The length of a bicycle crank arm is 0.183 m, and a downward vertical force of 104. N is applied by the foot. What is the magnitude of the torque about the pivot point when the arm makes the following angles with the upward vertical (12:00)?
a) 0.0 degrees
b) 30.0 degrees
c) 90.0 degrees
d) 180. degrees
To calculate the torque at different angles, we will use the formula for torque:
Torque = Force x Distance x sin(angle)
a) at 0.0 degrees: sin(0) = 0, so torque = 0
b) at 30.0 degrees:
Torque = 104 N x 0.183 m x sin(30)
Torque = 104 N x 0.183 m x 0.5
Torque = 9.552 Nm
c) at 90.0 degrees:
Torque = 104 N x 0.183 m x sin(90)
Torque = 104 N x 0.183 m x 1
Torque = 19.032 Nm
d) at 180.0 degrees:
Torque = 104 N x 0.183 m x sin(180)
Torque = 104 N x 0.183 m x 0
Torque = 0 Nm
Therefore, the magnitudes of the torque about the pivot point at different angles are:
a) 0.0 degrees: 0 Nm
b) 30.0 degrees: 9.552 Nm
c) 90.0 degrees: 19.032 Nm
d) 180.0 degrees: 0 Nm