Experiment 1G Uniform Circular Motion



Experiment 7: Uniform Circular Motion

Purpose

1) to study uniform circular motion

2) to study centripetal force

Apparatus

centripetal force apparatus, a timer, a ruler, slotted weights, equal-arm balance

[pic]

Fig. 1. Centripetal Force Apparatus: Fig. 2. Centripetal Force Apparatus:

Static Test in Operation

Theoretical Summary

Centripetal Force

In this experiment, you will spin a bob around a rotating shaft in uniform circular motion.

An object in uniform circular motion moves in a circle at a constant speed by a force directed towards the center of the circle (a centripetal force). The formula for centripetal force Fc is

Fc = m v2 where m = mass of the rotating object

r v = speed of the object

r = radius of the circle

We can find an equation for the velocity v

[pic] v = ∆x

∆t

by calculating the distance and time for one revolution. The distance is the circumference of the circle 2πr and the time is the period of revolution T. So:

v = 2πr

T

By substituting this for v in the equation for centripetal force, we arrive at formula (1):

| (1) |Fc = 4 π2 • m • r |

| |T2 |

Static Test of the Centripetal Force

Consider the bob hanging from the crossarm with the stretched spring and a cord with suspended weights attached to it as in Figure 1. The horizontal forces on the bob are provided by the spring and the tension in the spring due to the suspended weights. If the bob is not moving, we know that the net force is zero and the two horizontal forces are equal. The force exerted by the spring equals the force of gravity on the weights.

This gives us another technique for finding the centripetal force. The centripetal force in our experiment is provided by the spring that holds the bob to the rotating shaft. The force of a spring depends on the force constant of the individual spring and the distance it is stretched. If we stretch the spring the same distance it is stretched during the rotation, the force exerted by the spring will be the same as the centripetal force.

Procedure Part Ia. Static test of the steel spring.

(a) Detach the bob and record its mass Mbob. Clamp the pointer rod in some

intermediate position of your choice. Measure the distance from the middle of the

rotating shaft to the pointer rod to 0.1 cm accuracy, and record it as r1.

(b) Hang the bob exactly above the tip of pointer, by making two adjustments:

(i) move the crossarm horizontally (use its clamp)

(ii) raise or lower the bob by changing the length of string (by wrapping

it around its cleat).

As accurately as your eye can see, the tip of the bob and the pointer should be

within two millimeters of each other.

(c) Attach the steel spring and the cord to the bob. Pass the cord over the pulley and

load the hanger so that the bob is again exactly above the tip of the pointer (see

Figure 1). Record the total hanging mass as Mhanging1.

Remember: This static test allows you to measure the force exerted by the steel spring on the bob.

Procedure Part Ib. Uniform Circular Motion. Basic Runs.

(d) Remove the hanger and secure its cord by winding it around the bob. Practice

rotating the knurled section of the shaft with your fingers as shown in Figure 2 until you are able to maintain uniform circular motion, with the bob passing exactly over the pointer at every revolution as best you can. You can place a cardboard screen behind the bob for easier viewing if you wish.

(e) Determine the time TN it takes to complete N revolutions. Make three runs, with

N=50, 70, and 90 revolutions. Record TN for every run. ( You will need to continue

rotating with your fingers as you check the time.)

Suggestion: Check the value of T = TN / N from all three runs, to verify that they are consistent.

Procedure Part II. Changing the Radius.

(f) Repeat the steps (a) through (e) with two markedly different positions of the pointer. Label your new values by r2 and Mhanging2, and r3 and Mhanging3.

Important: Do not forget to adjust the cross-arm each time!

Procedure Part III. Changing the Mass.

(g) Add 50 to 100 grams to the mass of the bob using slotted weights. Record the

new mass as Mbob′. Repeat steps (a) through (e), recording the hanging mass in the

static test as Mhanging′. (Use your last radius r3 in this part.)

Lab Report

Part I.

(1) Calculate the average value of T = TN / N from your three runs. Using formula (1),

calculate Fc in newtons, rounding-off its value to three significant digits.

(2) From the static test, Using your value, calculate the tension in the cord

Mhanging1 ( g = Fstatic. Display the % difference δ between Fc and

Fstatic, that is

δ = Fc – Fstatic x 100%

Fstatic

Part II.

(3) Calculate the following using data from Parts I and II and fill out Table A:

|TABLE A: CHANGING THE RADIUS |

|Source of Data |r | | |Fstatic |δ |

| |(meters) |(sec)[pic] |Fc |(Newtons) |(%) |

| | | |(Newtons) | | |

|Part I | | | | | |

| Part II [pic] | | | | | |

| | | | | | |

Part III.

(4) Calculate the following using data from Parts II and III at r = r3and fill out Table B:

|TABLE B: CHANGING THE MASS |

|Source of Data |Mbob |r3 | | |Fstatic |δ |

| |(kg) |(meters) |(sec)[pic] |Fc |(Newtons) |(%) |

| | | | |(Newtons) | | |

|Part II Run 2 | | | | | | |

| Part III | | | | | | |

(5) Question #1: Explain why both values of F in Table B should theoretically

be equal while this is not true for the values of F in Table A.

(6) Question #2: To find Fc by Formula (1) you had to measure:

(i) masses. (ii) distances. (iii) time-intervals.

Estimate the expected % uncertainties in each of these three kinds of measurements

considering the apparatus you have used and the range of values you had.

Give objective reasons for your estimates.

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