# Need help finding the max velocity I can drive without flying off a hill

• Coronita
In summary, the conversation is discussing the maximum speed a car can have without flying off the road at the top of a hill with a radius of 50m. The participants explore the concept of circular motion and the forces involved, including the centripetal force and gravity. They also touch on the equation for critical speed and how it relates to the problem at hand. The conversation ends with the understanding that at the critical speed, the gravitational force must still be greater than the centripetal force for the car to remain on the ground.
Coronita
A car drives over the top of a hill that has a radius of 50m. What maximum speed can teh car have without flying off the road at the top fo the hill?

Soooo I know I'm supposed to treat the hill like a circle...no coefficient of friction given, not sure if I need that though, not really sure what direction to go in here, please help?

What is the magnitude of force required to keep an object in circular motion with radius r?

it's not 2pi r/t is it?

Coronita said:
it's not 2pi r/t is it?

That's not a force, check the units. You need to go back and review circular motion to answer the question.

I've been looking through the chapter on circular motion but all I've got are the rotational kinematic equations, I struggled with that chapter when we covered it too and that was 4 chapters ago >_<

k, best I've got is F=mv^2/r but I don't know the mass of the car, I can't just consider it to be mass-less can I?

Coronita said:
k, best I've got is F=mv^2/r but I don't know the mass of the car, I can't just consider it to be mass-less can I?

Just keep the mass as an unknown at this point. Now consider the force diagram for the car. Can you find an equation that must be satisfied for the car to remain in circular motion?

? :(

What force or forces act on the car?

kinetic friction, normal and gravity

We're interested in the forces in the vertical direction, which corresponds to forces in the radial direction if we view this as a circular motion problem. Can you include the centripetal force in an equation describing the car when it remains in circular motion?

I've found the equation for critical speed inside of a circle, Vc=rg^1/2 is it related to that at all?

Coronita said:
I've found the equation for critical speed inside of a circle, Vc=rg^1/2 is it related to that at all?

I've read through this section of the chatper a few times but I'm still not understanding why it's true

Well the centripetal force

$$F_c = \frac{mv^2}{r}$$

is the radial force required to maintain circular motion. In the case of the car, this force must come from gravity. For slow speeds, the gravitational force,

$$F_g=mg,$$

will generally be greater than the required centripetal force, so the car stays on the ground. For high enough speeds, the required centripetal force will be higher than Fg, and the car will hop off the ground. If the critical speed is the maximum speed before the car leaves the ground, can you guess what condition on the forces must be satisfied at the critical speed?

Gravity must still be greater than the centripetal force. So we're looking for the point at which centripetal force is the closest it can get to Fc without surpassing it?

I have to be somewhere in 20 minutes >_< Thank you so much for your patience though! I'll have to come back to this one later.

## 1. How do I calculate the maximum velocity I can drive without flying off a hill?

To calculate the maximum velocity, you will need to consider several factors such as the angle of the hill, the weight and speed of your vehicle, and the friction between your tires and the road surface. Using these variables, you can use a physics equation to determine the maximum velocity.

## 2. Is there a specific formula I can use to calculate the maximum velocity?

Yes, you can use the formula v = √(rgtanθ), where v is the maximum velocity, g is the gravitational acceleration, r is the radius of the hill, and θ is the angle of the hill. However, this formula assumes ideal conditions and may not be accurate in real-life situations.

## 3. Can I use a speedometer to determine the maximum velocity?

No, a speedometer only measures the current speed of your vehicle and does not take into account the other variables that affect the maximum velocity. It is not a reliable tool for determining the maximum velocity on a hill.

## 4. Do different types of vehicles have different maximum velocities on a hill?

Yes, different vehicles have different weights, friction coefficients, and engine power, which can affect the maximum velocity on a hill. For example, a heavier vehicle may have a lower maximum velocity compared to a lighter one.

## 5. Are there any safety precautions I should take when trying to find the maximum velocity on a hill?

Yes, it is important to always prioritize safety when conducting this experiment. Make sure to choose a hill with a gradual slope and no sharp turns, and have a spotter present to ensure the safety of yourself and others. It is also recommended to wear protective gear and perform the experiment in a controlled environment.

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