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Chapter 12: Q. 62 (page 333)

A 120-cm-wide sign hangs from a 5.0 kg, 200-cm-long pole. A cable of negligible mass supports the end of the rod as shown in Figure P12.62. What is the maximum mass of the sign if the maximum tension in the cable without breaking is 300 N?

Short Answer

Expert verified

Maximum mass it can support is 30.54 kg

Step by step solution

01

Given Information

A 120-cm-wide sign hangs from a pole.

Mass of pole = 5.0 kg,

Length of pole 200-cm= 2m

A cable supports the end of the rod with maximum tension= 300 N

02

Explanation

First draw the diagram to understand and solve the problem as below

Now equate the clockwise and anti-clockwise torque

mg脳(80cm)+(5kg)g脳(100cm)+mg脳(200cm)=TSin胃脳(200cm)


Substitute

sin胃=250(2502+2002)=0.78andT=300N

We get,

mg脳(0.80m)+(5kg)g脳(1m)+mg脳(2m)=(300N)(0.78)脳(2m)2.8m+5kg=468gkgm=15.27kg

Maximum mass of sign board = M =2m =30.54 kg.

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