Question

A small sphere is hung by a string from the ceiling of a van. When the van is stationary, the sphere hangs vertically. However, when the van accelerates, the sphere swings backward so that the string makes an angle of θ with respect to the vertical. Find the acceleration of the van when θ = 12.8°.

Answer 1

`a = 2.23 m/s^2`

Step-by-step explanation:

As the small sphere is suspended by the string then the force due to tension is given as

`T cos\theta = mg`

`T sin\theta = ma`

now we will have

`tan\theta = (ma)/(mg)`

here we will have

`a = g tan\theta`

here we know that

`\theta = 12.8^o`

so we will have

`a = (9.81)tan12.8`

`a = 2.23 m/s^2`