What is the magnitude of the centripetal acceleration of the car as it goes around the curve?

Question

A 2,000-kilogram car travels at a constant speed of 15 meters per second around a circular curve of radius 20 meters. What is the magnitude of the centripetal acceleration of the car as it goes around the curve?

 

Explain and show all work please.

Answer 1

In general, Force = ma where m is mass and a is acceleration.  The specific form for Centripetal Force = -mv²/r where:

• m = mass = 2000 kg
• v = velocity = 15 m/s
• r = radius = 20 m

 

Equate the two equations for Force:

 

      -mv²/r = ma

      -v²/r = a

 

Plug the values for v and r in to get the answer.  The unit of acceleration is m/s².