Lab: Uniform Circular Motion

LAB: UNIFORM CIRCULAR MOTION

APPARATUS:

Centripetal Force Apparatus

Slotted Mass Set with Weight Hanger

Metric Ruler

Stop Watch

Triple Beam Balance

BACKGROUND:

The purpose of this experiment is to observe a rotating object, use circular motion equations to calculate the centripetal force acting on the object, and then attempt to measure the force directly by stretching the spring to the same length it had while spinning the hanging bob.

First, you will rotate the apparatus so that the hanging bob travels in a circle passing over the indicator rod (as shown above). Using the mass of the hanging bob, the period of revolution, and the radius of the circular path, you will calculate the centripetal force that should be required to keep the object (the hanging bob) in motion.

To check this value, you will try to measure the amount of force the spring exerts on the hanging bob while it is rotating. Since there is no gauge or meter showing the force exerted by the spring, you will measure the spring force by hanging weights over a pulley until the bob hangs at rest over the indicator rod (as shown in part 2). When the bob is in equilibrium, the weight hanging over the pulley will be equal to the spring force pulling back on the hanging bob.

PROCEDURE:

Part 1

1. Measure and record the mass of the rotating object (hanging bob). The triple-beam balance measures in grams, to the nearest tenth of a gram. You will need to convert the mass to kilograms before performing your calculations later in the lab.

2. Hang the object from the end of the support arm as shown in the diagram above, and attach the spring between the object and the central shaft. It is best if the object hangs vertically above the indicator rod at the height of the spring attachment before the spring is attached, so that the string is vertical and the spring is horizontal when stretched. Use the leveling screws (if necessary) to level the platform so that the object does not start rotating when released, and adjust the counterweight (if necessary) so that the support arm is roughly balanced over the central shaft.

3. Measure and record the radius of rotation from the center of the rotating shaft to the indicator rod. Your ruler measures in centimeters, but you will need to convert the radius to meters before performing the calculations below.

4. Rotate the shaft so that the hanging bob is rotating directly above the indicator rod. Record the time to make 50 revolutions, keeping the object above the indicator rod each time it passes. Repeat twice more for a total of three measurements, recording the time to make 50 revolutions for each trial and then averaging your three times together.

Part 2

Now, we will attempt to measure the actual force the spring exerts on the hanging bob while it rotates. Since we don’t have a gauge that shows the force being exerted by the spring, we have to do it by stretching the spring to the same length it had while the bob was rotating. We’ll keep the spring stretched by hanging weights over a pulley so that the bob hangs in equilibrium over the indicator rod. It is important for the string connecting the bob to the pulley to be horizontal so that the tension corresponds to the horizontal force that kept the bob in motion in Part 1.

5. Tie a line to the outer edge of the bob and tie the other end around a weight hanger. Drape the line over the pulley and add weights from the slotted mass set to the weight hanger until the spring stretches to the position shown above (with the bob directly above the indicator rod).

6. Make sure the string is horizontal, or as close to horizontal as possible, before it passes over the pulley. If necessary, adjust the height of the pulley so that the string pulling outward on the mass is completely horizontal.

7. Record the total mass hanging over the pulley, including the mass of the weight hanger itself, and convert this value to kilograms. Then, calculate the weight of the assembly hanging over the pulley. Since the weight hanger is in equilibrium, the total weight should be equal to the tension in the string, which will therefore match the spring force pulling inward on the bob. This force represents the measured centripetal force acting on the bob.

CALCULATIONS:

Finally, we will calculate the predicted centripetal force value based on the circular motion equations.

8. Using the data from step 4, calculate the period (in seconds) and frequency (in hertz) of the rotating object.

9. Calculate the linear speed of the object as it rotates (in meters per second).

10. Calculate the centripetal acceleration of the rotating object.

11. Calculate the centripetal force required to keep the object moving in a circular path. This represents the calculated centripetal force acting on the bob.

12. Now that you have two measures of the centripetal force acting on the bob—one measured directly by stretching the spring, and one calculated by observing the circular motion of the bob—calculate the percent difference between your two values. How well do your results support the theoretical relationship between centripetal force and circular motion?

