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Physics / College Physics 1 / Chapter 9 / Problem 1

College Physics | 1st Edition | ISBN: 9781938168000 | Authors: Paul Peter Urone, Roger Hinrichs

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Solved: (a) When opening a door, you push on it

Chapter 9, Problem 1

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QUESTION:

Problem 1PE

(a) When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850m from the hinges. What torque are you exerting relative to the hinges? (b) Does it matter if you push at the same height as the hinges?

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QUESTION:

Problem 1PE

(a) When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850m from the hinges. What torque are you exerting relative to the hinges? (b) Does it matter if you push at the same height as the hinges?

ANSWER:

Solution 1PE

Torque in rotational motion is the analogue of force in a linear motion. The mathematical expression of torque is given as $\tau{}=rF\ sin\ \theta{}$ , where $r$ is the distance of the point at which the force is applied and the pivot point about which the object rotates and $\theta{}$ is the angle between the force and the position vector of the line joining points of applied force and the pivot point.

Part a

Step 1 of 2

Given data:

The force $F=55.0$ N

The distance $r=$ 0.850 m

The angle $\theta{}=9{0}^{0}$

Therefore, the torque $\tau{}=rF\ sin\ 9{0}^{0}$

$\tau{}=0.850\times{}55.0\times{}sin\ 9{0}^{0}$ N $\cdot{}$ m

$\tau{}=46.75$ N $\cdot{}$ m

Therefore, the exerted torque is 46.75 N $\cdot{}$ m.

Part b

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