Question

if the coefficient of static friction between a cars tires and the pavement is 0.62, calculate the minimum torque that must be applied to the 66- cm -diameter tire of a 1080- kg automobile in order to lay rubber (make the wheels spin, slipping as the car accelerates). assume each wheel supports an equal share of the weight.

Answer 1

To calculate the minimum torque, we determine the friction force using the coefficient of static friction and the car's weight distributed over four tires, and then multiply the friction force by half the diameter of the tire.

The question involves calculating the minimum torque required to make the wheels of a car slip or spin on the surface, given that the coefficient of static friction is 0.62, and assuming each wheel supports an equal share of the automobile's weight.

First, calculate the force of static friction for one tire:
Friction force = coefficient of static friction x normal force
Since the normal force equals the weight supported by each tire, we have:
Normal force = (total weight of car / number of tires) = (1080 kg × 9.8 m/s2) / 4
Friction force = 0.62 × normal force

To find torque, we use:
Torque = force x radius
Since the tire's diameter is 66 cm, the radius is half of that. Hence, torque = friction force x (diameter / 2).