The length of a bicycle pedal arm is 0.152 m, and a downward force of 146 N is applied to the pedal by the rider's foot. What is the magnitude of the torque about the pedal arm's pivot point when the arm makes the following angles with the vertical?
(a) 30°
(b) 90°
(c) 180°
To find the magnitude of the torque about the pedal arm's pivot point, we need to use the formula:
Torque = Force x Perpendicular Distance
The perpendicular distance is the distance between the pivot point and the line of action of the force. In this case, it is the length of the pedal arm.
Given:
Length of the pedal arm (L) = 0.152 m
Force (F) = 146 N
(a) When the arm makes an angle of 30° with the vertical:
In this case, the perpendicular distance is the vertical component of the arm's length. So, we need to find the vertical component first.
Vertical component of the pedal arm = Length of the pedal arm × sin(angle)
Vertical component = 0.152 m × sin(30°)
Now, to find the torque:
Torque = Force × Vertical component
Torque = 146 N × (0.152 m × sin(30°))
(b) When the arm makes an angle of 90° with the vertical:
In this case, the perpendicular distance is the length of the pedal arm.
Torque = Force × Length of the pedal arm
Torque = 146 N × 0.152 m
(c) When the arm makes an angle of 180° with the vertical:
In this case, as the arm is directly opposite to the applied force, the torque is zero.
So, the magnitude of the torque about the pedal arm's pivot point for the given angles are:
(a) Torque = 146 N × (0.152 m × sin(30°))
(b) Torque = 146 N × 0.152 m
(c) Torque = 0 N