Rocket Acceleration Calculation: Pendulum Swing During Liftoff Explained

[rr263]

Homework Statement

An astronaut notices that a pendulum which took 2.46 seconds for a complete cycle of swing when the rocket was waiting on the launch pad takes 1.26 seconds for the same cycle of swing during liftoff. What is the acceleration of the rocket?(Hint: Inside the rocket, it appears that g has increased.)

Homework Equations

T=(2pi)sqrt(L/g)

The Attempt at a Solution

I know I am supposed to use the above equation, but I don't know how to use it to solve for acceleration. Using g=9.8m/s^2 and the initial period, I solved for L and got 0.621m. Do I even need to do that for this problem? The fact that the problem said that "g" increased within the rocket is what confuses me the most. Am I solving for a new/increased value of "g" and using that as acceleration? If so, when I solved the problem this way, I got g=15.4 m/s^2 (using the second period and 0.621m as L), but this was incorrect.

I really need help with this problem as my teacher disabled the hints option. Thanks in advance.

 

[pgardn]

Homework Statement

An astronaut notices that a pendulum which took 2.46 seconds for a complete cycle of swing when the rocket was waiting on the launch pad takes 1.26 seconds for the same cycle of swing during liftoff. What is the acceleration of the rocket?(Hint: Inside the rocket, it appears that g has increased.)

Homework Equations

T=(2pi)sqrt(L/g)

The Attempt at a Solution

I know I am supposed to use the above equation, but I don't know how to use it to solve for acceleration. Using g=9.8m/s^2 and the initial period, I solved for L and got 0.621m. Do I even need to do that for this problem? The fact that the problem said that "g" increased within the rocket is what confuses me the most. Am I solving for a new/increased value of "g" and using that as acceleration? If so, when I solved the problem this way, I got g=15.4 m/s^2 (using the second period and 0.621m as L), but this was incorrect.

I really need help with this problem as my teacher disabled the hints option. Thanks in advance.

How did you get 0.621? I got something different. Did you forget to square both sides of the equation at some point? There is a square root sign.

 

[rr263]

yeah you are right. i did do something qrong. i redid it and got 1.50

 

[Redbelly98]

1.50 m is correct. What do you get for the new g value using 1.50 m and the shorter period?

Note: this new g value is not the acceleration of the rocket.

 

[rr263]

Thanks. Sorry it took so long to respond I have been at work all day. Anyways, with using 1.50m as the length and the shorter period of 1.26 seconds, I get a new value of "g" as 37.3 m/s^2

 

[Redbelly98]

Sounds good. So, what must the rocket's acceleration be, to produce an apparent "g" of 37.3 m/s^2?

 

[rr263]

This is where I get stuck. I know that in order to accelerate, the rocket must overcome this new "g" value, but I don't know what equation I would use to figure out the rocket's acceleration.

 

[Redbelly98]

Okay. Well, for example:

If the rocket were not accelerating at all, the apparent g would just be the usual 9.8 m/s^2.

If the rocket accelerates at 1.0 m/s^2, the apparent "g" becomes 10.8 m/s^2.

etc.

 

[rr263]

I got it! Thank you so much! Wow I didn't think it could have been that easy! Thanks again!