Uniform Circular Motion

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Title: Uniform Circular Motion Group 33: Van Tran, Elyse Gallagher, Shrenik Patel Experiment Date: October 10th, 2023 Goals: The goal of today’s lab is to observe the circular rotation of a cube on a turntable, and see the centripetal force that is acting upon it. We will first test the hypothesis that static friction is the source of the centripetal force, and aim to understand the concepts of tangential velocity and central acceleration. Procedure: Part I: ● Place 2 cubes on the turntable, one on the rough surface, the other on the smooth surface ● Increase DC voltage to 4V and click on the button ● Turn up voltage slowly in 0.1 V increments until the objects fly off ● Once set up, start records (no longer than 10s) Part II: ● Transfer to video to Capstone ● Analyze the video ● Track movement of each object on Capstone Part III: ● Create a graph and display the tangential velocity vT of the cube vs. time ● From the graph, estimate the tangential velocity at the point when the cube flies off the turntable Precautions and Sources of Error : Precautions of errors can include incorrectly tracking the points of the cube. The video recording of the circle might not have been placed properly resulting in a hard video to analyze. Another thing is the rate of the increments in which we increased the turntable. Data:

Rough Radius

Smooth Radius Rough Vt

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Smooth Vt

Rough Radians

Smooth Radians

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Questions: Question 1. What force or forces are acting on the cube as it rotates in a circle at constant speed? Draw a free body diagram for the cube as seen from the side. On your diagram, indicate the

direction of the force(s) acting on the cube. The forces acting on the cube as it rotates are the centripetal force and gravitational force. When the cube is rotating there is also an additional force acting on it called the tangential force. Question 2. How can the hypothesis for this lab be tested experimentally? In a few sentences, describe at least one way to test the hypothesis experimentally by using the rough and smooth surfaces available on the turntable. From the hypothesis for the lab a turntable with a rough surface should have a block on it. This is because of the friction the surface provides, one can see that the block is at rest. The block is sliding outward when the rough surface is replaced by a smooth surface. In the first instance, resistance from friction prevented the block from advancing. This indicates that the friction was radiating inward. Question 3. When the cube falls off the edge of the turntable, which path will it take according to Newton’s 1st Law? Use the figure at right showing the top-down view of the turntable to select a path A through E. Consider the horizontal plane only (not vertical motion). Path B F c F g F T V

Question 4. Angle in radians is often an unfamiliar unit, so let’s gain more familiarity by looking at our graph of radians vs. time. About how many radians did your cube move through from start to finish of your tracking? Check for internal consistency: How many radians are there in a circle? Is the number you are reporting reasonable? Rough surface trial: (47 rotations)( )= 295.31 radians 2? Smooth surface trial: (35 rotations)( )= 219.91 radians 2? For the rough trial, the cube moved 295.31 radians. For our smooth trial, the cube moved 219.91 radians. There are radians in a circle and we found that the result we got is 2? reasonable. Question 5. What simplified expression did you obtain for the coefficient of friction? Does the expression depend on the mass of the cube? Fnet r =Σfr Fcp=fs=μsFn=μsmg=mvt 2 /r=ma r μs=vt 2 /rg The expression does not depend on the mass of the cube. Discussion: In the lab we observed circular rotation of a cube on a turntable. From there we could observe what forces were acting on it. We observed that the forces in play were centripetal, tangential, and gravitational forces. We were able to test the hypothesis by placing our cube and putting it on two surfaces of different texture. The first texture we observed was rough and the second was smooth. We found that the cube stayed on longer on the smooth surface opposed to the rough surface. Thinking about this conceptually the expected outcome should have been the opposite where the cube should have stayed on longer for the rough surface as opposed to the smooth surface. This is because it takes more force to move an object on a rough surface than a smooth one due to the difference in friction.

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