   Chapter 8, Problem 27P

Chapter
Section
Textbook Problem

A uniform plank of length 2.00 m and mass 30.0 kg is supported by three ropes, as indicated by the blue vectors in Figure P8.27. Find the tension in each rope when a 700.-N person is d = 0.500 m from the left end. Figure P8.27

To determine
The tension on each rope.

Explanation

Given info: The length of the plank (l) is 2.00 and  mass of the plank (m) is 30.0 kg.

Explanation:

The free body diagram is,

The torque on the left edge about an axis perpendicular to the page is zero. Therefore,

(700N)d+(294N)(l2)=(T1sin40ο)l

Substitute 2.00 m for l and 0.500 m for d.

(700N)(0.500m)+(294N)(2.00m2)=(T1sin40ο)(2.00m)

Rearrange the expression to find the value of T1 .

T1=(700N)(0.500m)+(294N)(2.00m2)(sin40ο)(2

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