Speed of a car rolling down a hill

In summary, a car will reach the maximum speed at the bottom of a long hill if you never place your foot on the brake or the accelerator.
  • #36
Thecla said:
By the way would you feel safe in a car free rolling down a 30 degree slope that is 20 miles long? Would you worry the car will fall apart?

As long as you carefully tape the doors shut, you should be fine... :wink:

1627657540214.png

https://arstechnica.com/cars/2020/0...pe-was-rolling-downhill-in-promotional-video/
 
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  • #37
Thecla said:
Summary:: Will a car make it to the bottom of a long hill?
... a 5% grade. You start it and put it in neutral or drive and it starts to roll down. You never place your foot on the brake or the accelerator and suppose the hill is 200 miles long.
So, we're talking about a straight grade starting 10 miles high?

Doesn't sound like planet Earth, maybe we need to specify the atmospheric and gravity conditions too?

Nothwithstanding that quip (a pathetic attempt at engineering humour, maybe), but if it really was that long then we're probably talking about different air densities on the descent, so it will surely begin to slow down at the end once into denser air, and pass exactly through a terminal velocity speed at some point.

So need to specify the starting altitude as it would likely reach terminal velocity quicker and earlier. Some of those routes between New Mexico and Colorado might alter the arithmetic!

... 100mph sounds reasonable, considering engineering estimates ...
 
  • #38
cmb said:
So, we're talking about a straight grade starting 10 miles high?

Doesn't sound like planet Earth, maybe we need to specify the atmospheric and gravity conditions too?
The hill has been reduced to 20 miles long and 1 mile high in post#31.

As an aside, Olympus Mons on Mars certainly fits the description of the original mountain, complete with virtually no atmosphere to interfere. Perhaps Elon Musk will do this experiment someday with a Tesla on Mars.
 
  • #39
I think we are making it more complicted than it needs to be.I will shorten the hill ,but make it steeper . Also ignore different strengths of gravity and different air resisatance. A 30 degree slope down a hill of indefinite length. Will the car, a normal sedan with normal tires, reach maximum velocity before it reaches the bottom,will the car fall apart(blown tires,etc), or will this car be able to reach a speed of 300 miles per hour?
 
  • #40
Thecla said:
A 30 degree slope down a hill of indefinite length. Will the car, a normal sedan with normal tires, reach maximum velocity before it reaches the bottom,will the car fall apart(blown tires,etc), or will this car be able to reach a speed of 300 miles per hour?
No, it won't reach 300 mph, because of air resistance. Since we are talking maximum speed of about 100 mph, normal car mechanical components can easily withstand the forces acting at this speed. And since the hill is of indefinite length, it will necessarily reach its terminal velocity before reaching the bottom (since there is none).
 
  • #41
Thecla said:
I think we are making it more complicted than it needs to be.I will shorten the hill ,but make it steeper . Also ignore different strengths of gravity and different air resisatance. A 30 degree slope down a hill of indefinite length. Will the car, a normal sedan with normal tires, reach maximum velocity before it reaches the bottom,will the car fall apart(blown tires,etc), or will this car be able to reach a speed of 300 miles per hour?
I do not believe it will reach 300 ##mph##. Consider that if the car was dropped from an aircraft it would not reach 300 ##mph## terminal velocity. Here is a terminal velocity calculator to ply with. Given a car in free fall with air drag on the order of 100-130 ##mph## it is only going to be less rolling down a ##30°## hill.

http://www.calctool.org/CALC/eng/aerospace/terminal

You would have a shot at reaching 300 ##mph## on Mars.
 
  • #42
bob012345 said:
... Given a car in free fall with air drag on the order of 100-130 ##mph## it is only going to be less rolling down a ##30°## hill.

http://www.calctool.org/CALC/eng/aerospace/terminal
I get 374mph when I do that calculation with that calculator and realistic numbers. What numbers are you using?

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  • #43
cmb said:
I get 374mph when I do that calculation with that calculator and realistic numbers. What numbers are you using?

View attachment 286944
My area was too big by 10x.
 
  • #44
bob012345 said:
My area was too big by 10x.
Well, the interesting point there is that it wouldn't be an over-estimate if the car is falling bottom side down, rather than pitched nose forward.

