Lab 4 - PHY 207-lab4 PDF

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Physics 207

Lab #4- Centripetal Motion

Introduction:

The objective of this lab is to study and understand centripetal force and learn how to calculate it. Also, to learn about the accepted value of the centripetal force and how to calculate it. It is important to learn about centripetal force because it is one of the important forces that we often deal with. The centripetal force is the force that keeps objects rotating in an orbit. We deal with many rotating objects in our everyday life, and therefore understanding what the centripetal force is and how it works is essential. The expected result of this lab is to experimentally find the value of the centripetal force through the equations and using the measured value of the radius and the speed and find the accepted value of the centripetal force. Also, getting close values for the experimented and accepted centripetal force is expected. We were able to measure the radius and the speed and calculate the centripetal force and get a value that is within the uncertainty of the actual value.

Procedure:

First, we leveled the base to make sure that it is not on an angle, and therefore there will be no y-component from the tension in the string and have only gravitational force acting in the y-axis. This is important because it reduces the number of forces involving in the experiment. That also reduces the number of calculations that have to be made, and therefore there would be less sources of error.

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Secondly, we adjusted the length of the needle, so that the bob reaches it when it is disconnected from the spring. Then, we measured the value of the centripetal force experimentally. We calculated the value of the centripetal force experimentally through the use of the equation, Fc =mac=m*v2/r. To calculate the centripetal force using that equation we need to find the mass of the bob, the radius in which the bob rotates around, and the speed at which the bob is rotating. To get the length of the radius, we measured the distance between the needle and the pole. Since the spring stretches and compresses, so we measure the distance between the needle and the pole to serve as the average radius throughout the rotation.

Following, we calculated the velocity of the bob by recording the time it takes for the bob to complete 5 complete periods. Using that time, the 5 revolutions by the total time to get the time per revolution of the bob. To calculate velocity, use the following formula V= (2*π*r)/t. Finally, we used the electric scale to obtain the mass of the of the bob. To calculate the experimental value of the centripetal acceleration, use the values recorded and plug in the formula Fc = m*v2/r.

Finally, to find the real centripetal force, add mass to the other side of the spring until the bob reaches the needle and record that mass. Use the following formula, Fc =mg, to calculate the real centripetal force. Then, compare the experimental value and the real value of the centripetal force to see if the experimental value is within the uncertainty of the accepted value.

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Data:

Experimented centripetal force

Mass of the bob = 0.4448 kg

Radius = 0.168 m

Total time for 5 revolutions = 4.3 seconds

Time per revolution = 1.163 seconds

Velocity = 0.908 m/s

Centripetal force = 2.183 N

Accepted Centripetal Force

Mass added to the other end of the pole = 0.240 kg

Centripetal force = (0.240) * (9.8) = 2.35 N

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Sample calculations: 

To convert the radius from centimeters to meters use the following formula, radius (m) = radius (cm)/100. Radius (m) = 16.8cm/100 = 0.168 m.



To calculate time per revolution from the total time use the following formula, time per revolution = total number of revolutions / total time. Time per revolution = 5/4.3 = 1.163 s.

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To calculate the velocity of the bob, use the following formula, V= (2*π*r)/t. V= (2*π*0.168)/1.163 = 0.908 m/s.



To calculate the experimented value of the centripetal force, use the following equation, Fc = m(v2/r). Fc = 0.4448(0.908^2/0.168) = 2.183 N.

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To convert mass from grams to kilograms use the following equation, mass = g/1000. Mass = 240/1000 = 0.240 kg.



To calculate the value of the real centripetal force, use the following equation, Fc = mg. Fc = (0.240) (9.8) = 2.35 N.

Questions:

1. What is the centripetal force pulling the bob towards the center?

The centripetal force is the force that keeps the bob in circular motion. If the centripetal force was eliminated, the bob would leave the orbit motion and change to a straight motion away from the center of the orbit. In the case of the bob, the centripetal force is the force of tension in the string that keeps the bob in circular motion. Also, the centripetal acceleration, which is a component in the centripetal force, is always directed towards the center. The centripetal force

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we calculated experimentally is equal to 2.183 N, and the accepted value of centripetal force is 2.35 N.

