Pendulum Problem...

Classical Mechanics Level 2

A 0.8 kg sphere hangs on a string from the ceiling of an automobile traveling on a level road.

The car has a constant horizontal acceleration and the string is displaced an angle θ = 60° from the vertical.

To a person sitting inside the car, it appears that the sphere is motionless (the angle between the sphere and the vertical is constant).

What is the magnitude of the acceleration of the car?

Consider g = 9.8 m/s^2


The answer is 16.97.

Satyen Nabar by Satyen Nabar , 48, India

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2 solutions

Satyen Nabar
Sep 6, 2014

In Horizontal axis sin 60 = Force/Tension in string = ma/T

In vertical axis, cos 60 = Force/Tension in string= mg/T

sin 60/ cos 60 = tan 60 = a/g

a = 16.97

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Emanuel Sygal
Oct 11, 2014

When traveling in a frame with acceleration A A , we can replace g g by g e f f = g − A g_{eff}=g-A , as vectors, or equivalently think of a fictitious force of − m A -mA pointing in direction opposite to the motion. by looking at the triangle formed, we see tan ⁡ θ = A g \tan\theta=\frac{A}{g} . Hence A = g 3 A=g\sqrt3 .

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