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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.

Respuesta :

Answer:

[tex]\theta=28.07^{\circ}[/tex]

Explanation:

Speed of van, v = 28 m/s

Radius of unbanked curve, r = 150 m

Let [tex]\theta[/tex] is the angle with the vertical. In case of banking of road,

[tex]T\ cos\theta=mg[/tex].............(1)

And

[tex]T\ sin\theta=\dfrac{mv^2}{r}[/tex]..........(2)

From equation (1) and (2) :

[tex]tan\theta=\dfrac{v^2}{rg}[/tex]

[tex]tan\theta=\dfrac{(28)^2}{150\times 9.8}[/tex]

[tex]\theta=28.07^{\circ}[/tex]

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

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