   Chapter 7, Problem 10CQ

Chapter
Section
Textbook Problem

A car of mass m follows a truck of mass 2m around a circular turn. Both vehicles move at speed v. (a) What is the ratio of the truck’s net centripetal force to the car’s net centripetal force? (b) At what new speed vtruck will the net centripetal force acting on the truck equal the net centripetal force acting on the car still moving at the original speed v?

(a)

To determine
The ratio of net centripetal forces of truck to car.

Explanation

Given Info:

The mass of the car is m .

The mass of the truck is 2m .

Both the vehicles are moving in a same speed v .

Explanation:

Formula to calculate the centripetal force is,

Fc=mv2r

• m is the mass of vehicle
• v is the velocity of vehicle
• r is the radius of the circle that the vehicles are following

The centripetal acceleration is,

ac=v2r

Since, the vehicles are travelling in a same circular path and the speed of the vehicles is the same; the centripetal acceleration for both the vehicles is same

(b)

To determine
The new speed of the truck where the net centripetal force acting on the truck is equal to the net centripetal force acting on the car moving at its original speed.

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