Distance travelled by a car considering only air friction?

In summary, a 3-ton car would travel about 17 meters if its initial speed was 17 km/h and only air's friction was considered.
  • #1
Suekdccia
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TL;DR Summary: Distance traveled by a car considering only air friction?

How much distance would a 3-ton car travel if its initial speed was 17 km/h and we only take into account air's friction? (Assume that the car has an airfoil-like shape, so that the resistance against the air is very low)

I tried to calculate this with the formula Vf² = Vi² + 2·a·d (taking as 0.05 the coefficient of friction of the airfoil-like car against the air) and the resulting distance is 22,84 meters, but it seems too low to me. Am I messing up with something?
 
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  • #2
Suekdccia said:
I tried to calculate this with the formula Vf² = Vi² + 2·a·d (taking as 0.05 the coefficient of friction of the airfoil-like car against the air)
Air resistance is not like friction, it depends on the velocity. What research have you done into solving problems that involve air resistance? Wikipedia might be a good place to start...

Update with a link -- https://en.wikipedia.org/wiki/Drag_(physics)
 
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  • #3
You should not use that formula because acceleration is not constant in your case.
Its value will be very high when velocity of the car is still high, but that value will progresively tend to zero at a square ratio as the velocity is degraded by air drag.
 
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  • #4
Suekdccia said:
I tried to calculate this with the formula Vf² = Vi² + 2·a·d (taking as 0.05 the coefficient of friction of the airfoil-like car against the air)
Solving that formula for d gives me about 17 meters.

Suekdccia said:
and the resulting distance is 22,84 meters, but it seems too low to me. Am I messing up with something?
Our numbers do not agree. Yes, in addition to using the wrong formula, you seem to be messing something up. Please show your work.
 
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  • #5
Here is how you arrive at the equation you used:

The work done ##W## is defined as:
$$W = \int Fdx$$
Knowing that ##F=ma##, the work done based on acceleration is:
$$W= \int madx$$
If we want to know the work based on velocity alone:
$$W = \int madx = \int m\frac{dv}{dt}dx = \int m\frac{dx}{dt}dv = \int mvdv$$
Both equations should give the same amount of work, so:
$$\int_{v_i}^{v_f} mvdv = \int_{x_i}^{x_f} madx$$
$$\frac{1}{2}m(v_f^2 - v_i^2) = ma(x_f - x_i)$$
$$v_f^2 = v_i^2 + 2a(x_f - x_i)$$
Which is the equation you used. This assumes that ##F = ma##, where ##a## is constant.

But that is not the case here. The problem identifies the force ##F## that you need to use with the work ##Fdx##. And the work done based on velocity is still ##mvdv##. All you need to do is to equate both as done previously and resolve the integrals. [Hint: the air friction force varies with velocity.]
 
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1. What is air friction and how does it affect a car's distance travelled?

Air friction, also known as drag, is the resistance force that acts against an object moving through air. It is caused by the collision of air particles with the surface of the object. This force can slow down the object's motion and decrease its distance travelled.

2. How does the shape of a car affect its distance travelled due to air friction?

The shape of a car plays a crucial role in determining the amount of air friction it experiences. A streamlined or aerodynamic shape can reduce the surface area of the car that comes in contact with the air, thus reducing the drag force and allowing the car to travel a greater distance.

3. Does the speed of the car affect the distance travelled due to air friction?

Yes, the speed of the car does affect the distance travelled due to air friction. As the speed increases, so does the drag force, resulting in a decrease in the distance travelled. This is why cars with high speeds have more aerodynamic designs to reduce drag and increase their distance travelled.

4. What are some factors that can affect the amount of air friction experienced by a car?

Apart from the shape and speed of the car, other factors that can affect the amount of air friction experienced by a car include the density of the air, the temperature, and the altitude. Higher altitudes and lower temperatures can result in thinner air, reducing the amount of air friction.

5. Is there a way to calculate the exact distance a car will travel due to air friction?

Calculating the exact distance a car will travel due to air friction is a complex task as it depends on various factors such as the car's speed, shape, and environmental conditions. However, using mathematical models and simulations, scientists can estimate the distance travelled by a car considering only air friction.

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