Which raises the next question, if you were to have a car in freefall through air, would aerodynamics pitch it nose first to max terminal velocity, or tumble from one attitude to another, or find the minimum terminal velocity bottom-down?

And then the next question back to the op; if a vertical fall is too steep to stop it tumbling on its way down and a 5% grade isn't, what is the maximum grade before one can expect a car becomes aerodynamically unstable?
 
  • #45
cmb said:
Well, the interesting point there is that it wouldn't be an over-estimate if the car is falling bottom side down, rather than pitched nose forward.

Which raises the next question, if you were to have a car in freefall through air, would aerodynamics pitch it nose first to max terminal velocity, or tumble from one attitude to another, or find the minimum terminal velocity bottom-down?

And then the next question back to the op; if a vertical fall is too steep to stop it tumbling on its way down and a 5% grade isn't, what is the maximum grade before one can expect a car becomes aerodynamically unstable?
A car careening down a steep incline should have a lift component as well as a drag component. If the lift becomes significant it will compromise the normal force required to hold the vehicle against the incline and it will fly off into a tumbling catastrophe. One would need the details of a design to figure the lift of a car vs. velocity.
 
<h2>1. What factors affect the speed of a car rolling down a hill?</h2><p>The speed of a car rolling down a hill is affected by several factors including the slope of the hill, the weight of the car, the friction between the wheels and the road, and any external forces acting on the car such as wind resistance or gravity.</p><h2>2. How does the slope of the hill affect the speed of a car rolling down?</h2><p>The steeper the slope of the hill, the faster the car will accelerate due to the force of gravity. This means that a car rolling down a steeper hill will reach a higher speed compared to a car rolling down a gentler slope.</p><h2>3. Does the weight of the car impact its speed when rolling down a hill?</h2><p>Yes, the weight of the car does impact its speed when rolling down a hill. Heavier cars have more mass, which means they require more force to accelerate. This means that a heavier car will typically roll down a hill at a slower speed compared to a lighter car.</p><h2>4. How does friction affect the speed of a car rolling down a hill?</h2><p>Friction between the wheels and the road surface can slow down the speed of a car rolling down a hill. This is because the frictional force acts in the opposite direction of the car's motion, creating resistance and reducing its speed. This is why cars with worn out or smooth tires may roll down a hill slower compared to cars with new, grippy tires.</p><h2>5. Can a car reach a constant speed when rolling down a hill?</h2><p>No, a car cannot reach a constant speed when rolling down a hill. This is because the force of gravity will continue to accelerate the car until it reaches the bottom of the hill or encounters an opposing force, such as friction. However, the car's speed may appear constant if the slope of the hill is gentle and the opposing forces are minimal.</p>

1. What factors affect the speed of a car rolling down a hill?

The speed of a car rolling down a hill is affected by several factors including the slope of the hill, the weight of the car, the friction between the wheels and the road, and any external forces acting on the car such as wind resistance or gravity.

2. How does the slope of the hill affect the speed of a car rolling down?

The steeper the slope of the hill, the faster the car will accelerate due to the force of gravity. This means that a car rolling down a steeper hill will reach a higher speed compared to a car rolling down a gentler slope.

3. Does the weight of the car impact its speed when rolling down a hill?

Yes, the weight of the car does impact its speed when rolling down a hill. Heavier cars have more mass, which means they require more force to accelerate. This means that a heavier car will typically roll down a hill at a slower speed compared to a lighter car.

4. How does friction affect the speed of a car rolling down a hill?

Friction between the wheels and the road surface can slow down the speed of a car rolling down a hill. This is because the frictional force acts in the opposite direction of the car's motion, creating resistance and reducing its speed. This is why cars with worn out or smooth tires may roll down a hill slower compared to cars with new, grippy tires.

5. Can a car reach a constant speed when rolling down a hill?

No, a car cannot reach a constant speed when rolling down a hill. This is because the force of gravity will continue to accelerate the car until it reaches the bottom of the hill or encounters an opposing force, such as friction. However, the car's speed may appear constant if the slope of the hill is gentle and the opposing forces are minimal.

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