Answered: A door has a width of 1 m. The hinge…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A door has a width of 1 m. The hinge attaches the door on the left. This time, Andrea pushes on the right end of the door with a force of 30 N at angle θ=90∘θ=90∘. Bob pushes on the door in the opposite direction of Andrea. He applies a force of 30N30N perpendicular to the door at the midpoint of the door’s width.

The net torque vector on the door is ____ z Nm to the door.

Expert Solution

Step 1

Given,

Width, d= 1m, Force, F= 30 N, and angle, $θ = 90^{0}$ .

Step 2

The torque can be calculated as,

$τ = rFsinθ$

Putting the values we get,

$\begin{array}{rcl} τ & = & \frac{d}{2} \times F \times sinθ \\ = & \frac{1 m}{2} \times 30 N \times \sin 90 \\ = & 15 Nm \end{array}$

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