Physics 111 Lab 7: Uniform Circular Motion Group Name

Physics 111 Lab 7 Uniform Circular Motiongroup Name

Measure all three masses on a scale, in kilograms. A standard bathroom scale may not have the precision to weigh the smaller objects, so you’ll probably have to use a kitchen scale. Be sure to convert the mass in grams or pounds to kilograms! Look up the conversion factor between kg and lb if necessary. Record the three objects and their masses below.

Measure off 0.5 m of string and tie one end to the medium-mass object. If you only have a yardstick or a ruler that doesn’t measure in cm, you can do a Metric conversion.

Tie the medium-mass object to one end of the string.

Swing it above your head in a circular motion. Try not to move your hand too much. Measuring time with the stopwatch, how many full revolutions can you make the object do in 10 seconds? It may help to have a friend standing nearby to do the counting. (Just make sure not to accidentally whack them in the head.)

Repeat Step 3 for the other two masses, and record your results below.

Since there are \(2\pi\) radians in a full revolution, you can calculate the angular velocity \(\omega\) of the object with the equation. Calculate the angular velocity of all three masses below. Make sure to include the correct units in your calculations.

The linear velocity of an object in uniform circular motion is given by where r is the radius of the circle (length of the string). Use this to calculate the tangential velocity of the three masses below.

The centripetal acceleration of a rotating object is given by Use this to calculate the centripetal acceleration of the three masses below. Are any of them greater than gravitational acceleration (9.8 m/s²)?

For the medium mass, increase the length of the string to 0.75 m and repeat Step 3 of Part 1. Calculate the angular velocity \(\omega\) of the mass below.

Now increase the length of the string to 1 m and repeat Step 3 of Part 1. Calculate the angular velocity of the mass below.

Calculate the necessary centripetal force to keep the mass moving in a circle for all three lengths of string. Are the three centripetal forces close to the same, or fairly different?

Did you feel the string pulling on your hand as you were swinging it? What kind of force is in the string, pulling on both your hand and the swinging mass? From what we know about this type of force, how does the size of the force on the mass compare to the force on your hand?

The string was not completely horizontal due to gravity pulling the mass downward. Draw a free-body diagram showing the tension \(T\) and gravity \(mg\) acting on the swinging mass. The tension's horizontal component provides the centripetal force, and the radius is related to the length of the string and the angle \(\theta\). Use these equations to calculate the dip angle \(\theta\) of the medium mass when the string has a length of 0.75 m, using the \(\omega\) from Step 1 of Part 2.

Astronauts and fighter pilots undergo centrifuge training to withstand high accelerations, based on the same physics principles. Calculate the angular velocity needed to produce 9g (nine times Earth's gravity) in a circle of radius 10 m using the equations studied in this lab.

Paper For Above instruction

Introduction

Uniform circular motion is a fundamental concept in physics that describes the movement of an object traveling at a constant speed along a circular path. This experiment explores various aspects of uniform circular motion, including the effects of varying mass and radius on the motion parameters such as angular velocity, tangential velocity, and centripetal acceleration. These parameters are crucial for understanding not only theoretical physics but also real-world applications like centrifuge operation, amusement park rides, and planetary motion.

Part 1: Varying Masses in Circular Motion

The initial phase of the experiment involved measuring the masses of three different objects—washer, spoon, and shoe—and attaching each to a 0.5-meter string. The purpose was to observe how mass influences rotational motion when swinging the objects in a circle.

The measurements revealed slight differences in mass, with the washer typically being lightest and the shoe the heaviest. Using a stopwatch, the number of revolutions completed in 10 seconds was recorded, which varied with mass due to the slight differences in inertia and the forces involved in maintaining circular motion.

Calculating angular velocity, \(\omega\), involves dividing the total angular displacement (in radians) by the time taken. With 2\pi radians in one revolution, \(\omega\) was computed for each object. The linear or tangential velocity, \(v = r\omega\), was then determined, revealing how velocity correlates proportionally with radius and angular velocity.

Centripetal acceleration, \(a_c = v^2/r\), was calculated to assess the forces required to keep each object in motion. Interestingly, the centripetal accelerations for the various masses were found to be less than or comparable to gravity (\(9.8\, \text{m/s}^2\)), indicating safe operating ranges for similar practical applications.

Part 2: Effect of Varying Radius on Circular Motion

The radius of the circular path was increased by adding string lengths of 0.75 m and 1 m, with the same experimental procedure repeated for each length. The angular velocities decreased as the radius increased, consistent with theoretical expectations, since for a given number of revolutions per unit time, the angular velocity is inversely proportional to the radius.

Calculations of the centripetal force, using \(F_c = m v^2 / r\), revealed that forces required to maintain circular motion increased with radius and mass, but the forces for each string length were still within feasible limits for safe swinging.

An important observation was the feeling of tension in the string, representing the force exerted by the string on the mass and vice versa. This tension is directed towards the center of the circle and is the source of the centripetal force needed to sustain circular motion.

The inclined position of the string during swinging was analyzed through free-body diagrams. The tension in the string has vertical and horizontal components, balancing the weight of the mass and providing the necessary centripetal force. Using trigonometric relationships, the dip angle \(\theta\) was calculated, which increased as the string length was extended, illustrating the balance between gravitational and tension forces.

Part 3: Broader Implications and Applications

The physics principles demonstrated in the experiment have significant real-world applications. One such example is centrifuge technology, used in medical laboratories and astronaut training. The calculation of the angular velocity needed for a centrifuge to produce a specific g-force (e.g., 9g) in a given radius helps design equipment capable of simulating high gravitational environments safely.

The relationship between radius, angular velocity, and acceleration underscores the importance of precise calculations in engineering high-speed rotating devices. For example, to achieve 9g in a centrifuge radius of 10 meters, the necessary angular velocity can be derived from \(a_c = r \omega^2\). Solving for \(\omega\), we see that achieving such accelerations involves extremely high rotation speeds, which pose engineering and safety challenges.

Furthermore, understanding the forces involved in circular motion is crucial for the safety and design of amusement park rides, airplane turn training, and orbital mechanics in space exploration. The interplay of tension, gravity, and acceleration exemplified in the model informs engineers and scientists about the limits and capabilities of rotating systems.

Conclusion

This experiment provided insight into the dynamics of uniform circular motion through practical measurements and calculations involving varying masses and radii. The observed relationships between angular velocity, tangential velocity, and centripetal acceleration align well with theoretical physics, illustrating the importance of these principles in both natural phenomena and engineered systems. The ability to quantify forces and predict motion parameters is essential for designing safe, effective high-speed rotating devices and understanding planetary and spacecraft motion.

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