Question

A particle m is suspended by a massless string inside a trolley of mass m. Force F is being applied on trolley to move it on friction less surface. The angle theta between the string and vertical when particle is in equilibrium with respect to trolley."

Answer 1

Answer on Question #61021-Physics-Mechanics-Relativity

A particle $m$ is suspended by a massless string inside a trolley of mass $m$ . Force $F$ is being applied on trolley to move it on friction less surface. The angle theta between the string and vertical when particle is in equilibrium with respect to trolley.

Solution

Inside of the car speeding up on a horizontal road with acceleration 'a'.

$\theta =$ constant angle with vertical by the string

T= Tension in the string

$\mathrm{m} =$ mass of the ball

mg=ball's weight

ma= pseudo force

$$a = \frac {F}{m + m} = \frac {F}{2 m}.$$ $$\tan \theta = \frac {g}{a} = \frac {g}{\frac {F}{2 m}} = \frac {2 m g}{F}$$ $$\theta = \tan^ {- 1} \left(\frac {2 m g}{F}\right).$$

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