Question

7. A block is suspended by a rope from the ceiling of
a car. When the car rounds a 30 m radius horizontal
curve at 20 m/s what angle does the rope make with
the vertical?
(a) 0°
(b) 30°
(d) 530
(c) 370​

Answer 1

Answer:

At the angle of $53^o$ the makes the rope vertical.

Given:

A block is suspended by a rope from the ceiling of a car.  The car rounds a 30 m radius horizontal curve at 20 m/s  

To find:

What angle does the rope make with the vertical

Solution:

Centripetal acceleration $= \frac{v^{2}}{r}$  

$=\frac{20 \times 20}{30} = 13.33$

$\tan \theta=\frac{a c}{g}$ where g is the acceleration due to gravity , 9.8 $\frac{m}{s^{2}}$

$\theta = \arctan \left(\frac{13,33}{9.8}\right) = 53$ degrees.

Result:

The rope makes vertical at the angle of $53^o$.