Solution Found!
Answer: A 60.0-cm, uniform, 50.0-N shelf is supported
Chapter 11, Problem 8E(choose chapter or problem)
A \(60.0-\mathrm{cm}\), uniform, \(\text { 50.0-N }\) shelf is supported horizontally by two vertical wires attached to the sloping ceiling (Fig. E11.8). A very small \(\text { 25.0-N }\) tool is placed on the shelf midway between the points where the wires are attached to it. Find the tension in each wire. Begin by making a free-body diagram of the shelf.
Equation Transcription:
Text Transcription:
60.0-cm
50.0-N
25.0-N
25.0 cm
75.0 cm
20.0 cm
Questions & Answers
QUESTION:
A \(60.0-\mathrm{cm}\), uniform, \(\text { 50.0-N }\) shelf is supported horizontally by two vertical wires attached to the sloping ceiling (Fig. E11.8). A very small \(\text { 25.0-N }\) tool is placed on the shelf midway between the points where the wires are attached to it. Find the tension in each wire. Begin by making a free-body diagram of the shelf.
Equation Transcription:
Text Transcription:
60.0-cm
50.0-N
25.0-N
25.0 cm
75.0 cm
20.0 cm
ANSWER:
Solution 8E
Step 1:
First, we have to draw the free body diagram for the shelf. It is represented in figure 1.
Total length of the shelf, L = 60 cm = 0.6 m
Position of center of gravity, Lg = 30 cm = 0.3 m
Position of the tool from the left side, Ltool = 20 cm = 0.2 m
Position of center of gravity from right wire, Lg’ = 20 cm = 0.10 m
Position of the tool from the right wire, L’tool = 20 cm = 0.2 m
Total torque on the system can be considered as zero since the system is in rest.
Moment on left side of the shelf = 0
Therefore, we can write,
That is,
Or,
Therefore, tension on the right string,
