Procedure: Take the rotating table and remove both the ring and the disk. Take a

Question

Procedure: Take the rotating table and remove both the ring and the disk. Take a piece of string and wrap it around the axle once. Measure the length of the string to find the circumference. uem Tie the end of the string around a hook on the axle and wind the string around it. Thread the string though the pulleys as seen in the setup in the front of the room. Place 200 g on the end of the string and the disk and ring on the rotating table. Raise the mass to a height and measure. 74c m Release the mass and measure the time it takes to reach the ground. If the string runs out before hitting the ground, adjust the string length or pulleys Repeat for 350, 500, and 650 g. . · . · . Analysis: Calculate the axle radius From the height and time, calculate the acceleration of the falling mass. . .7 What is the acceleration of the string tangent to the axle? Explain. .Calculate the angular acceleration of the axle from the tangent acceleration. oc, , , , Draw a free body diagram of the falling mass. Using the free body diagram, calculate the tension in the string. Draw a free body diagram of the axle (as seen from above). On the diagram, draw the force, the radius, and the angle. Using the free body diagram, calculate the torque on the axle. Plot torque (y-axis) vs angular acceleration (x-axis) with a trendline. What is the slope? According to the theoretical equation, what does the slope represent? From the height, calculate the potential energy of the mass. From the height and time, calculate the final velocity of the mass. What is the velocity of the string tangent to the axle? Explain. Calculate the angular velocity of the axle from the tangent velocity Calculate the kinetic energy of the mass. From the spin time, calculate the angular velocity of the rotating table. Calculate the kinetic energy of the rotating table. .

Explanation / Answer

Hello,

You have not provided the complete data like diagram and experimental setup. However, From the the analysis part, I can help you solve the second table.

Let's start from Potential energy U, It is given as U = m*g*h where m is the mass, g is the gravity and h is the height of the mass from the datum. If this is your string height, then just put string height in place of h and solve for U.

Next is velocity of falling mass. For this you can use the kinematics equation,

V2 - u2 = 2*a*h where V is the final velocity which you need to calculate, u will most probably be zero, h is the height you used while calculating the acceleration of falling mass and a is the acceleration of falling mass.

KL can then be calculated using 0.5*m*V2 where V is the velcoity you just calculated and m is mass (falling mass)

Then to find KR , You need to use 0.5*I*w2 where I is the moment of inertia of rotating table which is given as 0.003. w is the angular velocity of rotating table which you can find by using your spin time which you didn't provide.  

One more thing, you can always use the rotational kinematics equation to find unkown. You might be know three linear kinematics equation. Rotation kinematics equations are same

w = wo + a*t

w2 - w2o = 2*a*h ....remember here a is the angular acceleration. wo will be zero as you must have started from rest.

Important - the relation between angular velocity (w) and tangential velocity (v) is

v = r*w where r is the radius of object.

If you have any doubt, please let me know.

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