(a) The magnitude of torque at 45.0° is 12.6 N·m.
(b) The magnitude of torque at 90.0° is 17.0 N·m.
(c) The magnitude of torque at 135.0° is 12.6 N·m.
Torque, represented by the symbol τ, is the product of the applied force and the lever arm's length, multiplied by the sine of the angle between the force and the lever arm. In this scenario, the bicycle pedal arm has a length (lever arm) of 0.170 m, and a downward force of 100 N is applied.
(a) At an angle of 45.0° between the arm and the vertical, the torque is calculated using the formula τ = r * F * sin(θ). Substituting the values, the magnitude of torque is 0.170 m * 100 N * sin(45.0°), resulting in approximately 12.6 N·m.
(b) When the angle is 90.0°, the sin(90.0°) term becomes 1, making the torque τ = r * F * sin(θ) equal to 0 N·m. This is because the force is acting perpendicular to the lever arm.
(c) At an angle of 135.0°, the torque is again determined using τ = r * F * sin(θ). Substituting the values, the magnitude of torque is 0.170 m * 100 N * sin(135.0°), resulting in approximately -12.6 N·m. The negative sign indicates that the torque is acting in the opposite direction due to the angle exceeding 90.0°.