BATTLE OF THE REVOLVING DOOR GOAL Apply the basic definition of torque. PROBLEM Two disgruntled businesspeople are trying to use a revolving door, which is initially at rest (see Fig. 8.3.) The woman on the left exerts a force of 625 N perpendicular to the door and 1.20 m from the hub's center,

Question

BATTLE OF THE REVOLVING DOOR

GOAL Apply the basic definition of torque.

PROBLEM Two disgruntled businesspeople are trying to use a revolving door, which is initially at rest (see Fig. 8.3.) The woman on the left exerts a force of [latex]625 \mathrm{~N}[/latex] perpendicular to the door and [latex]1.20 \mathrm{~m}[/latex] from the hub's center, while the man on the right exerts a force of [latex]8.50 imes 10^{2} \mathrm{~N}[/latex] perpendicular to the door and [latex]0.800 \mathrm{~m}[/latex] from the hub's center. Find the net torque on the revolving door.

STRATEGY Calculate the individual torques on the door using the definition of torque, Equation 8.1,

[latex] au = rF[/latex] [8.1]

and then sum to find the net torque on the door. The woman exerts a negative torque, the man a positive torque. Their positions of application also differ.

Accepted Answer

Calculate the torque exerted by the woman. A negative sign must be supplied because [latex]\overrightarrow{\mathbf{F}}_{1}[/latex], if unopposed, would cause a clockwise rotation:

[latex] au_{1}=-r_{1} F_{1}=-(1.20 \mathrm{~m})(625 \mathrm{~N})=-7.50 imes 10^{2} \mathrm{~N} \cdot \mathrm{m}[/latex]

Calculate the torque exerted by the man. The torque is positive because [latex]\overrightarrow{\mathbf{F}}_{2}[/latex], if unopposed, would cause a counterclockwise rotation:

[latex] au_{2}=r_{2} F_{2}=(0.800 \mathrm{~m})\left(8.50 imes 10^{2} \mathrm{~N} ight)=6.80 imes 10^{2} \mathrm{~N} \cdot \mathrm{m}[/latex]

Sum the torques to find the net torque on the door:

[latex] au_{ ext {net }}= au_{1}+ au_{2}= - 7.0 imes 10^{1} \mathrm{~N} \cdot \mathrm{m}[/latex]

REMARKS The negative result here means that the net torque will produce a clockwise rotation.

Q. 8.1

Chapter 8

Q. 8.1

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