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sveta [45]
3 years ago
13

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 hang

s 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.
Physics
1 answer:
Elis [28]3 years ago
5 0

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

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