Debunking the Myth: Speed of a Car Ramp-Up onto Moving Truck Explained

[Uk_Ghost]

The situation is this: A truck is moving at 70mph with a ramp leading into it at the back. A car with front-wheel drive is behind it doing 75mph. The car goes up the ramp and into the truck. Here is where the dispute starts.

My theory: Once the front wheels of the car are on the ramp the car's overall speed would then be accelerated because it has mounted a moving platform. Granted it wouldn't go to 175mph because of factors like wind resistance and the fact its going up a ramp but it would not be enough to completely kill the speed of the car at that speed and it would still increase considerably. This would result in the car going through the truck very quickly.

My friend's theory: Once the car has mounted the ramp it would only be doing 5mph. He seems to think the truck's speed would be subtracted from the car's speed. His logic is "i saw it on Mythbusters but i can't explain anything errrrrrggggghhhhh".

Please help me out.

 

[cepheid]

Your friend is correct.

"Speed" is only meaningful if you specify what it is being measured relative to. Motion is not absolute. To illustrate this point, consider how the problem appears to two different observers. Observer 1 is stationary (at rest, has zero speed) *relative to* the road. From his point of view, the truck is moving down the road at 70 mph, and the car is moving down the road in the same direction at 75 mph, gaining on the truck. If the drivers don't accelerate or hit the brakes, these speeds *relative to the road* don't change, even when the car reaches the truck and drives inside of it.

Now consider the same problem from the perspective of of observer 2, inside the truck. In this frame of reference, the truck is stationary. Therefore, to this observer, the car appears to be approaching the truck from behind at 5 mph (the difference between their velocities). We say that 5 mph is the relative velocity between the car and the truck. When the car reaches the ramp at 5 mph, it drives up it and enters the truck at 5 mph.

Both perspectives are correct, and both perspectives describe the same result. So the relationship is:

(velocity of car relative to road) - (velocity of truck relative to road) = (velocity of car relative to truck.)

 

[Uk_Ghost]

But i fail to see how that would work. This is the way i see it. If you were able to hold a car above the ground and then started its wheels spinning at 75mph, when you dropped it the car would shoot forward once in contact with the ground. Same as if you were standing on a platform which is moving at 70mph and you started walking at 5mph in the same direction. Your overall speed to someone outside would be 75mph because you are adding it to the speed of the platform. Which is why i think that if a car moving at 75mph entered a platform moving at 70mph their speeds would be added together (excluding the resistances which would enevitably slow the car down of course).

 

[cepheid]

Same as if you were standing on a platform which is moving at 70mph and you started walking at 5mph in the same direction. Your overall speed to someone outside would be 75mph because you are adding it to the speed of the platform.

Correct.

Which is why i think that if a car moving at 75mph entered a platform moving at 70mph their speeds would be added together (excluding the resistances which would enevitably slow the car down of course).

I don't see how this follows from your moving walkway example. If you drive up in a scooter behind a moving walkway, and you're going at 75 mph relative to the observer at the side of the walkway, and the walkway itself is going 70 mph relative to that bystander, your speed relative to the walkway will be 5 mph forward (because, measuring both velocities in the frame of reference of the bystander, yours is faster by 5 mph).

 

[TurtleMeister]

Your friend is also correct about the Myth Busters episode. It was successfully done, but not at such high speed. When the wheels hit the ramp they must suddenly slow down to 5mph. That may cause some spinning for a very short time but it is doable. Note that only the spinning wheel has to slow down, not the car.

 

[cepheid]

Actually, I think I might be wrong, if it the scooter gets on the walkway, and its tires maintain the same rotational speed, then the velocity of the scooter may indeed change from 75 mph relative to the road to 75 mph relative to the walkway, because the tire rotation speed always determines the linear velocity of the vehicle relative to the surface over which it is moving.

I would be right if we were just talking about a shuttle entering the bay doors of a larger, slower moving spacecraft in front of it. But because of the way tires translate rotational motion into translational motion, I think you may have a point here...

EDIT: Nope. TurtleMeister confirms my original thinking. So when the vehicle hits the moving platform, its tire rotational speed actually slows down in order for the vehicle to maintain the same road speed? How does that work?

 

[CarlAK]

maybe this time someone will "solve" this :)

https://www.physicsforums.com/archive/index.php/t-11889.html

 

[Uk_Ghost]

So why wouldn't your speed be added to that of the walkway? if you're doing 75 mph and the walkway was moving at 70 mph then once you were on top of it your overall speed would be 145 mph surely.

