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Chapter 1: Q11-48P (page 1)

A claw hammer is used to pull a nail out of a board. The nail is at an angle of 60o to the board, and a force F鈫�1of magnitude 400 N applied to the nail is required to pull it from the board. The hammerhead contacts the board at a point A, which is 0.800 m from where the nail enters the board. A horizontal force F鈫�2is applied to the hammer handle at a distance of 0.300 m above the board. What magnitude of force F鈫�2is required to apply the required force (F鈫�1) to the nail? (Ignore the weight of the hammer.)

Short Answer

Expert verified

The magnitude of F2 is 92.4 N.

Step by step solution

01

The given data

Given that a claw hammer is used to pull a nail out of a board. The nail is at an angle of 60o to the board, and a forceF鈫�1 of magnitude 400 N applied to the nail is required to pull it from the board. The hammer head contacts the board at a point A, which is 0.800 m from where the nail enters the board. A horizontal forceF鈫�2 is applied to the hammer handle at a distance of 0.300 m above the board.

Force F1=400N

02

Formula used

Torque蟿=Fl

Where Fis force exerted and l is distance.

03

Draw a free-body diagram of the beam

The moment arm for the force F1 is 0.08msin60掳.

The moment of arm for F2 is 0.3 m.

Applying equilibrium condition on torque

This gives torque蟿=0

Therefore,

F20.3m=F10.8msin60掳F2=400N0.231=92.4N

So the magnitude of F2 is 92.4 N

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