Question

At one position during its cycle, the foot pushes straight down with a 410-N force on a bicycle pedal arm that is rotated an angle ϕ=71∘ from the vertical. Part A If the force is applied r=0.19m from the axis of rotation, what torque is produced? Express your answer to two significant figures and include appropriate units.

Answer 1

To find the torque produced by a force on a bicycle pedal arm, use the formula T = rF sin(φ) with the given force, distance, and angle. For a 410-N force applied 0.19 m from the axis at a 71-degree angle from vertical, the torque is approximately 74 N·m.

Step-by-step explanation:

To calculate the torque produced by a force applied to a bicycle pedal arm, we will use the formula for torque, which is T = rF sin(φ), where T represents the torque, r is the distance from the axis of rotation to the point where the force is applied, F is the magnitude of the force, and φ is the angle between the force and the vertical. Given that the force is 410 N, the distance r is 0.19 m, and the angle φ is 71°, we calculate the torque as follows:

T = rF sin(φ) = 0.19 m × 410 N × sin(71°) ≈ 0.19 m × 410 N × 0.946 ≈ 74 N·m

So, the torque produced is approximately 74 N·m.

Answer 2

The torque produced by the force applied to the bicycle pedal arm can be calculated using the formula T = rF sin(φ), where T is the torque, r is 0.19 m, F is 410 N, and φ is 71°. The calculated torque is 77.9 N⋅m to two significant figures.

Step-by-step explanation:

To calculate the torque produced by the force applied to the bicycle pedal arm, we can use the following formula:

T = rF sin(φ)

where T is the torque, r is the distance from the pivot point to the point where the force is applied (0.19 m), F is the magnitude of the force (410 N), and φ is the angle between the force and the radial vector from the pivot point to the point of force application (71°).

To find the torque, first convert the angle to radians:

φ = 71° = (71°)(π/180°) = 1.24 radians (approx.)

Now, plug in the values:

T = (0.19 m)(410 N) sin(1.24 radians)

T = 77.9 N⋅m (to two significant figures)

Therefore, the torque produced is 77.9 N⋅m.