Question

The fishing pole in the figure below makes an angle of 20.0° with the horizontal. What is the magnitude of the torque exerted by the fish about an axis perpendicular to the page and passing through the angler's hand if the fish pulls on the fishing line with a force

F = 107 N
at an angle 37.0° below the horizontal? The force is applied at a point
L = 2.11 m
from the angler's hands.
_______ N · m

Answer 1

The magnitude of the torque exerted by the fish is approximately 188.8 N · m, using the formula T = rF sin θ and given values for the angle, force, and length of the lever arm.

Step-by-step explanation:

To calculate the torque exerted by the fish, we'll use the formula T = rF sin θ, where T is the torque, r is the distance from the axis to the point where the force is applied, F is the force applied, and θ is the angle between the direction of the force and the lever arm.

Given that the fishing line forms a 37.0° angle below the horizontal, and the fishing pole makes a 20.0° angle with the horizontal, the angle between the force and the lever arm is θ = 20.0° + 37.0° = 57.0°.

The length of the lever arm, L is 2.11 m, and the force applied by the fish, F, is 107 N.

The torque is therefore calculated as follows:

T = 2.11 m × 107 N × sin(57.0°)

To find sin(57.0°), we can use a calculator:

sin(57.0°) ≈ 0.838

Now we can compute the torque:

T = 2.11 m × 107 N × 0.838 ≈ 188.8 N · m

So the magnitude of the torque exerted by the fish is approximately 188.8 N · m.

Answer 2

The magnitude of the torque exerted by the fish on the fishing pole is approximately 189.3 N · m, calculated using the torque formula T = rF sin(θ) with the force applied at an angle and the distance from the pivot point.

Step-by-step explanation:

The question asks for the magnitude of the torque exerted by a fish on a fishing pole, assuming the pole makes an angle with the horizontal and the fish applies a force at an angle below the horizontal. To calculate the torque, we can use the relation T = rF sin(θ), where T is the torque, r is the distance from the pivot, F is the force applied, and θ is the angle between the direction of the force and the lever arm.

The force applied by the fish is 107 N at an angle of 37.0° below the horizontal, and the fishing pole is L = 2.11 m from the angler's hands. We are looking for the component of the force perpendicular to the rod since torque depends on this perpendicular component. The angle to consider in torque calculation is the angle between the applied force and the direction of the rod, which is 20.0° + 37.0° = 57.0° since the force is below the horizontal and the rod is above it. Therefore, the magnitude of the torque is:

T = rF sin(θ) = (2.11 m)(107 N) sin(57.0°) ≈ (2.11 m)(107 N)(0.838) ≈ 189.3 N · m.