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Chapter 1: Q6DQ (page 356)

6. You are balancing a wrench by suspending it at a single point. Is the equilibrium stable, unstable, or neutral if the point is above, at, or below the wrench鈥檚 center of gravity? In each case give the reasoning behind your answer. (For rotation, a rigid body is in stable equilibrium if a small rotation of the body produces a torque that tends to return the body to equilibrium; it is in unstable equilibrium if a small rotation produces a torque that tends to take the body farther from equilibrium; and it is in neutral equilibrium if a small rotation produces no torque.)

Short Answer

Expert verified

The equilibrium is stable, neutral or unstable if the point is above, at, or below the wrench鈥檚 center of gravity respectively.

Step by step solution

01

Center of gravity

The center of gravity is the point on a body where the total weight of the body is concentrated.

02

Equilibrium of the center of gravity

1. If you balance the wrench above its center of gravity, after a small displacement the torque will return to its initial position and it will oscillate. Then the equilibrium will be stable.

2. If you balance the wrench at the center of gravity, after a small displacement there will be no torque since the gravitational force at the point is neutral.

3. If you balance the wrench below its center of gravity, after a small displacement the torque would tend to turn the wrench around the point of balance completely, which implies the equilibrium is unstable.

Therefore, the equilibrium is stable, neutral, or unstable if the point is above, at, or below the wrench鈥檚 center of gravity respectively.

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