Grade 11Mechanics

A trolley is accelerated horizontally with acceleration a . Find the maximum angular displacement of the pendulum hanging inside it.

ABC

7 Years agoGrade 11

3 Answers

Arun

7 Years ago

Dear student

If given please attach an image. So that it will be easy to solve.

Regards

Arun (askIITians forum expert)

Raj Shakya

7 Years ago

we can balance the net force on the pendulum

horizontally ma = Tsin $\theta$ ------i

vertically mg = Tcos $\theta$ ------ii

dividing i by ii

tan $\theta$ = a/g

$\theta$ = tan inverse of (a/g)

Rajdeep

7 Years ago

HELLO THERE!

Let’s understand the theory first!

We are said, that:

The pendulum is inside a trolley, which has an acceleration a. If the mass of the bob of pendulum is m, then it will experience a pseudo force of magnitude = ma in the opposite direction of acceleration of the trolley.

Also, let the maximum angular displacement be Theta ( $\theta$ ). On the bob, a downward force of mg is acting, which is balanced by the horizontal component, i.e., cosine component of the Tension on the string.

So, we get the equation T cos $\theta$ = mg …....(i)

Now, the sine component of the Tension is equal to the pseudo force acting on the bob. This can be understood when you draw the free body diagram of the situation.

So, we get another equation as: T sin $\theta$ = ma …...(ii)

Dividing (ii) by (i),

$\frac{Tsin\theta}{Tcos\theta} = \frac{ma}{mg} \\\\or, tan \theta = \frac{a}{g} \\\\or, \theta = tan^{-1}(\frac{a}{g})$