Physics Formal Lab Report Information

GENERAL INTRODUCTION: A formal lab report is a technical document that focuses on three areas of scientific investigation. The three areas of focus include a Design Component, a Data Collection and Processing Component, and a Conclusion and Evaluation Component.

ü The Design Component includes a Title Page, Objectives, Materials, Experimental Setup Diagram, and Procedure Steps.

ü The Data Collection and Processing Component includes Measured Data, Calculations, Graphs, and Calculated Data.

ü The Conclusions and Evaluations Component includes the Summary/Conclusion.

Format issues to remember when doing a formal lab report.

§ This is a lab that someone could do to test your results. It should allow the reader to recreate your lab and compare their data to yours. All statements should be clear and concise.

§ Nothing should be hand written or drawn.

§ Only use the front side of paper. All pages of the body should be numbered at the bottom center or bottom right hand corner. The title page will not be numbered.

§ Each item in the body MUST be in the proper sequence. Starting a new page for each section is not required.

§ NOT putting things in the proper sequence or create tables is considered a major format error and up to eight points could be deducted from your grade. Failing to number pages would be a minor format error and up to five points could be deducted from your grade.

WRITE UP SEQUENCE: Each of the following make up the lab report and should be placed in the following sequence. The numbers in parentheses following each section indicate the point value for that particular portion of the overall formal lab report grade.

· TITLE PAGE. Include the title of lab, your name, date of lab, class/block, and names of your lab partners (typed smaller or different from your name) (5)

· BODY. Format (8)

o Objective(s): A written statement(s) describing the purpose of the lab. (4)

o Materials: A list of materials needed to complete the lab. (3)

o Experimental Setup Diagram(s)/Picture(s): A picture or diagram of the lab setup that can be used to clarify items or measurements. This lab needs two diagrams. One showing the apparatus with the parts labeled. The other should be a diagram of the apparatus during part 2 showing the forces along the string, spring and on the mass hanging (M). Reminder: It cannot be hand-drawn (10; 5 points each)

o Procedure Steps: A numbered or bulleted list of detailed steps to perform the lab. For any step that involves making a measurement or performing a calculation, the location of the recorded data or calculation in the report should be referenced. (10)

o Data: 2 Titled data tables with column headings

o Measured Data Table: contains ANY measurement completed in the lab with unit and the correct degree of precision based on the measuring device. (5)

o Calculated Data Table: contains ANY calculated number during the lab. Include what the number represents and a unit for the number. (5)

o Data Processing

o Calculations: Any calculation performed for the lab must be shown here. If an equation is used, the original equation must be included, as well as the substitution of numbers and answer in 3 or 4 significant digits with units. (20)

o Summary/Conclusion: A paragraph that includes the following three things:

1. A reference to the objective- Was the objective met? What numbers/reasons led you to the conclusion about the objective?

2. What possible errors could have occurred during the lab? If you state human error, be specific as to what the error is. Discuss the value of your percent difference calculation.

3. Are there any suggestions or improvements to the investigation process? (10)

o Additional Questions: You will need to include detailed responses to the following additional questions in your report. Reminder: Nothing should be hand-drawn. (20)

Additional Questions:

1. Using the “top view” diagram above, draw three separate vectors to represent the centripetal force, centripetal acceleration, and linear velocity of the rotating object at a single instant.

2. What is a centripetal force? During the lab, what provided the centripetal force acting on the rotating object? How do you know?

3. Does the centripetal force acting on the mass cause it to change speeds? Explain.

4. Sketch a “side view” free-body diagram showing all forces acting on the rotating object as it passes over the indicator rod in Part 1 of the experiment. Are the forces on the object balanced or unbalanced during this part of the experiment?

5. Sketch a “side view” free-body diagram showing all forces acting on the object as it hangs over the indicator rod in Part 2 of the experiment. Are the forces on the object balanced or unbalanced during this part of the experiment?

6. Explain the relationship between the measured and calculated values of centripetal force you obtained in this experiment. Should they be equal in magnitude? Why or why not?

7. For an object moving in a circular path:

(a) How does radius affect the centripetal force?

(b) How does velocity affect the centripetal force?

(d) If the mass and the radius are held constant and the period (T) is reduced to 1/2 of its original value, how much does the centripetal force change from its original value? Explain your answer.