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Rotational Kinematics lab

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1. Use the velocity components to determine the direction of the velocity vector. Is it in the expected direction? 1. From the x-t and y-t images, the two curves show a sine and cosine relationship, indicating that the object is in uniform circular motion. Since position over time behaves as a sine and cosine function, this means that the velocity is their derivative, and the direction of the velocity is always perpendicular to the direction of the radius, so the velocity vector varies in the tangential direction, which is consistent with the theory of circular motion. The formula used to calculate speed 2. Analyze enough different points in the same video to make a graph of the speed of a point as a function of distance from the axis of rotation. What quantity does the slope of this graph represent? In this experiment, we investigated the relationship between radius, linear velocity and acceleration in uniform circular motion by analyzing the motion of three different points on a r...

Second Project

 In our group, it was just me, Venessa, so both Vanessa and I had a very heavy workload. Venessa used 3D printing to create the parts of the car and recorded video of the car moving and differentiated between the video and the physical modeling programmed into the computer. I built the physical model and used the conservation of energy and Newton's second law to come up with formulas for the linear acceleration and maximum speed and used these to create a program to simulate our car. The final slides were made by me and Vanessa.

Angular Velocity Lab

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  Analysis In this experiment, we analyze the energy conversion process of the system by comparing the experimentally measured velocity with the theoretically predicted velocity. In the experiment, we used the displacement 𝑥 and time t to estimate the terminal velocity of the falling object using the equation: The theoretical predicted velocity is derived using an energy conservation model, calculated as: where m is the mass of the suspended weight (0.1 kg), h is the drop height, r is the radius of the wire wrap, and I is the moment of inertia of the disk (estimated at 0.0014 kg-m²). We performed a comparative analysis using three different radius values to calculate the predicted velocities for each case and compared them to the velocities measured in the experiments to assess the accuracy of the model and the sources of error. Conclusion By comparing the experimentally measured velocities with the theoretical predictions, we find that the predicted velocities are generally sligh...

Inclined track experiment

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  Data obtained in the classroom Formula for finding velocity and how to find efficiency To analyze the energy efficiency of the magnetic bumper, we conducted multiple trials using a cart released from various heights on an inclined track. By measuring the initial and rebound heights of the cart, we were able to determine its velocity before and after the collision using the equation v = 2 g h v = \sqrt{2gh} v =( 2 gh)^1/2 ​ . The energy efficiency of the bumper was then calculated using the ratio of the final to initial kinetic energy, given by Efficiency = ( v 2 v 1 ) 2 Date Analyze The efficiency of the magnetic bumper was found to be between 72% and 78% , indicating that about 22%–28% of the mechanical energy is lost during the collision. This loss is likely due to friction, deformation of the bumper, and air resistance. The data also show a slight trend: as the initial velocity increases, the efficiency slightly decreases, which may suggest greater energy loss at higher impac...

Frictional Force

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  Data collected from the experiment The formula to calculate the normal force and friction force is Predicted Friction Force Mass change graphs and tables tables graphs In the graph above, the orange line represents the predicted relationship f k = μ k N f_k = \mu_k N f k ​ = μ k ​ N , using a theoretical coefficient of kinetic friction μ k = 0.4 \mu_k = 0.4 μ k ​ = 0.4 . The experimental data yields a fitted slope of approximately 0.8911, indicating that the actual friction observed in our experiment was significantly higher than the expected value. Hight change graphs and tables tables graphs In the height-changing trial, the measured coefficient of kinetic friction was μₖ ≈ 0.315 , with a high linearity of R² = 0.9574 . This closely matches the predicted value of μₖ = 0.4 , supporting the direct proportionality between kinetic friction and normal force. Uncertainty To evaluate the uncertainty in our experimental method, we conducted four repeated trials at the same setup. The s...

Car Pulled by Rope

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  This is when we did the experiment. Experimental data Experimental and calculated data The formula used to calculate speed How do the predicted velocity and the measured velocity compare in each case?  Did your measurements agree with your initial prediction?  If not, why?  I calculated the magnitude of v using the formula I worked out in class and found the prediction V to be much larger than the magnitude of v I did in the lab. Their percentage difference ranged from 26% to 74%. This could be due to the fact that the formula does not involve friction or air drag, or it could be due to measurement errors in the experiment. Does the launch velocity of the car depend on its mass?  The mass of the block?  The distance the block falls?  Is there a choice of distance and block mass for which the mass of the car does not make much difference to its launch velocity? From the velocities obtained from the experiment and the formula. If the mass of the block ...

Hanging Bridge Lab

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Graph of experiments and calculations Data from experiments  formula was used to calculate the height Calculation uncertainty Where do the two curves match?   From the graphs of the data, it can be seen that when the central mass M<0.09, the experimental data are in good agreement with the theoretical curve ( predicted equation). Where do the two curves start to diverge from one another?   When M > 0.1 kg, the experimentally measured vertical displacement is significantly larger than the theoretically predicted value. What does this tell you about the system?  Show that the theoretical model (assuming no friction and no elasticity) is only applicable to the small mass case and that the actual system has pulley friction or rope elasticity effects. What are the limitations on the accuracy of your measurements and analysis? There is an uncertainty of ±0.005 m in the height measurement. (This was obtained by me and my team by measuring the same mass and t...