Introduction:
Without circular motion, life as we know it would not be possible. For human existence to endure, the earth must rotate in a circular motion around the sun. Uniform circular motion is the motion in which an object moves in circle at a constant velocity with a constant radius. A centripetal acceleration is the instantaneous rate of change which acts towards the center of the circle. Since the centripetal acceleration is directed towards the center of the circle, the net force is directed inwardly. The purpose of the lab is to find the relationship between the frequency in horizontal circular motion and the radius, mass, and centripetal force.
Hypothesis:
If the magnitude of the force causing circular motion (Ft) increases, then the frequency of revolution of an object in uniform circular motion will also increase. This is because the centripetal force needs to increase in order to increase the centripetal acceleration, which then increases the velocity.
If the radius of the circular path increases, then the frequency of revolution of an object in uniform circular motion will decrease, and if the radius of the circular path decreases, then the frequency of revolution of an object in uniform circular motion will increase. This is because as radius increases, it takes more time to complete a revolution and when radius decreases, it takes less time to complete a revolution.
If the mass of an object increases, then the frequency of revolution of an object in uniform circular motion will decrease, while if the mass of an object decreases, then the frequency will increase. This is because
If the magnitude of the force causing circular motion (Ft) increases, then the frequency of revolution of an object in uniform circular motion will also increase. This is because the centripetal force needs to increase in order to increase the centripetal acceleration, which then increases the velocity.
If the radius of the circular path increases, then the frequency of revolution of an object in uniform circular motion will decrease, and if the radius of the circular path decreases, then the frequency of revolution of an object in uniform circular motion will increase. This is because as radius increases, it takes more time to complete a revolution and when radius decreases, it takes less time to complete a revolution.
If the mass of an object increases, then the frequency of revolution of an object in uniform circular motion will decrease, while if the mass of an object decreases, then the frequency will increase. This is because
Materials:
- Reinforced plastic tube with smooth ends
-1.5 m of fishing line or strong smooth string
-3 one-holed rubber stoppers of equal size
- Metal masses of 50g, 100g, and 200g
- Washers
- Small masking tape
- Reinforced plastic tube with smooth ends
-1.5 m of fishing line or strong smooth string
-3 one-holed rubber stoppers of equal size
- Metal masses of 50g, 100g, and 200g
- Washers
- Small masking tape
Figure 1: The materials and the way it needs to be set up.
Procedure:.
1. Prepared data table.
2. Measured and recorded the mass, in kilograms, of each rubber stopper.
3. With one rubber stopper attached securely to one end of the string, hung a 100 g mass on the other end of the string and began twirling the stopper in the stopper in such a way that its path remained horizontal and at a constant radius.
4. Used the following method to control a constant radius of 56.7cm: attached a paper or a small piece of masking tape 1 cm below the bottom of the tube when r=56.7cm. With this radius, a constant mass of one rubber stopper, and a tension force of 0.98N (caused by the 100g mass), twirled the stopper at constant speed and measured the time for 20 complete cycles. repeated this measurement three times. calculated the frequency of revolution. entered data into table.
5. Repeated step 4 using a tension force of 1.96 N, then 2.94 N, placed the appropriate mass on the end of the string both times.
6. With the mass constant at one rubber stopper and the tension force constant at 1.96 N, measured the time for 20 complete cycles when r= 23.9cm, r = 38cm and r= 63.4 cm. repeated measurements three times for accuracy. calculated the frequency and recorded the data.
7. With a constant radius of 63.4 cm and a constant tension force of 1.96 N, and measured the time for 20 complete cycles when stopper mass was 14.92g, 14g, 17.8g. Calculated the frequencies and recorded the data.
1. Prepared data table.
2. Measured and recorded the mass, in kilograms, of each rubber stopper.
3. With one rubber stopper attached securely to one end of the string, hung a 100 g mass on the other end of the string and began twirling the stopper in the stopper in such a way that its path remained horizontal and at a constant radius.
4. Used the following method to control a constant radius of 56.7cm: attached a paper or a small piece of masking tape 1 cm below the bottom of the tube when r=56.7cm. With this radius, a constant mass of one rubber stopper, and a tension force of 0.98N (caused by the 100g mass), twirled the stopper at constant speed and measured the time for 20 complete cycles. repeated this measurement three times. calculated the frequency of revolution. entered data into table.
5. Repeated step 4 using a tension force of 1.96 N, then 2.94 N, placed the appropriate mass on the end of the string both times.
6. With the mass constant at one rubber stopper and the tension force constant at 1.96 N, measured the time for 20 complete cycles when r= 23.9cm, r = 38cm and r= 63.4 cm. repeated measurements three times for accuracy. calculated the frequency and recorded the data.
7. With a constant radius of 63.4 cm and a constant tension force of 1.96 N, and measured the time for 20 complete cycles when stopper mass was 14.92g, 14g, 17.8g. Calculated the frequencies and recorded the data.
Analysis:
(d)
(e)
(f) FBD Diagram of the mass in circular motion in this investigation.
(e)
(f) FBD Diagram of the mass in circular motion in this investigation.
Evaluation:
(g) As the frequency increases, accuracy decreases since it is harder to maintain a perfect horizontal circle.
(h) Sources of Error
1. Not maintaining a perfect horizontal circle
2. Did not count the correct number of revolutions because the system was too fast
3. Timer did not start on time – may have been delayed
Synthesis:
(g) As the frequency increases, accuracy decreases since it is harder to maintain a perfect horizontal circle.
(h) Sources of Error
1. Not maintaining a perfect horizontal circle
2. Did not count the correct number of revolutions because the system was too fast
3. Timer did not start on time – may have been delayed
Synthesis:
- Newton’s First Law: The tension force from the string is causing the stopper to move in a circular motion. However, when the tension force is removed, then inertia will cause the stopper to continue in the direction the tension force is released at.
- Newton’s Second Law: There is a centripetal acceleration which means that a net force is present in the system that is directed inwardly. This net force is what causes the stopper to move in a circular motion.
- Newton’s Third Law: The person’s hand is slightly moving, causing the tension force for the object to move in a circular motion. The force that is applying to the hand is equal to the tension force in magnitude but opposite in direction.
Conclusion:
In conclusion, the purpose of the lab was to identify the relationship between the mass, magnitude, radius and frequency.The purpose of this lab was to identify the relationship between radius, mass, the magnitude of the force, and frequency. The hypothesis was right for if the radius increase, then the frequency will also increase. it was also right for if the magnitude of the force increases, then the frequency will also increase. But we we were wrong for if the mass of the stopper increases, the right answer is that if the mass of the stopper increases then then then the frequency will increase.
In conclusion, the purpose of the lab was to identify the relationship between the mass, magnitude, radius and frequency.The purpose of this lab was to identify the relationship between radius, mass, the magnitude of the force, and frequency. The hypothesis was right for if the radius increase, then the frequency will also increase. it was also right for if the magnitude of the force increases, then the frequency will also increase. But we we were wrong for if the mass of the stopper increases, the right answer is that if the mass of the stopper increases then then then the frequency will increase.