zero

so we can use energy conservation here to find the applied force

So we will have

work done by all the forces = change in kinetic energy of the beam

so we will have

`W_g + W_(beam) = \Delta K`

`mg(L + x) - F_(avg) x = 0`

`1230(9.81)(7.07 + 0.159) = F_(avg) (0.159)`

so we will have

`87227.3 = F_(avg) (0.159)`

`F_(avg) = 5.48 * 10^5 N`