Inclined track experiment----ZiTong Cheng

 Questions：

Equipment

 You will have a meter stick, a stopwatch, cart masses and wooden blocks to create the incline. You may also use the video analysis equipment to estimate the effect of friction for measuring the efficiency. 

  Predictions

 Whiteboard Question (odd):  Calculate the energy efficiency of the bumper (with friction and without) in terms of the least number of quantities that you can easily measure in the situation of an inclined track.

Make a drawing of the cart on the level track before and after the impact with the bumper.  Define your system. Label the velocity and kinetic energy of all objects in your system before and after the impact.

Write an expression for the efficiency of the bumper in terms of the final and initial kinetic energy of the cart.

Write an expression for the energy dissipated during the impact with the bumper in terms of the kinetic energy before the impact and the kinetic energy after the impact.

Whiteboard Question:  How will friction effect your result? 

Even Table Hints:  Find a useful range of heights and inclined angles that will not cause damage to the carts or bumpers. Make sure that the cart will never contact bumper (end stop) during the impact. Decide how you are going to measure the height of the cart.

General hints:   Be sure to take sufficient data to estimate uncertainty.  You will want to estimate the effect of friction. Make a schedule to test the effect of friction by the video analysis equipment. How can you find the average frictional force when the cart moves on the inclined track? How much energy is dissipated by friction?

Even Tables:  Take the measurements necessary to determine the kinetic energy before and after the impact with the bumper.  What is the most efficient way to measure the velocities with the video equipment?  Take data for several different initial velocities.

Analysis

 

Calculate the efficiency of the bumper for the inclined track.  Does your result depend on the velocity of the cart before it hits the bumper?

Calculate the efficiency of the bumper for the level track.  Does your result depend on the velocity of the cart before it hits the bumper?

 

Conclusion

What is the efficiency of the magnetic bumpers?  How much energy is dissipated in an impact? State your results in the most general terms supported by your analysis. Is the effect of friction significant?

Answer:

In this experiment, we used a cart, magnetic bumpers, an inclined track setup, and video analysis tools to study the energy changes during a collision and to calculate the energy efficiency of magnetic bumpers. By measuring the cart’s velocity before and after the impact, we can determine the change in kinetic energy and analyze the effect of friction.

First, for the inclined track setup, we measured the cart’s path length $d$, height difference $h$, and mass $m$ to estimate the mechanical energy. In the presence of friction, the cart loses some energy while sliding down. Using video analysis tools (such as Tracker), we tracked the cart's motion and determined its initial and final velocities ($v_i$ and $v_f$) by calculating displacement over time between video frames. The initial kinetic energy is $K{E}_i=\frac{1}{2}m{v}_i^2$, and the final kinetic energy is $K{E}_f=\frac{1}{2}m{v}_f^2$. The efficiency of the bumper is given by $\text{efficiency}=\frac{K{E}_f}{K{E}_i}$, representing how much of the kinetic energy is retained after impact. The energy dissipated during the collision is $\mathrm{\Delta }E=K{E}_i-K{E}_f$.

We repeated the experiment on a level track to eliminate the effect of gravitational acceleration on the cart’s motion. In this case, the only energy losses come from friction and the bumper itself. By comparing the efficiency on the inclined and level tracks, we further analyzed whether friction had a significant impact.

According to the experimental data, the cart with a mass of 1.1 kg had an initial velocity of 0.737 m/s and a final velocity of 0.42 m/s on the inclined track, yielding an efficiency of approximately 33%. On the level track, the initial velocity was 0.57 m/s and the final velocity was 0.42 m/s, resulting in an efficiency of about 54%. This indicates that more energy is lost on the inclined track, primarily due to friction.

Friction has a significant effect on the result. On the inclined track, frictional force $f_k=\mu mg\cos \theta$ does negative work, reducing the cart’s kinetic energy before it reaches the bumper. Ignoring friction would lead to an overestimation of the cart’s actual kinetic energy, and therefore an inaccurate bumper efficiency. To estimate energy loss due to friction, we can release the cart from the same height and measure how far it travels, then use kinetic energy changes to calculate the average frictional force.

The final conclusion is that the efficiency of magnetic bumpers ranges between approximately 33% and 54%, depending on the cart's initial velocity and the type of track. More energy is lost on the inclined track due to friction, which is a non-negligible factor. The energy dissipated in each collision is about 46% to 67% of the initial kinetic energy. While magnetic bumpers do not fully preserve kinetic energy, they provide consistent and predictable performance, making them valuable in practical applications. A complete analysis must consider kinetic energy, friction, total system energy changes, and experimental uncertainties.