PHYS 1401 - General Physics I

Centripetal Force

Leader: _____________________________ Recorder: ___________________________

Skeptic: _____________________________ Encourager: _________________________

Equipment

Rotational motion apparatus Stop Watch

Ruler or meter stick 2 x Mass sets, gram

Digital calipers Mass Hanger

Introduction

In this lab we will investigate uniform circular motion. In particular, we will investigate the net force, known as centripetal force, required whenever an object is constrained to move in a circle. By uniform circular motion, we mean motion at a constant speed.

Q1. If an object moves at a constant speed in a circle, does it accelerate? Explain.

Q2. If an object is accelerating, then does it have a net force acting on it? Explain.

We saw in class that for an object to move in a circle it must have an acceleration directed towards the center of the circle and with magnitude given by a_c = .

Q3. If the object has a mass m, write an expression for the net force on the object when moving in uniform circular motion.

We refer to the net force as the centripetal force. The centripetal force is not a fundamental force such as gravity. Instead, it is simply the result of some other force which constrains the object to move in a circle.

Q4. When a car goes around a curve on a flat road what force causes the car to follow the curve of the road?

Q5. If you ride on a carnival ride which goes in a circle, what force causes you to move in a circle?

In this experiment, you will measure the force on an object of known mass which is attached by a spring to a rotating shaft on a very low friction bearing. You will rotate the shaft at a constant speed. Because of the object’s inertia, it will appear to fly out. As it flies out, it will stretch a spring.

Q6. What exerts the force on the mass causing it to move in a circle? Explain.

Safety

There are a few safety points to consider in this lab.

1. You will be rapidly rotating a heavy mass. Please keep your face, hair, jewelry, and limbs away from the apparatus while turning.

2. Start and stop the apparatus slowly as rapid starts and stops can cause the apparatus to fall over.

Procedure

The apparatus for this experiment is shown in figure 1 below.

1. Set-up

To begin the experiment, disconnect the large black mass from the apparatus and measure the mass with the electronic balance.

mass = kg

Next, we will go through a procedure that will make the apparatus operate smoothly. Suspend the mass from the loop of pulley cord dangling from the support arm so that it lies 1 to 2 mm above the indicator rod. If necessary, loosen the nut on top of the mass and rotate the mass so that the hubs on the mass are aligned between the shaft and pulley. Be sure to tighten the nut again after doing this. Finally, make sure that the rotation shaft is vertical. Do this by rotating the support arm to several locations around the circle, steadying the arm and releasing it. If at each location the arm doesn't rotate, then the shaft is vertical. If not, adjust the height of the three support screws (loosen the nuts first, and tighten afterwards) in the base until the shaft doesn't rotate. Your apparatus should now be ready for the experiment.

2. Try the experiment without the spring

Q7. Prediction: If you disconnect the spring so that the mass hangs vertically, will the mass remain hanging vertically if you start spinning the shaft. Explain.

Disconnect the spring from the mass. Firmly hold the base and slowly spin the shaft so that the apparatus spins at a constant rate.

Q8. Did the mass remain vertical? Was your prediction correct?

Q9. Draw a free body diagram for the mass in this situation (while rotating).

Q10. In this situation, what provides the centripetal force causing the mass to move in a circle?

Q11. Use your answer to Q9 and Q10 to explain why the mass couldn't hang vertically in this situation.

Figure 1 Apparatus for determination of centripetal force.

3. Try the experiment with the spring.

Reattach the spring.

Q12. Prediction: If you connect the spring will you be able to spin the apparatus so that the mass will hang vertically. Explain.

Firmly hold down the base of the apparatus and rotate the shaft at different speeds to determine if you can make it hang vertically

Q13. Were you able to find a speed so that the mass hung vertically? Did this agree with your prediction?

Q14. Draw a free body diagram for this situation (while rotating) and use the free body diagram to explain why the mass could hang vertically in this situation, but not when the spring isn't attached.

