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

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

Grade:11

3 Answers

Arun
25750 Points
5 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
16 Points
5 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
231 Points
5 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})
 
And, theta is the maximum angular displacement.
 
THANKS!

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