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LAB: UNIFORM CIRCULAR MOTION

Step 4: Change the number of washers (add or remove 2 each time) to change the balancing force (centripetal force). Since Fc = (4 Π² r m) / T² (see Equ4), by changing Fw (weight of the washers), the period and the radius should change. Remove the paper clip and repeat step3. First get a feeling of what the radius should be and the speed in order for the stopper not to move in or out the tube. Then place the clip back to check your expertise.

Record the data in row 2 of TABLE2. Each group’s member should try. Record the average time T. You should get about the same radius.

Step5: Repeat step 4 for trial 3 and 4 (if enough washers).

Step6: According to Equ4 : Fc = (4 Π² r m) / T² . Compute Fc for each trial and record the value in the TABLE1. Each member of the group should do her/his own computation. Check with the others at the end.

ANALYSIS

1) Fw is the accepted value for the centripetal force. Fc is the experimental value based on your expertise in finding r and T for a given mass m (stopper). Calculate the experimental error for each trial of this experiment : (Fc - Fw) / Fw x 100

Trial 1 : ______________ Trial 2: ___________________

Trial 3: _______________ Trial 4: __________________

2) Can you explain those experimental errors ? Are the errors tend to increase as you add more washers ? As you increase the mass of washers, the speed of the stopper will increase too to balance it.

3) What did you learn ? Was the purpose accomplish ?

PLEASE FILL THE BLANKS/ THIS IS AN INDIVIDUAL WORK.

A BLANK NOT FILLED = -5%. TRY TO BE NEAT. LABEL YOUR GRAPH.

PURPOSE

To get a better understanding of the centripetal force that keeps an object into a circular path. You will compute the centripetal force using the formula derived from Newton’s laws (Fc = m ac) and you will compare it to its try value.

DISCUSSION

Consider an object moving in circle at a constant speed (like a car in a circuit).

In 10th grade you learnt the first law of Newton:

If there is no net force acting on a moving object of mass m:

The object will keep moving at a __________ speed but in the same _______________.

If the car moves in circle, its direction changes. So there is a net force acting on it. This force is called the centripetal force.

Equ1 Fc = _________. (see chapter) r is the radius of the circle,

V the speed of the object and m its mass.

This force pulls the object out of a straight-line path and into a circular path.

The distance around a circle (perimeter) is

Equ2 d = ____________. (use r the radius).

Let’s call T the time required for one complete revolution. (the time for the object to go around once). The speed of the object moving in a circular path at a constant speed is:

Equ3 V = ______________ (use Equ2 , use r and T to write the expression )

Plug Equ3 into Equ1 to find another expression for Fc. Use r, m and, T.

Equ4 Fc = __________________________

This is the relationship between the centripetal force Fc, the mass m of the object in circular motion, the radius r of the circle, and the time T for one complete revolution.

In this lab you will compute the centripetal force using Equ4 (using m and T) and compare it to the true value. You will discuss the % error between the true Fc and its calculated value.

PROCEDURE

Step1: The equipment setup for this experiment consists of weights (washers) attached to a string, and a rubber stopper that swings in a horizontal circle (see figure). You will swing the stopper in circle and adjust the speed so that the stopper does not have a tendency to move in or out (constant speed), thus balancing the centripetal force Fc on the stopper with the balancing force weight of the washers. So the weight of the washer Fw is the centripetal force that keeps the stopper in an uniform circular motion.

GUYS, GIVE ME A BREAK. DON’T USE THE MATERIAL AS WEAPONS.

You will leave the class if you do so. Please clean up before you leave.

Step2: Place some washers on the string and practice rotating the stopper by rotating the stopper by placing a finger next to the string, then moving your hand in a circular motion. You want to move the stopper at a constant speed such as the washers are not moving up or down. A paper clip or alligator clip placed on the string below the tube will help you maintain a consistent motion by providing a point of reference as well as helping with length measurements.

Be careful of the moving stopper so it does not hit you in the head.

Step 3: After you have learned to move the stopper with a constant motion in a horizontal plane, you are ready to take measurements. In the TABLE 1, record the following:

r: The distance from the string at the top of the tube to the center of the stopper. r is the radius of the circle of rotation.

m : the mass of the stopper determined with a balance.

Fw: the balancing force (that produced the centripetal force). Fw is determined from the mass of the washers M times g (Fw = M g) . To find M, find the mass of 1 washer using a balance (Chemistry lab). Then multiply by the number of washers used to get M.

You have to understand that Fw is the true centripetal force. It pulls the stopper out of its straight line.

T: the time for one complete revolution. T is determined by measuring the time of a number of revolutions, then dividing the total time by the number of revolutions to obtain the time for one revolution. For example, 20 revolutions in 10s would mean that 10/20 or 0.5 s is required for one revolution. This data is best obtained by one person acting as a counter speaking aloud while another person acts as a timer. You need a stop watch.

Each group’s member should try the experiment. That way, you will get different time T.

Take the average. If you get different radius, take the average.

Record the data in the first row of TABLE 1.

In the TABLE 1:

Length of string: about 30cm long

WEAR GOOGLES

TRIAL	Mass of washers M (convert to kg)	Weight of the washers Fw (N)	Radius r (convert to meters )	Time T (seconds)	Centripetal force Fc Fc = (4 Π² r m) / T² (N)
1
2
3
4