To calculate the torque (
\( au \)
) produced when a force is applied at a distance from a pivot point, we can use the following formula:
Torque (
\( au \)
) = Force (
\( F \)
) × Distance (
\( r \)
) × sin(θ)
Where:
\( F \)
= the magnitude of the force applied (in Newtons)
\( r \)
= the distance from the pivot point to the point where the force is applied (in meters)- θ = the angle between the force vector and the lever arm (in degrees or radians)
In this scenario:
- The force applied (
\( F \)
) is 60 N. - The shaft of the pedal (
\( r \)
) is 16 cm, which we need to convert into meters for our calculations. 16 cm is equal to 0.16 m. - If we assume that the force is applied perpendicular to the lever arm (which is typically the case when pedaling a bicycle), then the angle θ is 90 degrees, and sin(90°) equals 1.
Now we can plug these values into the formula:
Torque = 60 N × 0.16 m × sin(90°)
Torque = 60 N × 0.16 m × 1
Torque = 9.6 N·m
Therefore, the magnitude of the torque about point P when a 60 N force is applied to the bicycle pedal is 9.6 N·m.