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Chapter 17: Problem 8

If three nonparallel forces hold a rigid body in equilibrium, they must a) be equal in magnitude c) be non-concurrent b) be concurrent d) form an equilateral triangle

Short Answer

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Question: For three nonparallel forces to hold a rigid body in equilibrium, they must: Answer: (b) be concurrent

Step by step solution

01

Understanding equilibrium conditions for rigid bodies

A rigid body is said to be in equilibrium if the net force and net moment (torque) acting on it are both zero. In this case, we are given that the body is in equilibrium due to three nonparallel forces acting on it. We will now use this information to find the condition that these forces must satisfy.
02

Investigate the forces' directions and magnitudes

Since the forces are nonparallel, they must have different directions. However, the problem does not specify that the forces have equal magnitudes, so we cannot assume a). Therefore, the answer cannot be (a) be equal in magnitude.
03

Determine if the forces are concurrent or non-concurrent

The condition for a rigid body to remain in equilibrium is that the vector sum of the forces acting on it must be zero. In other words, the forces must balance each other out. In this case, the forces are not parallel, so the only way for them to balance each other out is if they are concurrent (meaning their lines of action intersect at a single point). If the forces are not concurrent, they will create a net torque, and the rigid body will not be in equilibrium. Therefore, the answer is (b) be concurrent.
04

Eliminate other options based on the previous steps

Since we have determined that the forces must be concurrent for the rigid body to be in equilibrium, we can eliminate option (c) be non-concurrent as it contradicts our finding. Also, option (d) form an equilateral triangle does not necessarily have to be true, as it implies that the forces have equal magnitudes, which is not given in the problem statement. In conclusion, for three nonparallel forces to hold a rigid body in equilibrium, they must: (b) be concurrent

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