Lab 6 - This is lab 6, Rotational Kinetic Energy. PDF

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This is lab 6, Rotational Kinetic Energy....

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Introduction: The goal of this lab was to understand the rotational properties, such as understand the concept of angular velocity, inertia movement and also the rotational kinetic energy. In addition, the goal of this lab was to get familiar with and analyze the rotational and translational motion of energy systems. Apparatus: PASCO interface in the computer, PASCO capstone software in the computer, rotary motion sensor, pulley, ring stand, masses, string, disk and meter stick. Procedure: Part I: ● Make sure to examine the steps in order to see how the mass of hanging is from the sting that will pass over the pulley which attaches to a rotary motion sensor with a large disk. ● Test to see if everything is working okay, check the whole setup. ● Turn on the PASCO on the computer and set up the system ready ● Make a table and graph display of the angular velocity ● Wind up the string on the medium pulley. ● Measure and record the height ● After the mass has hit its low point stop data collection. ● Measure and record the height of the bottom of hanging mass ● Measure the radius radius of the medium pulley wheel on the motion sensor. ● Take data for at least two more runs as did before. Part II: ● Use your measured values to calculate the initial potential energy. ● For each of the runs, compare the initial total energy to the final energy and determine the percent difference between the two. ● Calculate the Max_speed of hanging mass (m/s), Kinetic energy of hanging mass (kg), Rotational energy of hanging mass (J), Potential energy of hanging mass (J), Percentage of difference % Precautions: To make this experiment better, we can try to prevent the sources of errors to improve the results of the experiment. In order to make it better measure the mass carefully and measure the height very precisely etc.

Source of errors: The possible sources of errors can be the uncertainty of the instruments of measurement: the scale to measure the mass; the chronometer that is used by the system to measure the time to get the speed, the ruler used to measure the height. Data:

Table 1: Radius of medium pulley

0.025

Radius of disk (m)

0.062

Mass of disk (kg)

0.347

Mass of hanging mass (kg)

0.1

H_top (m)

0.31

H_bottom (m)

0

Table 2: Run 1

Run 2

Run 3

Max_angular velocity (rad/s)

27.46

25.25

27.75

Max_speed of hanging mass (m/s)

0.6865

0.63125

0.69375

Kinetic energy of hanging mass (kg)

0.0235641125

0.019923828

0.024064

Rotational energy of disk (J)

0.2514513249

0.212606054

0.25679

Potential energy of hanging mass (J)

0.3038

0.3038

0.3038

Table 3: Potential energy of hanging mass (J)

Initial total energy (J)

Kinetic energy of hanging mass (J)

Rotational energy of disk (J)

Final total energy (J)

Percentage of difference

Run 1

0.3038

0.3038

0.0235641125

0.2514513249

0.2746

9.61158657

Run 2

0.3038

0.3038

0.019923828

0.212606054

0.2329

23.33772219

Run 3

0.3038

0.3038

0.024064

0.25679

0.2811

7.472021066

Calculations: Sample calculation for run 1: ● Max angular velocity obtained from capstone.

● Max_speed of hanging mass (m/s)= max angular velocity* radius of medium pulley Max_speed of hanging mass (m/s)=27.46*0.025=0.6865 ● Kinetic energy of hanging mass (kg)=0.5*mass of hanging mass*(max_speeed of hanging mass)2 = 0.5*(0.1)*(0.6865)2 =0.0235641125 ● Rotational energy of hanging mass (J)=0.25*mass of disk*(radius of disk)2 (max_angular velocity)2 = 0.25*(0.347)(0.062)2 (27.46)2 =0.2514513249 ● Potential energy of hanging mass (J)=mass of hanging mass*9.8*(h_top − h_bottom) Potential energy of hanging mass (J)=(0.1)(9.8)(0.31 − 0)=0.3038 ● Percentage of difference % potential energy of hanging mass−(kinetic energy of hanging mass+rotational energy of disk) = potential energy of hanging mass (0.3038)−(0.0235641125+0.2514513249) = (0.3038)

9.61158657

Questions: 1. The rotary motion sensor measures the angular velocity of the axle passing through it. However, we will need the angular velocity of the disk, how can we find the angular velocity of the disk given the angular velocity of the axle? If the disk is mounted on the axle and both are rotating, they must be rotating at same angular velocity, if the disk is resting on the axle and both are spinning together, their angular velocities should also be the same. 2. Determine a conservation of energy equation that compares the total energy of the system at when it is at rest with the hanging mass at its maximum height to the total energy of the system when the mass is at its lowest point. Write your equation in terms of measurable quantities (, etc). Define the lowest point of the hanging mass as = 0. Use the equation for given above. If necessary, check your textbook for the rotational kinetic energy equation and any other relevant equations. Double check your equation with your instructor before you continue. Initial=mgh, Initial=m(9.8)(0.31)=0.3038 Final=½*Idisk*⍵^2+1/2Iring*⍵^2 because we calculate the rotational energy as ½*inertia*angular velocity Final=½(1/2mr^2)(⍵)^2+1/2mr^2(⍵)^2 Final=½(½*0.1*(0.062)^2)(26.82)^2+½(0.1)(0.025)^2(26.82)^2 Final=0.0916044341 According to these calculations and results the initial velocity is larger than the final velocity this can be due to some energy being lost as heat, not all the potential energy turned into kinetic energy instead, some energy dissipated as heat.

3. Did energy appear to be conserved in your experiment? Support your answer with your data. The energy appear to be somewhat conserved in our experiment, looking at run 1 the initial energy is 0.3038 and final energy is 0.2746, and the percent deviation turned out to be 9.6% which means some of the kinetic energy was lost and not all was conserved. 4. Was there a consistent trend to your runs when comparing the calculated initial energy to the calculated final energy (e.g. was the initial energy always higher)? Yes, there was a consistent trend to our runs when comparing the calculated initial energy to the calculated final energy, and yes the initial energy was alway higher than the final energy.

5. What sources of error are present when limiting our analysis to the rotational kinetic energy of the large disk, and the PE and KEt of the hanging mass? The possible sources of errors can be the uncertainty of the instruments of measurement: the scale to measure the mass; the chronometer that is used by the system to measure the time to get the speed, the ruler used to measure the height. 6. Is it likely that you could reduce the percent difference between your initial and final energy values by considering the rotational kinetic energy of the axle and pulley of the rotary motion sensor? Support your answer mathematically with a rough estimate If we consider the mass of the pulley and axle to be less than half that of the hanging mass that is, the hanging mass is 0.1 and if we consider the pulley and axle to be 0.05 and we do the calculation for rotational kinetic energy (using exactly the same values for rotational speed) we get a kinetic energy of 0.036.

Results and discussion: The goal of this lab was to understand the rotational properties, such as understand the concept of angular velocity, inertia movement and also the rotational kinetic energy. In addition, the goal of this lab was to get familiar with and analyze the rotational and translational motion of energy systems. Overall, our data was close to what was expected and that can be seen by looking at the data and the percent difference above, that some of the kinetic energy was lost and not all was conserved. The Percent of difference that we got could be due to the sources of errors:the uncertainty of the instruments of measurement: the scale to measure the mass; the chronometer that is used by the system to measure the time to get the speed, the ruler used to measure the height, the errors could be eliminated in the future to get better results in the future. In addition, the initial energy was always larger than the final energy according to our data which can be seen in all the runs but looking at run 1 we got the initial energy to be 0.3038 and final energy to be 0.2746, which tell us that the initial stayed larger than final energy which is what was expected....