Viper and toy car - who's fastest?

[Mastogana]

Hi there!

This is my first post, and I discovered this forum after I saw the tv show "Mythbusters", after searching about a physics forum to ask a question:

In one particular episode, they made a Dodge Viper and a toy car descend a road (the toy car was in a toy ramp) with about a 30º angle, only with the power of gravity. Which reached the bottom first?

Well, from their experiment, the Viper reached bottom (a 400 meter descent) about 4 seconds faster than the toy car.

Acording to the laws of physics, in a perfect environment (no friction and wind resistance) both cars would reach the bottom at the same time, at about 0,2 ms-1 acceleration.

But my question is, why does the car reaches the bottom first?

I don't know much about wind resistance (I tried to use a force with a value deducted from the volumic mass of the air to resist the movement of both cars, but I don't know if this is the right way to do it) and friction (supposing they both have friction, I think maybe the acceleration values should be smaller but more or less equal to both cars).

Is this a simple question, solved by equations and math (I love aplying physics and maths to real life situations ) or there are a lot of variables that influence this velocity variation (aerodinamics, the tipe of wheels, etc).

I hope I'm not asking a stupid question!

 

[Danger]

Welcome to PF, Mastogana.
I never saw that episode, so I don't know exactly what the set-up was. It's quite possible that a toy car, being so much less dense, could reach its terminal speed before the 400m point, and thus cease accelerating. Also, axle friction is probably a higher-impact element in a toy.

 

[Mastogana]

I also think that that is it!

Tell me more about terminal speed! By logic I think that that means that both cars acceleration will decrease acording to their mass/density? So that's why the toy car reaches a point where its velocity is always the same first?

Tell me more damm it, physics is awesome :D!

 

[mgb_phys]

Air resistance is roughly proportional to the cross section area for 2 objects with the same shape, so not quite density.
Even if the cars were the same density (made of the same materials) then the toy assuming it is 1/10 the size of the real car will have 1/100 the cross section and so 1/100 the air resistance but only 1/1000 the mass.
So the air resistance will have a 10x greater effect on it's slowing down.

 

[russ_watters]

The toy wouldn't reach a terminal velocity, but it would accelerate slower because it is less dense. Also, for heavier objects like cars, the rolling resistance is much lower compared to it's weight than for a toy.

 

[Integral]

Due to the short distance and resulting low speeds air resistance would not be a factor for the larger car. I saw parts of this episode, they had a lot trouble getting a clean run with the toy car. Laying out 400m of toy car track is no mean feat. They encountered buckling at places where the sun hit the track, the toy would hit the raised edge and come to a stop. It took significant effort to get a full run. I would bet that the toy car would reach a terminal velocity, not due to air resistance but due to a rolling friction which increases with speed.

 

[Cyrus]

Acording to the laws of physics, in a perfect environment (no friction and wind resistance) both cars would reach the bottom at the same time, at about 0,2 ms-1 acceleration.

Be careful, in this case this is not true. The dodge viper has big heavy wheels. This means more energy is tied up in spinning its larger wheels than the smaller toy car, so its linear kinetic energy will be smaller.

You have to split up the mgh energy into 1/2*m*v^2 + 1/2*I*w^2

Also, you can't ignore friction between the wheels and the ground, but you can ignore friction in the bearings.

 

[Cyrus]

I would bet that the toy car would reach a terminal velocity, not due to air resistance but due to a rolling friction which increases with speed.

Actually, as long as the slope of the ramp is constant the rolling friction will be constant with speed.

 

[Integral]

Actually, as long as the slope of the ramp is constant the rolling friction will be constant with speed.

Perhaps this is an approximation, which may or may not apply to the toys used. There are many factors in this sort of problem which are very hard to nail down in a real world experiment.