# Pendulum hanging in a car

1. Homework Statement
Problem:
A pendulum with a 1kg mass hangs from the roof of a car travelling on a level road. The pendulum string makes an angle of 10° with the vertical as shown. Determine the cars acceleration (Hint: The acceleration of the car is the same as that of the pendulum)
(i'm assuming this is centripetal acceleration as it's on a centripetal force worksheet).
Known Variables:
g = -10m/s/s
mass = 1kg
string is assumed massless, ridgid, and even tension throughout.

2. Homework Equations
a=v^2/r
F=ma

3. The Attempt at a Solution
[PLAIN]http://k.min.us/imvCIg.jpg [Broken]

The problem isnt so much in the calculation, which is what i solved in the picture.

My question is, why does the pendulum make the 10° angle with the vertical? Would it be the cause of a reaction force since the tension is pulling the object in a horizontal direction? Is it because it wants to go in its original direction?
If it is a cause of the latter, wouldn't taking this corner at a higher velocity cause the angle to be smaller, since centripetal acceleration is a power relationship of velocity? Also if it is the latter again, can someone explain to me why its velocity is always in a different trajectory than that of the car? Couldn't they equalize? (and therefore be straight up and down along the vertical)
Can someone explain this intuitively to me?

And extending upon this question, why does a pendulum go back and forth when a car is accelerating?

Any insight would be fantastic, thanks!

- Mat

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supratim1
Gold Member
It is because of something called as Pseudo Force. since the frame of car is accelerating, we cannot apply Newton's laws directly. in order to apply them, we use a pseudo force, opposite to the direction of the acceleration of the frame (car). the pseudo force = -ma, where m = mass of pendulum, and a = acceleration of frame (car), but just opposite in direction.

when you balance its components with tension and gravity, you find that 10 degree angle.

It is because of something called as Pseudo Force. since the frame of car is accelerating, we cannot apply Newton's laws directly. in order to apply them, we use a pseudo force, opposite to the direction of the acceleration of the frame (car). the pseudo force = -ma, where m = mass of pendulum, and a = acceleration of frame (car), but just opposite in direction.

when you balance its components with tension and gravity, you find that 10 degree angle.
That's the mathematical end of it, but it isn't a clear definition of what is happening. Can you explain this intuitively? or perhaps with an example? I want to figure out why its doing that, not how to solve for it.

Thanks

- Mat

supratim1
Gold Member
Hello Mat!

you can imagine it as due to inertia of the pendulum. when the car begins to accelerate from rest, the bob wants to remain still. so it hangs on in the same position, but the car moves ahead. after sometime, the bob gains same acceleration as the car, but it remains hanging at an angle.

was i able to explain clearly?

• navneet9431
Hello Mat!

you can imagine it as due to inertia of the pendulum. when the car begins to accelerate from rest, the bob wants to remain still. so it hangs on in the same position, but the car moves ahead. after sometime, the bob gains same acceleration as the car, but it remains hanging at an angle.

was i able to explain clearly?
I think so, thank you!

supratim1
Gold Member
thats nice...welcome!

1. Homework Statement
Problem:
A pendulum with a 1kg mass hangs from the roof of a car travelling on a level road. The pendulum string makes an angle of 10° with the vertical as shown. [...]
No it doen't. Have you even tried this? I have. It just swings around erratically with every moderation of the accelerator pedal, every curve, and every bump. And you haven't even given initial conditions of the pendulum. Should every car be factory equipped with a pendulum for the benefit of high school science professors to connect with physical reality we wouldn't be given such silly questions.

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