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

θ =28.07⁰

Step-by-step 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= (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)

`(F_(n)sin\theta)/(F_(n)cos\theta) = ((mv^(2) )/(r) )/(mg)`

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

`\theta=tan^(-1) (v^(2) )/(rg)`

v = 28 m/s

r = 150 m

g = 9.8m/
`s^(2)`

θ = 28.07⁰