I can understand if you're assuming the vehicles are driving alongside each other because then they are traveling on the same surface and the car's speed would only be 5 mph faster than the truck but I'm saying if the car was to enter a ramp on the back of the truck. Once the car's wheels are on top of the ramp would they not still be moving at 75 mph? Which would propel you forward on top of the truck's ramp at that speed.

 

[Uk_Ghost]

EDIT: Nope. TurtleMeister confirms my original thinking. So when the vehicle hits the moving platform, its tire rotational speed actually slows down in order for the vehicle to maintain the same road speed? How does that work?

That's what i want to know. Somehow when the car enters the ramp its tyres stop. I don't know why this is, surely the engine is still making them rotate at that speed.

 

[cepheid]

Once the car's wheels are on top of the ramp would they not still be moving at 75 mph?

Well, TurtleMeister and people in the thread that CarlAk linked to seem to be saying that upon hitting the ramp, the tires would actually slip...

 

[Uk_Ghost]

Ah now that i can grasp. If its a question of friction then i can see why it would stop. Not because the tyres are moving any slower than they were but because they are unable to get the grip needed to be propelled so suddenly at that speed. So the amount of acceleration would rely purely on the friction existing between the ramp and the tyres.

 

[cepheid]

Ah now that i can grasp. If its a question of friction then i can see why it would stop. Not because the tyres are moving any slower than they were but because they are unable to get the grip needed to be propelled so suddenly at that speed.

Yeah, but I don't know if that's the right answer, so I hope others can comment.

 

[TurtleMeister]

When a plane touches down on the runway, there is a short period of skidding until the wheels ramp up to speed. It's just the opposite when the cars wheels hit the ramp. However, there is the addition of the cars engine which also must ramp down. The driver may need to make an adjustment as he enters the ramp. I saw the episode on Myth Busters and it was done quite easily.

 

[willem2]

EDIT: Nope. TurtleMeister confirms my original thinking. So when the vehicle hits the moving platform, its tire rotational speed actually slows down in order for the vehicle to maintain the same road speed? How does that work?

Conservation of energy and conservation of momentum.

There's no way for the car to suddenly gain the kinetic energy to go 145 mph. There's
only a tiny bit of rotational energy in the wheels that might increase the speed with 1mph.
There's no force on the car to suddenly increase the momentum to give the car a speed of 145 mph.

If you had a very long truck and continued to accelerate, you will be much faster than a car that stayed on the road however, because you can put the car in 1st gear again. You will be robbing kinetic energy from the truck here, because you push yourself forwards by pushing the truck backwards. There's no way for this to happen instantaneously tough. The engine must produce the kinetic energy that the car will get because of its speed relative to the truck.

 

[Uk_Ghost]

So this is just a problem of inertia?

 

[Cleonis]

Ah now that i can grasp. If its a question of friction then i can see why it would stop. Not because the tyres are moving any slower than they were but because they are unable to get the grip needed to be propelled so suddenly at that speed. So the amount of acceleration would rely purely on the friction existing between the ramp and the tyres.

Conversely, imagine what would happen in the theoretical case of the tires having infinite grip. Then as the front wheels of the front wheel drive car move onto the ramp the tires would have to slow down instantly to 5 mph, which would cause the car's engine to shut down. (More likely the gear box will be trashed.)

Since the tires have only so much grip they are certain to slip initially. They will have some traction though, so the driver must ease off the gas immediately. It's certainly a dangerous thing to do.

I also think that it's much more difficult with a front wheel drive car than with a rear wheel drive car.
If the car is rear wheel drive then the front wheels will roll onto the ramp relatively easily, and by the time the rear wheels move onto the ramp the car is in a good position.

With a front wheel drive car traction and steering is combined in the front wheels, and as the front wheels move onto the ramp, and momentarily slip, steering is also lost momentarily. I think that makes it much more dangerous.

The stunt of driving front wheel drive cars onto a moving ramp has been performed, for the 1969 movie 'The italian job'. The cars used were Mini Coopers. (In 2003 another movie called 'The italian job' was released, also featuring Mini Coopers, and a heist, but otherwise a different story).

Cleonis

 

[Uk_Ghost]

Thanks for the help everyone. That one has been bugging me for a while. Been over it with loads of friends but we could never come to a solid conclusion heh.