Question

A block is hung by a string from the inside roof of a van. when the can goes straight ahead at a speed of 28 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (r = 150m), the block swings toward the outside of the curve. The string makes an angle θ with the veritcal. Find θ.

Answer 1

Answer:

θ =28.07⁰

Explanation:

when van moves around an unbanked curve, horizontal component of normal force is equal to centripetal force

$F_{c}= F_{n} sin\theta$

$F_{n}sin\theta= \frac{mv^{2} }{r}$---(1)

There is no motion in vertical direction, so vertical component of normal force is balanced with weight of block i.e.

$F_{n}cos\theta= mg$----(2)

divide (1) and (2)

$\frac{F_{n}sin\theta}{F_{n}cos\theta} = \frac{\frac{mv^{2} }{r} }{mg}$

$tan \theta=\frac{v^{2} }{rg}$

$\theta=tan^{-1} \frac{v^{2} }{rg}$

v = 28 m/s

r = 150 m

g = 9.8m/$s^{2}$

θ = 28.07⁰