The wheel of a car has a radius of 0.390 m. The engine of the car applies a torque of 282 N · m to this wheel, which does not slip against the road surface. Since the wheel does not slip, the road must be applying a force of static friction to the wheel that produces a countertorque. Moreover, the car has a constant velocity, so this countertorque balances the applied torque. What is the magnitude of the static frictional force?

Answer is in N

To find the magnitude of the static frictional force, we first need to understand the relationship between torque, radius, and static friction.

The torque applied to the wheel can be calculated using the equation:

Torque = Force * Radius

Given that the torque applied to the wheel is 282 N · m and the radius of the wheel is 0.390 m, we can rearrange the equation to solve for the force (static friction):

Force = Torque / Radius

Substituting the given values, we have:

Force = 282 N · m / 0.390 m

Calculating this expression, we find:

Force ≈ 723.08 N

Therefore, the magnitude of the static frictional force exerted by the road on the wheel is approximately 723.08 N.