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Chapter 9: Q23 PE (page 317)

What force does the nail puller inExercise\({\rm{9}}{\rm{.19}}\)exert on the supporting surface? The nail puller has a mass of\({\rm{2}}{\rm{.10}}\;{\rm{kg}}\).

Short Answer

Expert verified

The force exerted by the puller on the supporting surface is \({\rm{1}}{\rm{.30 \times 1}}{{\rm{0}}^{\rm{3}}}\;{\rm{N}}\).

Step by step solution

01

Definition of the force

A force is an external factor that can change the rest or motion of a body. It has a size and a general direction.

02

Free-body diagram of the system

The diagram is shown below:

Here,\({I_i} = 45\;{\rm{cm}}\),\({I_o} = 1.80\;{\rm{cm}}\) and \(F = 50\;{\rm{N}}\) .

03

Calculation of the force

The torque about the pivot point is zero in equilibrium. So,

\(\begin{align}N{l_o} &= \left( {{l_o} + {l_i}} \right){F_i}\\N &= \frac{{\left( {{l_o} + {l_i}} \right){F_i}}}{{{l_o}}}\\N &= \left( {1 + \frac{{{l_i}}}{{{l_o}}}} \right){F_i}\end{align}\)

For the given values,

\(\begin{align}N &= \left( {1 + \frac{{45}}{{1.80}}} \right) \times 50\;N\\ &= 1.30 \times {10^3}\;N\end{align}\)

Thus, the force is \({\rm{1}}{\rm{.30 \times 1}}{{\rm{0}}^{\rm{3}}}\;{\rm{N}}\).

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Most popular questions from this chapter

If the maximum force the biceps muscle can exert is 1000N, can we pick up an object that weighs1000N? Explain your answer.

Consider a method for measuring the mass of a person’s arm in anatomical studies. The subject lies on her back, extends her relaxed arm to the side and two scales are placed below the arm. One is placed under the elbow and the other under the back of her hand. Construct a problem in which you calculate the mass of the arm and find its center of mass based on the scale readings and the distances of the scales from the shoulder joint. You must include a free body diagram of the arm to direct the analysis. Consider changing the position of the scale under the hand to provide more information, if needed. You may wish to consult references to obtain reasonable mass values.

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Figure \({\rm{9}}{\rm{.1}}\)

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