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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.

Proposed Exercise WorkEnergy 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 class=

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MathPhys

Answer:

152,000 N

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

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