Force around a horizontal circle

[bearhug]

A curve in a road forms part of a horizontal circle. As a car goes around it at constant speed 13.3 m/s, the total force on the car (due to friction with the road) has magnitude 127 N. If the driver would have been driving 16.8 m/s, what would the force have been instead?

∑F= mac = m* v^2/r This is the original equation I thought of using until I realized that I don't have r or m. When the problem mentions the total force as being 127N I assumed that was ∑F. Acceleration would be zero since speed is constant but that's not necessarily the same thing centripetal acceleration is it?

 

[Doc Al]

∑F= mac = m* v^2/r This is the original equation I thought of using until I realized that I don't have r or m.

That's the right equation. Since r & m don't change, perhaps you don't need to know them. (Think ratios.)

When the problem mentions the total force as being 127N I assumed that was ∑F.

Correct.

Acceleration would be zero since speed is constant but that's not necessarily the same thing centripetal acceleration is it?

Acceleration means a change in velocity, which can be a change in speed or direction. (Velocity is a vector.) When something moves in a circle at constant speed it is most definitely accelerating! It's direction is continually changing: it is being centripetally accelerated. ("Centripetal" just means towards the center--in order for something to go in a circle a force must pull it towards the center. In this problem, friction provides the centripetal force.)

 

[bearhug]

127N/13.3m/s = x/ 16.8m/s? x= 160.4 N

 

[Doc Al]

Careful: The force is proportional to the velocity squared.

 

[bearhug]

Thanks for pointing that out. I appreciate it.