Velocity/Acceleration Question

Let’s say I took a battery powered toy car, and turned it on so that the wheels spun straight forward. But I picked it up, so that there was no translational motion, but the tires were spinning at full speed. Then, I put down the car, with the tires at full speed. Would the car still need to accelerate to get to its cruising speed, or would it start off at that speed, since it’s tires are already going full speed?

I think contact with the ground would slow the tires’ spinning or the tires would not be able to grip the ground quick enough(like a burnout in a car). Or maybe, under the right conditions, the car would speed away at full speed, so in other words----- I don’t know.

Yes, it’s called “slippage”… sorry I don’t know more, but this should give you a starting point…

When the car is suspended above the ground with wheels running, its velocity in the x-direction (horizontal motion parallel to the floor) is zero. When you put it down on the floor, assuming a vertical drop with no motion on the part of your hand in the x-direction, its initial x-direction velocity is zero.

It must accelerate from zero to get to cruising speed.

I can see that it depends a lot on the nature of the car’s motive source (and suspension and tires) whether or not this method will be a quicker or slower route to cruising speed.

Before you put the car down the body of the car is not moving forward. For it to go from that to moving forward at full speed instantly would involve infinite acceleration. That would require infinite force. I don’t need to tell you (do I?) that there are no infinite forces involved here (or indeed anywhere). So it will certainly not immediately be at full speed.

The basic misconception that appears to be involved in your OP seems to be that the only thing that needs to be accelerated up to speed on a wheeled vehicle are the wheels. In fact of course the whole vehicle needs to be accelerated.

Broadly speaking I suppose you might say that the car would accelerate more quickly if dropped with the wheels are already up to speed than it otherwise would, since at least one element of the car is alread accelerated up to speed beforehand. But then all sorts of factors come in like breaking traction, stalling the engine etc and the results are going to vary so much depending on weights, tyre types, engine types etc that answering Ringo’s question is not possible.

As Ringo said, since the car has an initial translational velocity of zero, it has to accelerate to reach any kind of speed.

As for whether your method will allow for a greater rate of acceleration (if you measure the acceleration time by starting the timer when the dropped car’s tires first contact the ground), it depends on factors such as the type of tires, the weight of the car, and the output of the motor. In general, though, assuming any kind of reasonably high cruising speed (decent sized motor compared to the weight of the car), it should take longer to accelerate the car by spinning the wheels and dropping it versus allowing the car to accelerate on the ground from a standstill.

The friction between the tires and the ground is what causes translational acceleration in the car. So long as the tires are gripping the road, the maximum possible accelerating force for the car is the weight of the car times the coefficient of static friction. Past this static friction accelerating force, the tires start spinning faster than the car is moving forward, the tires slip, and the maximum accelerating force becomes the weight of the car times the coefficient of kinetic friction. Since kinetic friction is less than static friction for most materials (certainly true for rubber), a car that slips will accelerate more slowly than one that doesn’t.

if the vehicle had no mass, the wheels had perfect contact with the surface (no slippage), there was no wind resistance or friction you could do it. And you could call it the Photon Express, and it would travel at the speed of light.

Here’s how to make it for real:

Make a movie of a toy car with its wheels rolling and going down something. Project it onto a screen in a room with a perfect vaccuum, and it travels to the screen at full acceleration instantly!

taggert, not a troll, but a physics consulting carpenter. You may try this trick at home and bore your friends speechless.

You’ve already got a few responses that are correct, but let me offer another, slightly different way to look a the problem. This may make more sense, or less sense, to you:

Any moving object stores energy. An object that translates (like your car, or a locomotive, or a baseball, or whatever) has a kinetic energy of (1/2)mv[sup]2[/sup], where m is its mass and v is its velocity. An object that rotates (like the wheels of your car, or a flywheel, or a top, or whatever) also has kinetic energy, in this case of (1/2)I[symbol]w[/symbol][sup]2[/sup], where I is its mass moment of inertia (a quantity that accounts for how much mass is at the “edge” of the object, and how much is in the middle), and [symbol]w[/symbol] is its rotational speed.

When you first turn on the car, the motor changes the electrical potential energy (from the battery), and accelerates the wheels, where the energy is stored as kinetic energy [(1/2)I[symbol]w[/symbol][sup]2[/sup]]. If you now drop the car onto the floor, the most efficient (i.e., ideal) energy transfer would use the energy stored in the wheels and transfer it to kinetic energy moving the car forward (with some left over, because the wheels would still be spinning). Since you can’t create energy out of nothing, to speed up the car, you need to slow down the wheels. Furthermore, since the wheels have relatively low mass compared to the car, you need to slow down the wheels a lot to speed up the car just a little.

Reality is even more complicated yet, because energy transfer is not instantaneous, so there is some span of time where the wheels are decelerating and the car is accelerating, and thus the wheels are slipping, losing energy through friction in the form of heat. My guess would be that the size of this energy loss is close to, or even larger than, the energy finally transferred to move the car forward.

As a practical application, instead of battery-powered cars, think of the toy friction-drive cars (the kind you rev up by running it across the floor). These cars have large flywheels inside; unlike the battery powered car, where the I of the wheels is small compared to the m of the car, these friction-drive cars have a large I. Drop one of those cars on the ground and you’ll notice the wheels slowing down (but not much!) as it accelerates the car up to speed.