Question

a man ties one end of a strong rope 8.72 m long to the bumper of his truck, 0.570 m from the ground, and the other end to a vertical tree trunk at a height of 2.91 m. he uses the truck to create a tension of 7.50 102 n in the rope. compute the magnitude of the torque on the tree due to the tension in the rope, with the base of the tree acting as the reference point.

Answer 1

The torque on the tree due to the tension in the rope is computed using the perpendicular distance from the pivot to the line of force and the tension. It equals 1755 N·m.

Step-by-step explanation:

To compute the magnitude of the torque on the tree due to the tension in the rope, with the base of the tree acting as the reference point, we need to use the formula τ = r * F * sin(θ), where τ is the torque, r is the perpendicular distance from the pivot to the line of action of the force, F is the tension in the rope, and θ is the angle between the rope and a line drawn horizontally from the pivot point.

The distance from the ground to where the rope is attached to the tree is 2.91 m - 0.570 m = 2.34 m. Hence, the torque is τ = 2.34 m * 750 N * sin(90 degrees), because the rope is vertical and the angle between a vertical line and a horizontal line is 90 degrees. The sine of 90 degrees is 1, so the torque is τ = 2.34 m * 750 N = 1755 N·m.

SUMUP all the final answer as points at last:

• Distance to pivot (perpendicular distance): 2.34 m
• Tension in the rope: 750 N
• Torque on the tree: 1755 N·m