Physics 111 Lab 7: Uniform Circular Motion Group Name 349090

Physics 111 Lab 7 Uniform Circular Motiongroup Name

Describe all three masses on a scale, in kilograms, converting if necessary. Measure off 0.5 m of string, tie one end to the medium-mass object, and swing it above your head in a circular motion. Record the number of revolutions in 10 seconds. Repeat for the other two masses and record your results. Calculate the angular velocity using ω = 2π × (revolutions / time). Calculate the tangential velocity using v = ωr. Calculate the centripetal acceleration using a_c = v² / r. Repeat the process for increased string lengths (0.75 m and 1 m) and compute the respective ω, centripetal forces, and analyze the forces involved. Draw free-body diagrams to understand the forces, including tension and gravity. Use equations to find the dip angle of the string when the length is 0.75 m. Additionally, determine the angular velocity needed to generate 9g of acceleration in a circle with a radius of 10 m.

Paper For Above instruction

The principles of uniform circular motion are fundamental to understanding many physical phenomena, from everyday activities like swinging an object to complex applications such as astronaut training. This laboratory exercise explores how mass, radius, and velocity influence the dynamics of objects in circular motion, providing insights into centripetal force, acceleration, and the forces acting on a swinging mass.

Part 1: Varying Masses

The initial phase of the experiment involved measuring three different objects with varying masses—specifically, a washer, a spoon, and a shoe—using a precise scale. Accurate measurement of mass is crucial, as it directly influences the dynamics of circular motion. The masses were recorded in kilograms after proper conversion from grams or pounds, ensuring consistency in SI units, which is essential for subsequent calculations.

Following measurement, each object was attached to a 0.5-meter string, and swung in a circular path above the head. This setup allowed the collection of data on the number of revolutions completed in 10 seconds, with multiple trials to enhance reliability. The angular velocity (ω) was calculated using the formula ω = 2π × (revolutions / time), where revolutions represent the count within the time interval of ten seconds.

The angular velocity directly relates to the rotational rate of the object, which further enables the calculation of tangential velocity (v) using the relation v = ωr, where r is the radius, i.e., the length of the string. The linear velocity reflects how fast the object moves along its circular path. Subsequently, the centripetal acceleration (a_c) was computed via a_c = v² / r, illustrating how the mass's speed influences the inward acceleration necessary to maintain the circular trajectory.

The collected data revealed that, while the angular velocities varied according to the mass, the macroscopic parameters such as linear velocity and acceleration depended primarily on the radius and the rotational speed, not directly on the mass. However, the tension in the string—equivalent to the centripetal force—must balance the inward force needed for circular motion, which was discussed through free-body diagrams. These diagrams depicted the tension in the string counteracting the combination of gravitational force and the inertial force arising from circular motion.

Part 2: Varying Radius

In the subsequent phase, the experiment extended to varying the radius of the circle by increasing the string length to 0.75 m and 1 m. For each length, the same measurements and calculations were performed. These steps provided critical insights into how the radius affects angular velocity and the forces involved in maintaining circular motion. As the radius lengthened, the angular velocity decreased for a fixed rotational rate, aligning with the inverse relationship between radius and angular velocity for a given tangential velocity.

The calculations showed that the centripetal force, given by F_c = m × a_c, where m is mass and a_c is the centripetal acceleration, behaved differently for different string lengths, but broadly followed theoretical expectations. For larger radii and similar velocities, the necessary tension increased. The observation that the tension force in the string was felt by the swinging hand underscored the direct role tension plays as the centripetal force, pulling inward on both the object and the hand.

Part 3: The Bigger Picture

The experiment also highlighted the significance of the string not remaining perfectly horizontal due to the effect of gravity, which pulls the mass downward. By drawing free-body diagrams and resolving forces into components, the vertical component of the tension was related to gravitational force, while the horizontal component provided the centripetal force. The analysis incorporated the angle θ the string makes below the horizontal, calculated via T sinθ = m a_c, leading to the relationship involving the dip angle and the tension T in the string.

Using the derived equations, the dip angle θ was computed when the string length was 0.75 m, showing how the mass's velocity influences the angle at which the string dips. Larger angular velocities produce larger dip angles, which increase with the square of ω, emphasizing the nonlinear relationship between rotational speed and the string’s inclination.

Finally, the experiment connected these classical concepts with real-world applications, such as centrifuge training for astronauts and fighter pilots. To simulate high gravitational forces, the required angular velocity for a person to experience 9g in a circle with radius 10 m was calculated. Applying the formula a_c = ω² r, the necessary angular velocity was determined, illustrating the magnitude of speeds involved in such rapid rotations. This calculation emphasizes how fundamental physics principles underpin high-performance training and safety protocols in aerospace contexts.

Conclusion

This laboratory provided a comprehensive exploration of the dynamics of objects in uniform circular motion, illustrating the relationships between mass, radius, velocity, and forces. The experiments confirmed theoretical predictions and deepened understanding of the interplay between tension, gravity, and centripetal acceleration. The insights gained from the analysis of forces and angles are critical for understanding complex rotational systems and their applications in engineering, space exploration, and safety training.

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