# Mass effects on toy car

In a theoretical experiment with only friction ( With floor and ramp ) and gravity, would the mass of a toy car affect its distance traveled after reaching the bottom of the ramp.

My hypothesis is that a car with heavier mass experiences larger friction on the ramp and with the floor surface, hence it reaches a slower velocity at the bottom, hence traveling a shorter distance. Would this be the case or do I need to consider the effects of momentum and kinetic energy?

I conducted this experiment at school and found the car with heavier mass traveled slightly less than a car with lighter mass. I was wondering if this a valid result or if some added friction of some sort is skewing my results?

My hypothesis is that a car with heavier mass experiences larger friction on the ramp and with the floor surface

The friction force depends on normal force magnitude which depends on mass, but the mass cancels out in the equation of motion. For the car going downwards the equation of motion is

$$\underbrace{m a}_{F_\text{net}} = \underbrace{m g \sin\theta}_{F_g} - \underbrace{\mu m g \cos\theta}_{F_f}$$

where $$a$$ is the downward acceleration magnitude along the ramp, and $$\mu$$ is coefficient of friction which is very small for a rolling wheel. Notice how car's mass appears from both sides of the equation, hence

$$\boxed{a = g (\sin\theta - \mu \cos\theta)}$$

This shows that both cars have the same downward acceleration, i.e. car velocity at the bottom of the ramp does not depend on its mass. At least not theoretically.

I conducted this experiment at school and found the car with heavier mass traveled slightly less than a car with lighter mass. I was wondering if this a valid result or if some added friction of some sort is skewing my results?

There will always be some margin of error. The equation of motion predicts that both cars will reach the same horizontal distance after leaving the ramp. However, there are many effects that we have not considered here, such as air resistance which depends on car's geometry etc. All these add up to measurements uncertainty.

Check similar question here:

Does mass affect distance travelled by a toy car?

• How would you intuitively understand why the velocity at the bottom of the ramp is the same regardless of mass, without equations? Apr 13, 2022 at 8:54
• @HaowenXie Does the velocity in free fall depend on mass? It does not, and ramp is similar to free fall in that respect. In the equation $m \vec a = \sum \vec F_i$, if all forces $\vec F_i$ are proportional to mass $m$ then mass cancels and the acceleration does not depend on the mass. This is why all objects regardless of their mass have acceleration $g$ in free fall. Again, this applies only when there is no drag. See related discussion here: Why does a crumpled paper fall down faster than a flat paper Apr 13, 2022 at 9:20