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Solved: Suppose the weight of the drawbridge in Figure
Chapter 9, Problem 12(choose chapter or problem)
Suppose the weight of the drawbridge in Figure 9.34 is supported entirely by its hinges and the opposite shore, so that its cables are slack.
(a) What fraction of the weight is supported by the opposite shore if the point of support is directly beneath the cable attachments?
(b) What is the direction and magnitude of the force the hinges exert on the bridge under these circumstances? The mass of the bridge is 2500 kg.
Figure 9.34 A small drawbridge, showing the forces on the hinges (F), its weight (w), and the tension in its wires (T).
Questions & Answers
QUESTION:
Suppose the weight of the drawbridge in Figure 9.34 is supported entirely by its hinges and the opposite shore, so that its cables are slack.
(a) What fraction of the weight is supported by the opposite shore if the point of support is directly beneath the cable attachments?
(b) What is the direction and magnitude of the force the hinges exert on the bridge under these circumstances? The mass of the bridge is 2500 kg.
Figure 9.34 A small drawbridge, showing the forces on the hinges (F), its weight (w), and the tension in its wires (T).
ANSWER:
Step 1 of 8
Given data:
Suppose the weight of the drawbridge in Figure is supported entirely by its hinges and the opposite shore so that its cables are slack. The mass of the bridge is 2500 kg.
Step 2 of 8
The free-body diagram for the bridge is as follows:
Here, F is the force due to the hinge, W is the weight of the bridge, and T is tension in the string,
Step 3 of 8
(a)
The expression to find the weight is:
\(W = mg \)
Here, m is the bridge's mass, and g is the acceleration due to gravity.
Substitute the values in the above expression, and we get,
\(W = 2500 \times 9.81\)
\(W = 24525\;{\rm{N}}\)
The first condition of equilibrium:
The net force is zero. Hence, the sum of