centforc cp1.doc

CENTRIPETAL (unbalanced, inwardly directed) FORCE LAB

Name: ______

Partners: ______

Purpose:

To verify the relationship between centripetal force (net inward force), mass, and speed of a whirling object.

Introduction:

An object moving with changing speed in the same direction is undergoing acceleration. If an object moves with constant speed but in changing directions, it is also undergoing acceleration. (Remember acceleration is the rate of change in velocity and since velocity is a vector, it is comprised of both speed and direction.) Both types of acceleration require forces. A change in direction is called centripetal (center seeking) acceleration, and the force producing it is called centripetal force. The equation relating centripetal force, mass, and velocity is

F=ma, where a=v2/r for an object changing direction. So…

F = mv2/r

where F, is the sum of the unbalanced, inwardly-directed force, m is the mass of the moving object, v is its velocity, and r is the radius of the orbit of the object. In this experiment each of the factors in this equation will be varied as an object is whirled on the end of a string. Centripetal force will be supplied by the tension force of the weight of a mass tied to a string that passes through a vertical tube (see figure above). The effect of gravity on the whirling object is offset by the resulting angle of the string with the horizontal. Thus, r can be taken as the length of the string between the end of the tube and the object (even though the string is not perpendicular to the tube) without introducing a significant error.

Equipment:

  • Plastic tube, about 15 cm long and 1 cm in diameter
/
  • Several 2-hole rubber stoppers of different masses

  • Nylon cord, about 1.5 m long
/
  • Meter stick

  • Stopwatch, or clock with sweep second hand
/
  • Tape

Procedure:

  1. Fasten one end or the nylon cord securely to the #6 rubber stopper. Pass the other end through the plastic tube and fasten 100-g mass to it.
  2. Adjust the cord so that there is 1.0 m of cord between the top of the tube and the stopper.
  3. Attach a piece of tape to the cord just below the bottom of the tube. Support the suspended mass with one hand and hold the plastic tube in the other.
  4. Whirl the stopper by moving the tube in a circular motion. Slowly release the 100-g mass and adjust the speed of the stopper so that the piece of tape stays just below the bottom of the tube.
  5. Make several trial runs before recording any data.
  6. When you have learned how to keep the speed of the stopper and the position of the piece of tape relatively constant, you are ready to start collecting data.
  1. Group 1: Varying the force
  1. On your data table, write, “varying the force” in the first column.
  2. Using the apparatus you have already set up, have your lab partner measure the time required for 20 revolutions of the rubber stopper. Record this time in the data table for trial 1 as time.
  3. Find and record the mass of the stopper.
  4. Repeat the procedure for Trials 2-8. Keep the radius the same as in Trial 1 and use the same rubber stopper, but increase the mass at the end of the cord.
  5. Use a range of 50g –500g for your hanging mass.
  6. Record the hanging mass, time for 20 revolutions, radius and mass of the stopper for each trial.
  1. Group 2: Varying the Radius
  1. On your data table, write, “varying the radius” in the first column.
  2. For Trials 2-8 keep the same #6 rubber stopper and use a hanging mass of 100 g for each trial, but vary the radius of revolution.
  3. The radius for the 8 trials should range from about 0.3 m to about 1.5 m.
  4. Record the hanging mass, time for 20 revolutions, radius and mass of the stopper for each trial.
  1. Group 3: Varying the Mass
  1. On your data table, write, “varying the mass” in the first column.
  2. For Trials 2-8, keep the radius constant at 1.0 m and keep 100 g of mass at the end of the cord, but vary the mass of the rubber stopper.
  3. To get a wide range of mass for the stopper, you may wish to tie several stoppers together in order to increase the mass (be careful you don’t change the radius). Record the hanging mass, time for 20 revolutions, radius and mass of the stopper for each trial.

Data Table:

Data / Calculations
Trial # / Hanging Mass (kg) / Stopper Mass (kg) / Total Time
(s) / Radius (m) / Inward Force
(N) / Time Period (s) / Circumference (m) / Speed (m/s)
1
2
3
4
5
6
7
8

Analysis

Calculations:

  1. Calculate the weight of the hanging mass and enter it in the table as the centripetal force.
  2. Find the period of revolution by dividing the total time by the number of revolutions. Calculate the circumference of revolution from the radius (C=2r).
  3. Divide the circumference by the period to find the speed.

Show all calculations for Trial 1. Enter the results of the calculations for all trials in the appropriate spaces above.

Graphs:

The follow graphs will help explore the relationship between the centripetal force, speed and radius for an object undergoing constant circular motion. Plot the dependent variable (speed) on the y-axis and the independent variable on the x-axis.

Plot the following three graphs:

  1. Plot a graph centripetal force vs. speed of Trials 1-8 using the Group 1 data. Start the scale and graph at 0,0 since there would be zero inward force required for a stopper having a speed of 0 m/s.
  2. Plot a graph of radius vs. speed for Trials 1-8 using the Group 2 data. Again start the scale and graph at 0,0.
  3. Plot a graph of mass vs. speed for Trial 1-8 using the Group 3 data.

Questions, Analysis & Conclusions:

Answer in complete sentence and provide enough explanation (including data) to support your conclusions!

  1. On the basis of the centripetal force vs. speed graph, what is the relationship between the speed of a whirling object and the inward force exerted on it?
  2. On the basis of the radius vs. speed graph, what is the relationship between the radius of revolution and the speed of a whirling object?
  3. On the basis of the mass vs. speed graph, what is the relationship between the mass and speed of a whirling object?
  4. Re-graph centripetal force vs. speed2 and radius vs. speed2. What is the relationship between the radius of revolution and the speed of a whirling object? What is the relationship between centripetal force and speed of a whirling object?
  5. While traveling in your car, you go around a curved section of road at a constant speed. From where does this force come? If you went around the curve three times faster, what would happen to the amount of required force? Which lab trials show this relationship?
  6. While traveling in your car, you go around a curved section of road at a constant speed. If you went around a curve that is ¼ the radius, how would you have to change your speed in order to have same amount of force on your tires? Which lab trials show this relationship?
  7. You’re strong enough to spin a hammer at a certain speed at a fixed radius. If you increased the mass of the hammer by 16 times, how would you have to change your speed in order to keep it from flying off? Which lab trials show this relationship?