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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A car accelerates down a hill (Fig. P4.87), going from rest to 30.0 m/s in 6.00 s. During the acceleration, a toy (m = 0.100 kg) hangs by a string from the car’s ceiling. The acceleration is such that the string remains perpendicular to the ceiling. Determine (a) the angle θ and (b) the tension in the string.

images

Figure P4.87

(a)

To determine
The angle of incline.

Explanation

Given info: A car accelerates from rest to 30 m/s in 6.00 s. Mass of the toy is 0.100 kg.

The free body diagram is given below.

  • T is the tension.
  • m is the mass of the toy.
  • g is the acceleration due to gravity.
  • a is the acceleration.

From the diagram,

mgsinθ=ma

On Re-arranging, the angle of incline is,

θ=sin1(ag)                                               (I)

The formula for acceleration is,

a=vut                                                      (II)

  • v is the final velocity.
  • u is the initial velocity

(b)

To determine
The tension in the string.

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