   Chapter 7, Problem 55AP

Chapter
Section
Textbook Problem

A car moves at speed v across a bridge made in the shape of a circular arc of radius r. (a) Find an expression for the normal force acting on the car when it is at the top of the arc. (b) At what minimum speed will the normal force become zero (causing the occupants of the car to seem weightless) if r = 30.0 m?

(a)

To determine
The expression for the normal force acting on the car at the top of the arc.

Explanation

Given info: The car is moving on a bridge of circular arc shape of radius r . The velocity of the car is v .

Explanation:

When the car is at the top point of the arc, the normal force will act vertically upward. The gravitational force will act vertically downward. There must be net force acting towards the centre of the circular arc in order to provide the centripetal acceleration. Hence the resultant force of the normal force and the gravitational force will act vertically downward and provide the centripetal acceleration.

mgN=mv2r

• v is the velocity at the lowest position
• m is the mass of the pendulum
• N i

(b)

To determine
The minimum speed at which the normal force becomes zero.

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