Circular Motion: Centripetal Force and Acceleration Experiment 3

Home , Centripetal force, Circular motion

NAME ______LAB PARTNERS ______

Station Number ______

INTRODUCTION

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

THEORY

The centripetal acceleration ac of an object moving in a circle of radius r with speed v is given by . 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 mass m is

. 2

If the object also has a torque 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 angular acceleration  by at =  r. The centripetal acceleration and the tangential acceleration are / perpendicular to one another and yield a total acceleration a given by .

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

. 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 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 time as shown in the graph to the right. The speed 2 for which the breakaway occurs is labeled as vc. This value of v is the value for which Mvc /r equals 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 moment of inertia of the system because the position of mass M changes.

EXPERIMENT NO. 3

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 ex- perimental precision. You will use two different values for M and two different values of r, both to be specified by your instructor. The details of the process are given once, and you will repeat the process three times to complete the table on page 16. The plastic block that holds the magnets is labeled with an A on one end and a B on the other. 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 to you by your instructor and record these valules on page 16.

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 it lowest position.

The timing disc has 30 holes. This means that the disk is divided into 30 equal parts. Calculate x for the radii that will be used and show your work below.

x for radius 1 = ______cm. x for radius 2 = ______cm.

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 Time Between Bands, and three different values for speeds. Since the program cannot tell which radius is being used, it will calculate tangential speeds for all three 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. Repeat this process five times.

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 the top figure on page 14. 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 % difference between the largest value of Fc and Fc, ave and insert this value in the % difference column.

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.

7. Repeat Parts 4 – 6 until the table below is complete. Show your calculations in the space below the table.

Mass of accelerated block = ______m1 = ______m2 = ______Radius M (kg) vc (m/s) Fc (N) Fc, ave (N) % difference (r) (m)

Mass of accelerated block + m1 = ______r1= _____

Mass of accelerated block + m2 = ______

Mass of accelerated block + m1 = ______r2= _____

Mass of accelerated block + m2 = ______

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.