2. How will you measure the Fc? In the lab we measured the experimented value of centripetal force and the accepted value of centripetal force. To measure Fc experimentally, we measured the radius from the pole to the needle with a ruler. Then, we weighted the bob on a scale and recorded its mass. Following, we found the velocity of the bob by timing 5 revolutions and calculating the time per revolution, and found velocity by using the equation, V= (2*π*r)/t to be 0.908 m/s. Finally, we were able to find the experimented value of the centripetal force by using the equation, Fc = m(v2/r). We found the experimented centripetal force to be 2.183 N. To calculate the accepted centripetal force, we attached a rope to the bob and added mass to the other end of the rope and continued on adding weight until the bob reached exactly vertically above the needle. Then, we found the accepted centripetal force, through the equation Fc = mg, to be 2.35 N.

3. Where is the center of the circle that the bob is traveling around?

The center of the circle that the bob is traveling around is the pole in which the string, attached to the bob, is attached to.

4. How will you measure r?

The string stretches and shrinks throughout the bob’s motion. Therefore, we made the measurement of the radius as the distance between the pole and the needle since the bob reaches

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the needle when it is unattached to the spring. The needle also acts as an average radius to the different distances the bob covers when it stretches and shrinks. Also, the needle successfully served as the radius because the bob was rotating at that radius throughout its motion.

5. How will you measure v?

To measure velocity, we used two components which are the number of revolutions and the total time. We chose to record the total time it takes for the bob to complete 5 full revolutions. We got the bob to rotate at a radius as close to the distance between the needle and the pole as possible, so the radius is almost exact. Then, we started timing when the bob was released and stopped exactly when the bob completed the fifth revolution. We wrote down the radius, the time, and the number of revolutions and used the following equation to find velocity, V= (2*π*r)/t. By timing 5 revolution instead of 1 we decreased the sources of error that is due to human delay in starting and stopping the timer.

6. Can making multiple measurements help?

Yes, making multiple measurements help in minimizing the error. For example, when measuring the radius, if the radius was measured multiple time that would reduce any sources of error that might occur when measuring the radius. Also, when finding the time per revolution, it is so important to measure the time for multiple revolutions and then divide the number of revolutions by the total time. That decreased the error in human response in starting and stopping the stop watch. Also, repeating the experiment at a different radius and velocity is helpful to make sure

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that the equations and measurements are accurate, and therefore the final result is accurate for centripetal force.

Conclusion

The result of that we got for the value of the centripetal force experimentally was within the uncertainty of the actual result. Many factors affected the outcome of our experiment. One of them is the condition of the instrument. The pole, in which the bob was connected to, was slightly moving. That affected the accuracy or our final result that we calculated for the velocity of the bob, and therefore affected our result for centripetal force. Also, the rope that we used to attach to the bob and add masses on the other end of it to obtain the accepted value of centripetal force were multiple ropes tied together to form one rope that was used in the experiment, which affected the tension in the cord and slightly changed our calculations. Finally, for the sources of error, is the angle involved with the base. We made sure that the base is leveled to avoid any forces acting in the y-direction other than the force of gravity and the normal force that have no effect on the movement. However, there is always a chance that the base is not perfectly leveled and therefore affect our calculations. To improve these factors next time, we could use instruments that are in a better condition. Therefore, we make sure that the tension is as close to exact as possible, and that the pole movement doesn’t involve and affect the results. Also, to avoid the error in tension, we can use a rope that is not made of multiple ropes tied up to make sure of the accuracy of the tension. Finally, we can use leveling instruments to make sure that the base is leveled. That way we can avoid all the sources of error that affected our final result and be able to come up with an experimental value closer to the accepted value. We learned in this lab how to experimentally find the value of the centripetal force with measuring the radius and

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calculating the velocity of the bob. Also, we learned how to find the accepted value of the centripetal force and compare it to the experimented value.

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