How Do You Calculate the Time for a Mass to Fall Using Moment of Inertia?

[jago-k1]

Homework Statement

How long does it take for the hanging mass to fall the same distance 31.5 cm?
I don't know how to solve for T with everything I have. Help please.

Homework Equations

mgh=(1/2)I(2h/tr)2 + (1/2)m(2h/t)2

The Attempt at a Solution

Okay, previous questions are[All correct]
1.
Two masses of 150. g are suspended from a massless rod at a distance of 9.0 cm from the center. What is the moment of inertial of the two-mass system about the center of the rod?

I=m1*R^2
since they are two masses that weigh the same
I= 2(.15kg)(.09m)^2=2.43E-03 Correct


2.
If the masses rotate with an angular velocity of 2.45 rad/s, what is the rotational kinetic energy of the system?

KEr=(1/2)Iw^2 = (2.43E-03 )(2.45 rad/s)^2 = 7.29E-03 J Correct


3.
Consider the setup shown in the lab manual but with the large masses removed from the support rod. If the hanging mass is 100. g and drops a distance 31.5 cm in a time of 6.1 s, what is the moment of inertia of the support rod and shaft? The radius of the shaft is 0.50 cm.

I=mr^2(gt^2/2h - 1) = 1.446E-03 kg m^2 Correct


4.
Now two masses each of 200 g are placed on the rod at a distance of 11.0 cm from the point of rotation. What is the TOTAL moment of inertia of the masses plus rod and shaft?
Yes, Computer gets: 6.286E-03 kg m^2

I=2MR^2+Io is what you get from #3
I=2(.2kg)(.11m)^2 + Io = 6.286E-03 kg m^2 Correct

 

[jago-k1]

BUMP if anyone can help out.

 

[ogb p]

First, it's great that you are actively trying to solve your homework problems. As a scientist, it's important to approach problems with curiosity and a willingness to try new things.

To solve for the time it takes for the hanging mass to fall a distance of 31.5 cm, we can use the equation for gravitational potential energy: mgh = (1/2)I(2h/t)^2, where m is the mass of the hanging object, g is the acceleration due to gravity, h is the distance fallen, and t is the time it takes to fall that distance.

Since we know the values for m, g, and h, we can rearrange the equation to solve for t: t = √(2h/mg). Plugging in the values, t = √(2*0.315 m)/(0.1 kg*9.8 m/s^2) ≈ 0.8 seconds.

I hope this helps! Remember to always show your work and double check your units to ensure you get the correct answer. Keep up the good work!