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Centripetal Experiment 10

INTRODUCTION

An object moves in a circle in many instances. Even if the object's (magnitude of the ) is constant, the velocity is changing because the direction of the is changing. The object is, therefore, being accelerated, and a force must act on the object to produce this . Such a force is called a centripetal force and is directed toward the center of the circle. The object of this experiment is to study and to understand how the various parameters affect centripetal and the subsequent acceleration. You will learn to apply Newton's second law of motion to circular motion when both tangential and centripetal are present.

THEORY

The centripetal acceleration ac of an object moving in a circle of radius r with speed v is given by ac = v2/r. (1)

This acceleration is directed toward the center of the circle. In accordance with Newton's second law of motion (F = ma), the magnitude of the centripetal force Fc which accelerates the m is given by 2 Fc = mv /r. (2)

If the object also has a applied, then it will experience a tangential acceleration at as well. This tangential acceleration results from a change in the tangential speed and is related to the α by at = α r. The centripetal acceleration and the tangential acceleration are perpendicular to one another and yield a total acceleration a given by 2 2 (1/2) a = [ac + at ] .

In this experiment, the centripetal force is provided by the attractive force Fmag between a magnet and a piece of magnetic material attached to a plastic block that is the accelerated mass M. The plastic block with the magnets inside it is locked down in a position that determines the radius of the circular motion the accelerated block having mass M undergoes. When the accelerated block gains sufficient speed v that the magnet can no longer hold it in place, mass M breaks away from the magnet and it moves out along the track until is strikes a stop at the end of the track. The equation that describes the circular motion of the block immediately before breaking away from the magnet is given by 2 Fmag = Mv /r. (3)

To perform the experiment, mass M (a block with added mass) is held in place by a magnetic force while everything is in equilibrium. The block is given an angular acceleration by applying a torque, which in turn increases its tangential speed v. When the product Mv2/r reaches the

Physics 1121 Experiment 10 Page 1 maximum centripetal force provided by the magnetic force, the block breaks away from the magnet and moves out along the track. This breakaway produces a “kink” in the graph of speed versus as shown in the graph at the top of the next page. The speed for which the breakaway occurs is labeled as vc. This 2 value of v is the value for which Mvc /r equaled Fmag, which may now be labeled as Fc. The difference between the slopes of the lines before and after breakaway occurs is a result of the change in the of of the system because of the motion of mass M. Figure 3.1

EXPERIMENT NO. 10

Before you become immersed in the details of the experiment, it is worthwhile to give you an overview of the entire procedure. Notice that four variables appear in Eq. (3): M, the mass being accelerated, v, the tangential speed of the mass, r, the radius of the circular motion, and Fmag, the maximum magnetic force providing the centripetal force. Our goal is to vary each of these parameters systemically and verify that Eq. (3) correctly describes circular motion to within experimental precision. You will use two different values for M and two different value of r, both to be specified by your instructor. The details of the process are given once, and you will repeat the process three to complete the table on page (to be filled in). The plastic block that holds the magnets is labeled with an A and a B on each end. The two magnets are inset into the plastic by slightly different amounts to produce slightly different forces, Fmag. Your instructor will tell you which end to place next to the accelerated block.

1. A sketch of the apparatus is shown to the right. Adjust the index mark on the accelerated mass M to the proper radius, as given by your instructor. Move the block containing the magnets next to M and lock the magnet holder block down with the wing nut.

2. Use the values for M and r given by your instructor and record them in the table on page 4. Figure 3.2

3. REVIEW THE SAFETY INSTRUCTIONS ON PAGES xi AND xii. These tracks will be moving quite fast, and it is important that you not get in their way while the experiment is in progress. To cause the tangential speed of the cart to increase, add mass (instructor provided) to the weight hanger that constitutes the falling mass and check to see that breakaway occurs before the falling mass reaches the bottom.

The timing disc has 30 holes. Calculate Δx for the radii that will be used.

Δx for radius 1 = ______m. Δx for radius 2 = ______m.

Physics 1121 Experiment 10 Page 2 4. Log in to the student account and, from the start menu, select the 1101 folder and Exp3.

In the Data window, you should see three headers: Time Between Bars, v# = # / dt, and v# = # / dt. Since the program cannot tell which radius is being used, it will calculate tangential for both radii. You will simply ignore the calculation that does not apply to each data set.

You will need only a few seconds of data. Launch the apparatus and click the Start button. About two seconds after breakaway, click the Stop button. The Data window should show Run # entries under each header.

5. To make a graph of your data, drag the desired Run # entry from the Data window to the Displays window and drop it on the Graph header. If you already have a graph open and wish to add a Run # entry to that window, drop the selected item on that specific Graph # entry instead of dropping on the Graph header.

The graph of the v## entry should look qualitatively like Figure 3.1. Before and after the kink, the data should approximate straight lines. We wish to find the value where the kink first becomes noticeable.

6. Choose the Smart Tool as instructed by your TA to find the value of vc.

Enter the value for vc in its correct location in the data table in Part 7.

Label the relevant features of the graph you used. List each member of the lab group, and print this graph for each member of the group.

Calculate Fc and the percent difference between Fc and Fmag.

Data Studio will allow you to keep many data sets active, but this can become quite confusing very quickly. Therefore, before going on to the next step, close all (tables and) graphs. In the main program menu select Experiment and Delete ALL Data Runs.

Physics 1121 Experiment 10 Page 3 7. Repeat Parts 3 – 6 until the table below is complete. You should obtain differences between Fmag and Fc of no more than 5 %. Please show all calculations in the below the table.

Fmag = ______Mass of accelerated block = ______m1 = ______m2 = ______Radius M (kg) v (m/s) v (m/s) F (N) % difference (r) (m) c c, ave c

Mass of accelerated block + m1 = ______r = _____ 1

Mass of accelerated block + m2 = ______

Mass of accelerated block + m1 = ______r = _____ 2

Mass of accelerated block + m2 = ______

Physics 1121 Experiment 10 Page 4 QUESTIONS

1. If the magnetic force were doubled, what critical velocity value would you measure, assuming the values for r and M in the first row of the table?

2. When you drive a car around a curve that is not banked, what force provides the centripetal acceleration? HINT: Think about turning a curve on ice. If the curve is banked, what additional force plays a role in providing the centripetal force? Draw force diagrams to clarify your thinking.

Physics 1121 Experiment 10 Page 5