Calculate the torque (magnitude and direction) about point O due to the force F in each of the cases sketched in Fig. E10.1. In each case, both the force F and the rod lie in the plane of the page, the rod has length 4.00 m, and the force has magnitude F = 10.0 N.

Verified step by step guidance

1. Identify the given values: The length of the rod (r) is 4.00 m, the magnitude of the force (F) is 10.0 N, and the angle between the force and the rod is 90 degrees.
2. Recall the formula for torque (τ), which is given by τ = r * F * sin(θ), where θ is the angle between the force and the lever arm.
3. Substitute the given values into the torque formula: τ = 4.00 m * 10.0 N * sin(90°).
4. Since sin(90°) is 1, the torque simplifies to τ = 4.00 m * 10.0 N * 1.
5. Determine the direction of the torque: Since the force is applied perpendicular to the rod and in the upward direction, the torque will cause a counterclockwise rotation about point O.

Key Concepts

Torque

Torque is a measure of the rotational force applied to an object around a pivot point. It is calculated as the product of the force magnitude and the perpendicular distance from the pivot to the line of action of the force. The direction of torque is determined by the right-hand rule, which indicates whether the rotation is clockwise or counterclockwise.

Lever Arm

The lever arm is the perpendicular distance from the pivot point to the line of action of the force. It is crucial in determining the torque, as torque is directly proportional to this distance. In the given problem, the lever arm is 3 meters, which is the distance from the pivot to where the force is applied.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the torque vector. To apply it, point your thumb in the direction of the axis of rotation, and curl your fingers in the direction of the force. The direction your thumb points indicates the direction of the torque. In this scenario, the force applied downward results in a clockwise torque about the pivot.