Final answer:
The mechanic tightens the nut with a torque of 30 newton-meters when using a 15cm long spanner and exerting a force of 200N.
Step-by-step explanation:
The question asks to calculate the torque applied by a mechanic when tightening the nut of a bicycle using a 15cm (0.15m) long spanner and exerting a force of 200N.
Torque (τ) is the measure of the force that can cause an object to rotate about an axis and is calculated by the equation:
τ = r * F * sin(θ)
Here, r is the distance from the axis of rotation to the point where the force is applied, F is the magnitude of the force applied, and θ is the angle between the force vector and the lever arm.
In this case, since the force is applied perpendicularly, the angle θ is 90 degrees and sin(θ) = 1. Thus, the torque applied by the mechanic is:
τ = r * F
τ = 0.15m * 200N
τ = 30 N.m
The mechanic tightens the nut with a torque of 30 newton-meters.