Question

A car of mass 1250 kg drives around a curve with a speed of 22 m/s.

a. If the radius of the curve is 35 m, what is the centripetal acceleration of the car? (3 points)

b. The maximum friction that the car's tires can apply is 20,000 N. What is the radius of the smallest circle the car can drive in at a speed of 22 m/s? (3 points)

Answer 1

Please let me know if anything I say is confusing, we really do want to help you understand.

for an object travelling in a circle, we can describe the motion with the equation:

\[F_{c} = \frac{ mv^2 }{ r }\]

where Fc is the centripetal force, m is the mass, v is the velocity, and r is the radius.

The centripetal force is the force that keeps the object moving in a circle (without this force, the object would simply move in a single linear direction)

Answer 2

so for a) you have the radius, the mass, and the speed. you can plug these into the equation Fc = mv^2 / r to get Fc. once you have Fc, simply use Newton's Second Law:

Fc = ma

and solve for a.

for b) The friction force (20,000N) is your centripetal force. so you can simply use Fc = mv^2 / r, plug in the mass and velocity, and solve for r.