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...
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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=2ghv = \sqrt{2gh}. The energy efficiency of the bumper was then calculated using the ratio of the final to initial kinetic energy, given by Efficiency=(v2v1)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 impact forces.

From the graphs, it can be seen that there is a slight decrease in efficiency as the initial velocity increases. This indicates that the higher the impact velocity, the more energy is lost, which may be due to increased deformation or rebound damping

Conclusion


In summary, the magnetic bumper is moderately efficient, preserving about three-quarters of the cart's kinetic energy after impact. The energy losses we observed in our experiments highlight how mechanical systems, especially those involved in collisions, dissipate energy in the form of sound, heat, or permanent deformation that is difficult to recover.

The inclined orbit device proved to be a convenient way to measure energy efficiency. Since we were able to calculate velocity from height alone, the reliance on video analysis and timing tools was minimized. However, it must be recognized that the inclined orbit creates friction, which may slightly reduce the measured efficiency compared to an ideal frictionless situation.

Our method is more straightforward in estimating energy changes using potential energy than the horizontal orbit method used for odd-numbered tables, but is slightly less accurate in isolating bumper performance alone. In summary, our data provide clear and consistent estimates of bumper efficiency and emphasize the role of friction and impact velocity in energy dissipation.





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