Question

Proposed Exercise: Work-Energy Theorem

In the situation illustrated in the figure below, a 365 pile hammer is used to bury a beam. The hammer is raised to a height of 3.0 (point 1) above the beam (point 2) and released from rest, sinking the beam of 7.4 (point 3). The rails exert on the hammer a constant friction force equal to 54 . Using the work-energy theorem, calculate (a) the speed of the hammer at the exact instant it reaches point 2 and (b) the mean force exerted by the hammer on the beam when moving it from position 2 to 3.
Tip: the force requested in item (b) is equal to the normal force that the beam exerts on
the hammer.

Answer 1

152,000 N

Step-by-step explanation:

(a) Initial potential energy = final kinetic energy

mgh = ½ mv²

v = √(2gh)

v = √(2 × 10 m/s² × 3.00 m)

v = 7.75 m/s

(b) Work done on pile hammer = change in energy

FΔy = 0 − (mgh + ½ mv²)

F (-0.074 m) = -((365 kg) (10 m/s²) (0.074 m) + ½ (365 kg) (7.75 m/s)²)

F (-0.074 m) = -11220.1 J

F ≈ 152,000 N