Oscillations concerning a pendulum

[Alex_Neof]

Homework Statement

A clock is regulated by a pendulum. The pendulum can be considered as a small weight connected to a rod of negligible mass. The period of oscillation of the pendulum can be adjusted by moving the weight up or down the rod. The angular frequency is given by $\omega ^2 =\frac{g}{L}$, where $L$ is the distance between the centre of the small mass and the pivot point of the pendulum.

The clock is placed on a spaceship accelerating from the surface of the Earth with
acceleration $a=3g.$ Calculate the period of vibration of the pendulum.

Homework Equations

$T = 2 \pi \sqrt{\frac{L}{g}}$

The Attempt at a Solution

The net acceleration is 2g.

Therefore,

$T = 2 {\pi} \sqrt{\frac{(50 \times 10^{-2})} {(2g)}}$

$T = 1.003544 = 1 s$

Does this seem correct?
Thank you!

 

[Suraj M]

The net acceleration is 2g.

How did you get this?

The clock is placed on a spaceship accelerating $from~ the~ surface~ of~ the~ Earth$ with
acceleration a=3g.a=3g.

 

[Alex_Neof]

$\sum F_y = ma = -mg + 3mg$

$ma = 2mg$

$a = 2g$

Taking forces radially downwards as negative.

 

[Suraj M]

Try to find the force acting on a body inside the shuttle rather than the total force acting on the space ship
Hint: you should consider pseudo force on the pendulum by Newtons 1st law

 

[Alex_Neof]

Suraj, is this correct?

$\sum {F_y} = m(3g) = - mg + T$

$T = m(4g)$

So,
$a = 4g$

Therefore,
$T = 0.71\ seconds$

Thank you.

 

[Alex_Neof]

Thank you !

 

[Suraj M]

a=4g

As you have taken forces downward as -ve ypu should be getting a as a -ve value, which you're not,
What is the T you have introduced?
also $∑F_y ≠m(3g)$
you got the right answer, but i doubt the method you have used..i do not mean to discourage you, but its better to know the right method, so that you can use it for another question.

 

[Alex_Neof]

Oh, the T is the tension of the string, which is upwards. How would I go about this? It's true I would rather know the method so I can apply the method again in the future.

 

[Suraj M]

the T is the tension of the string, which is upwards. How would I go about this?

Thats a good way to find out the total force acting on the bob, your T should be the resultant of 2 downward(-ve) forces, could you recognize those forces?

 

[Alex_Neof]

sorry, since the rocket is accelerating upwards at 3g, does that mean the clock inside is also accelerating upwards at 3g?

 

[Suraj M]

We'll it is, but when you're standing in a bus and the vehicle is accelerating forward at 5m/s² will you feel a forward force acting on you, or a backward force? apply your findings to the bob.

 

[Alex_Neof]

So the bob will 'feel' a force of 3mg downwards. Adding this to its weight mg will result in the tension being 4mg upwards.

 

[Suraj M]

yes the tension is 4mg upwards which is the one which balances out the downward force experienced by the bob, so you can get your new g' = a=-4g .. and you'll have your answer.
Just remember about the concept of pseudoforce in cases like this, body feels a force equal and opposite to the direction of its (accelerated) motion.

 

[Alex_Neof]

Thanks again Suraj.

Kind regards and all the best!

 

[Suraj M]

You're welcome,
All the best to you too .