Driving an RC car in a vertical loop, What formula to use?

In summary, the formula used to determine the minimum speed required for an RC car to complete a vertical loop in a concrete drain pipe is Mg < MV2/r, where M is the mass of the car and V is the velocity needed to maintain a circular motion with radius r. This formula is not applicable for planetary orbits, where the gravitational constant G and the masses of the two bodies are also taken into account. Additionally, the gravitational acceleration on Earth is represented by g, which is different from the gravitational constant G.
  • #1
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I once drove my RC car in a vertical loop in a concrete drain pipe.

If you know the diameter of the pipe, and the weight of the vehicle, what is the formula used to determine the minimum speed required for it to complete the loop?
 
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  • #2
At the top you want the force of gravity Mg to be less than the centripetal force needed to move in a circle radius r at velocity V. So...

Mg < MV2/r

Mass M cancels

Rearrange it to find V.
 
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  • #3
Wow I never would have thought that mass is irrelevant, but it makes sense. I thought it would have been way more complicated than that, taking into account the amount of time "at the top" and mass.

Would this formula be for a simple planetary orbit of constant speed and radius? Mg = MV2/r
 
  • #4
No because gm is only valid at the surface of a planet. You would need to use GmM/r2 instead. There is also the complication that both planets orbit about their common centre of mass (eg the moon does not orbit about the centre of the earth).

In case you haven't studied this: m and M are the masses of the two bodies. G isn't the same as g. "Big G" is the gravitational constant whereas "little g" is the gravitational acceleration on earth.
 
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1. How do you calculate the velocity needed to successfully drive an RC car in a vertical loop?

In order to calculate the velocity needed, you will need to use the formula: v = √(rg), where v is velocity, r is the radius of the loop, and g is the acceleration due to gravity (9.8 m/s²). This will give you the minimum velocity needed to complete the loop without falling off the track.

2. Can the weight of the RC car affect its ability to complete a vertical loop?

Yes, the weight of the RC car can play a role in its ability to complete a vertical loop. A heavier car may require a higher velocity to successfully complete the loop, while a lighter car may have an easier time completing it with a lower velocity. It is important to take the weight of the car into consideration when calculating the required velocity.

3. Is there a maximum radius for an RC car to complete a vertical loop?

Yes, there is a maximum radius that an RC car can successfully complete a vertical loop. This is due to the limitations of the car's motor and battery power. If the loop is too large, the car may not have enough power to maintain the necessary velocity to complete the loop without falling off the track.

4. What factors can affect the stability of an RC car when driving in a vertical loop?

The stability of an RC car in a vertical loop can be affected by several factors, such as the weight and distribution of the car, the type and condition of the tires, and the speed and angle at which the car enters the loop. It is important to make sure the car is balanced and in good condition before attempting a vertical loop.

5. Are there any safety precautions that should be taken when driving an RC car in a vertical loop?

Yes, there are some safety precautions that should be taken when driving an RC car in a vertical loop. Make sure the loop is securely attached to a stable surface and that there is enough space around it for the car to safely complete the loop. It is also recommended to wear protective gear, such as goggles, in case the car falls off the track. Always supervise children when they are driving an RC car in a vertical loop.

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