# Car driving onto a moving transporter

## Question:

I am having a serious discussion with a friend that has stemmed from a recent car commercial. We have asked a mutual friend who majored in Physics and she is not sure about her answer.

In the commercial you see a semi-truck traveling on a highway at about 60mph and a sports car slowly gaining on him. The semi is an auto-hauler and it's ramps fall down and start throwing up sparks. The sports car then lines up and goes up the ramp, stopping with out any signs of braking hard. We want to know if this is possible.

My fiancé's claims that because they are both going similar speeds, the auto would have no trouble stopping in the 2 seconds demonstrated in the commercial. This does not make sense to me. My trouble lies in the fact that the motor of the auto is still going at 60 (motor is spinning the tires at 60 mph) and has to continue going that speed until the car is completely on the ramp or it would lose ground. As soon as all 4 wheels are on the ramp they would still be going about the same speed. Could you stop the forward motion of the tires (and the car) in enough time? Would you have to brake very hard to achieve this?

He states that to follow my logic the car would then be going 120 mph in reference to the ground and I agree that this does not make sense. But to follow his logic, the tires could only move along the ramp of the truck at less than 10 mph and when your tires were rotating at 60 mph an instant before does not explain how the tires got stopped that quickly, you would be burning your tires off and that would be apparent in the commercial.

If these were simple blocks of metal going along, without an engine and tires being rotated by the forces that the engine produces, this would be a much simpler problem. The car would just glide up the ramp and the inertia would equal out for both.

Difficult to know where to start.First lets think of your auto-hauler (in the UK we call it a car transporter) travelling at 60 mph and a car freewheeling at 63 mph. To make this part of the answer easier lets assume no friction between the cars wheels and the road or ramp.

The car approaches the auto-hauler ramp at a relative speed of 3 mph and moves up the ramp at 3 mph. It will then obviously be really easy for the car to brake to a stop as it travels along the ramp and onto the body of the truck. The only difference between this case and a car freewheeling onto a stationary truck at 3 mph is the rotational kinetic energy of the wheels. This must be converted to heat and sound energy before the car stops (this is true in all the cases that I have considered).

Right – now for the powered car versions. I think that there are two cases, one with front wheel drive and one with rear wheel drive. (can I ignore the four wheeled drive case!?)

I will look at the rear wheel drive first.

As before lets think of an approach speed of 3 mph. The rear wheels are driving the car forward and the front wheels are in a sense freewheeling. So – the cars front wheels get onto the ramp and the car can the brake gently as the rear wheels approach the ramp.
However as soon as the rear wheels touch the ramp the car must brake. The driver will disengage the clutch to cut the power (VITAL in both powered options). You are quite right in saying that if it didn't happen the car would be travelling along the ramp at 60 mph! I suggest that the car's brakes are applied and it would slow down rapidly .

With front wheel drive the problem is similar but the braking must occur sooner as it is the powered wheels that will hit the ramp first.

In both cases whether you seen smoke from the tyres will depend on the skill of the car driver and how quickly they can declutch. If the powered wheels hit the ramp as they are driving the car forwards at 60 mph then the car will be moving at 60 mph relative to the truck and the driver will only have the length of the truck in which to brake.

Referring to your fiancé's comment about the car travelling at 120 mph relative to the road. This is what would happen but only if the car was still being powered with the clutch engaged. I can run at around 15 mph (for a short time!) but if I am in a train that is moving at 50 mph and I run along the corridor at 15 mph (relative to the corridor) I am travelling at 65 mph relative to the ground.

Your comments about the blocks are also helpful. If one block slides onto the back of another at 3 mph then the final speed will depend on the relative masses of both. Think of a lorry driving onto the back of a light trailer pulled by a car. As the lorry brakes to a stop as it drives up the ramp onto the trailer the car is left pulling the trailer AND the heavy lorry. This would slow the car down. This is not noticeable for the auto-hauler because it is much heavier than the car that drives onto it.

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