Question

The question ask:

A block is hung by a string from the inside roof of a van.When
the van goes straight ahead at a speed of 28m/s, theblock hangs
vertically down. But when the van maintains this samespeed around
an unbanked curve (radius=150m), the block swingstoward the outside
of the curve. Then the string makes anangle theta with the
vertical. Find theta.

Answer 1

`\theta=28.07^(\circ)`

Step-by-step explanation:

Speed of van, v = 28 m/s

Radius of unbanked curve, r = 150 m

Let
`\theta` is the angle with the vertical. In case of banking of road,

`T\ cos\theta=mg`.............(1)

And

`T\ sin\theta=(mv^2)/(r)`..........(2)

From equation (1) and (2) :

`tan\theta=(v^2)/(rg)`

`tan\theta=((28)^2)/(150* 9.8)`

`\theta=28.07^(\circ)`

So, the string makes an angle of 28.07 degrees with the vertical. Hence, this is the required solution.