Incline Track

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

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?

For the inclined track, with $v_i=0.737\text{m/s}$ and $v_f=0.42\text{m/s}$, the efficiency is approximately 33%. This result may vary with initial velocity due to energy losses from friction and bumper deformation.

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?

On the level track, with $v_i=0.57\text{m/s}$ and $v_f=0.42\text{m/s}$, the efficiency is about 54%. Friction's influence is minimized here, making the result less velocity-dependent compared to the inclined track.

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?

In the experiment, a 1.1 kg cart had an initial speed of 0.737 m/s and dropped to 0.42 m/s on an inclined track, showing about 33% efficiency. On a level track, it started at 0.57 m/s and also ended at 0.42 m/s, with a higher efficiency of 54%. This shows that more energy is lost on the incline, mainly due to friction.

Friction plays a big role on the inclined track. The frictional force $f_k = \mu mg \cos \theta$ does negative work, reducing the cart’s speed and energy before it hits the bumper. Ignoring this would give inaccurate efficiency results. To estimate energy lost to friction, we can release the cart from the same height and measure how far it travels, then use the change in kinetic energy to find the average friction force.

The best way to measure speeds is by using video analysis: set a scale, record at a high frame rate, and calculate the speed just before hitting the bumper ($v_i$) and the steady speed after impact ($v_f$). Running multiple tests with different initial speeds helps ensure accurate, reliable results and checks if efficiency changes with velocity.

In conclusion, magnetic bumper efficiency ranges from 33% to 54%, with more energy lost on inclined tracks due to friction. Around 46% to 67% of the initial kinetic energy is lost in each collision. While magnetic bumpers don’t perfectly conserve energy, they offer reliable, consistent results, making them useful in real-world settings. A full analysis should include kinetic energy, friction, system energy changes, and possible experimental errors.