# Homework Help: The effect of mass on roller coaster cars

1. Mar 8, 2004

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?

2. Mar 8, 2004

### 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.

Last edited: Mar 8, 2004
3. Mar 8, 2004

### pedestrian

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

4. Mar 8, 2004

### ShawnD

Although that is the logical explanation, the math disproves it.

Last edited: Mar 8, 2004
5. Mar 9, 2004

The formula doesn't take time into account. The heavier car starts more slowly because it has a greater mass, more inertia. So over the beginning part of the track, the heavier car is slower. Maybe over time it evens out but with the length of my track it doesn't?

6. Mar 9, 2004

### Daaf

Alright... a = f / m f = m * g
a = (m*g)/m = g. Add a cosinus or sinus and you'll have the exact amount. This all is thesame for each car though, it doesn't depend of it's weight. It has to be either friction or aerodynamics. And I am not into either of those. Strange problem!

7. Jul 30, 2010

### Jellybeans

Kinetic Energy = 1/2mv^2...therefore, as the mass is increased, the velocity is decreased. Hence the cart would take longer to to complete the roller coaster track because it travels at a lower velocity.