4. Quantitative Data Collection

We will investigate quantitatively how well the result describes the net force in this situation. We have already measured the mass, but we still need to determine the velocity, radius and force acting on the mass.

Practice the Procedure

To conduct the experiment, firmly hold down the base of the apparatus and rotate the shaft until the bottom of the mass just passes over the indicator rod. Be careful not to hit yourself with the rotating mass. Also when starting and stopping the apparatus, do so gradually as the apparatus will tend to tip over if you attempt to start and stop it too rapidly. Continue twisting the shaft so that the mass stays directly over the indicator rod. When the mass stays over the indicator rod, it is moving at a constant speed in a circle.

Measure the radius

We will now measure the radius of the circle which we will use to determine the speed at which the mass is moving around the circle. If not already stopped, slow the mass to a stop by gently putting your finger on the shaft. Use the caliper to measure the diameter of the shaft and the indicator rod and measure the distance from the shaft to the indicator rod with a ruler or meter stick. The radius of the circle that the mass is moving around is then 1/2 diameter of the shaft plus 1/2 the diameter of the indicator rod plus the distance between the shaft and the indicator rod. Measure the distance between the rod and the shaft as accurately as possible with the meter stick (at least to the nearest mm) and using appropriate unit conversions determine the radius in meters.

r = ____________ m

Measure the Speed

We can calculate the speed of the mass simply from the formula v = .

Q15. Write an expression, in terms of the radius r, for the distance traveled by the mass once around a circle.

The time it takes for the mass to travel once around the circle is called the period and is usually denoted by the letter T.

Q16. Use your result for Q15 to write an expression for the speed of the mass in terms of r and T.

Your answer to Q16 suggests that we can determine the speed by measuring the radius and the time for 1 revolution – the period.

Q17. What experimental errors might be introduced by trying to time just one period?

Q18. How can you modify the timing procedure to lessen the effect of the errors you identified in Q17?

In Q18 you probably determined that you could improve the accuracy of the experiment by timing more than one revolution. In this case we will time 10 revolutions.

Rotate the shaft so that the mass passes over the indicator rod. Using a stopwatch, measure the time, t, it takes the mass to make ten rotations. The period then will be given by

t = _____________ s T = ____________________ s

5. Determine the Centripetal force from the acceleration

Q19. Copy your measured values from above into the table below. Don’t forget units.

Mass

radius

Period

Q20. Determine the speed of the mass v = 2πr/T = ______________________ m/s

Q21. Determine the centripetal force = ________________________ N

6. Measure the Force Directly

At this point we have determined the centripetal force by finding the acceleration and then multiplying by the mass. Now we will directly measure the force exerted by the spring that causes the mass to move in a circle.

Bring the mass to a rest and attach the mass hanger to the second hub on the mass with the s-hook. Drape the pulley cord over the pulley. As you place masses on the hanger the spring should stretch. Add mass to the hanger until the object is directly above the indicator rod.

Q22. Draw free body diagrams for the suspended object and the hanging mass in this situation.

Q23. Use the FBD for the suspended mass to show how the tension in the string compares to the weight of the hanging mass.

Q24. Use the FBD for the bob to find how the tension exerted by the horizontal string compares to the tension exerted by the spring.

Q25. Conclude how the tension in the spring is related to the weight of the hanging mass.

Q26. Record the suspended mass in units of kg, being sure to include the mass of the hanger.

Total mass suspended from hanger in kg: m_h = ___________________________ kg

Q27. Determine the weight of the suspended mass

F_HE = m_hg = __________________ N

Q28. Explain why the weight of the suspended mass is equal to the tension in the spring and thus is equal to the centripetal force.

Q29. Record the value of the centripetal force determined from the weight of the suspended mass: F_c = ______________________ N

Q30. Compare the two values you have determined for the centripetal force (Q29 and Q21) by finding the percent difference between them

% diff = |Q21 – Q29|/[.5 (Q21+Q29)] x 100 % =

Q31. How well do you feel that described the net force in this experiment? Explain.