# The effect of mass on roller coaster cars

For my science fair project, I am testing the effect of changes in mass on the time it takes a car to complete a roller coaster track. The track is made of hotwheels track and has an initial ramp, two turns and a loop. I used the same car both times (once without added weight and once with an additional 10 grams). After testing for many trials, I found that the lighter car finished the track faster than the heavier car.
This is the opposite of what I thought would happen. I thought that because the heavier car had greater potential energy, it would go faster. As I research this question, I start the think that the two cars should have finished at the same time regardless of mass.
What is going on?

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ShawnD
Look at the formula for what happens in energy changes. Theoretically, mass should not make any difference.

$$mgh = \frac{1}{2}mv^2 + friction$$

$$mgh = \frac{1}{2}mv^2 + umg cos(\theta)d$$

factor out the mass

$$gh = \frac{1}{2}v^2 + ug cos(\theta)d$$

Everything left is a constant. Gravity doesn't change, the height of the car doesn't change, u (actually mew) doesn't change, the angle doesn't change. Velocity should not change either.

My original post had an explanation for why lighter was better but it was wrong. I'll half to think about this for a while.

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With the increase in mass you also increase the normal force the track exerts on the car and thus increase the force of friction between the track and the car which is why the heavier car takes longer

ShawnD
With the increase in mass you also increase the normal force the track exerts on the car and thus increase the force of friction between the track and the car which is why the heavier car takes longer
Although that is the logical explanation, the math disproves it.

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