# Car Coasting Down a Circular Hill: Which Free-Body Diagram is Correct?

• BrownBoi7
In summary, the conversation discusses a car coasting at a constant speed over a circular hill and which free-body diagram would be correct for this scenario. After some discussion and clarification on acceleration and circular motion, the correct answer is determined to be option A, with the net force being directed downwards and the acceleration acting downwards as well.
BrownBoi7
Car--Hill--Free body

A car coasts at a constant speed over a circular hill. Which of the free-body diagrams in the figure attached is correct? Explain.

My attempt:
I am thinking B. Since the car is at a constant speed, there's no acceleration. So there is no additional force acting downwards besides it's weight.

Which would you choose? Explain please.

Thanks

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BrownBoi7 said:
Since the car is at a constant speed, there's no acceleration.
Careful. Acceleration means a change in velocity, not necessarily speed.

That makes sense. I still haven't figured my answer yet. Should I still stick with B?

BrownBoi7 said:
That makes sense. I still haven't figured my answer yet. Should I still stick with B?
You tell me. Is the car accelerating? (Is its velocity changing as it goes over the hill?)

The car is constantly changing direction, along with it changes something else, why do you think that is?

Yes the car is constantly changing direction. Velocity is not constant in which case. This means there is some acceleration.

Should I go with 3?

BrownBoi7 said:
Yes the car is constantly changing direction. Velocity is not constant in which case. This means there is some acceleration.
Good!

What's the direction of the acceleration (and thus the net force)?

This question is very similar to centripetal motion.
There is a net force towards the center even if the speed is constant.The direction changes towards center.So the force is acting towards center

EDIT:(Changed to a spoiler)

W = mg ---acting downwards
N = Normal Force ---acting upwards opposite to W
A= acceleration --- acting downwards. Looking at the figure, it's clear the car is going downhill. So we can treat it as a circular motion problem?

Option A would best describe the scenario.

BrownBoi7 said:
W = mg ---acting downwards
N = Normal Force ---acting upwards opposite to W
All true.

A= acceleration --- acting downwards. Looking at the figure, it's clear the car is going downhill. So we can treat it as a circular motion problem?
The key is not that the car is going downhill, but that it is going over a circular hill. Yes, this is a circular motion problem. So what's the direction of the centripetal acceleration? Use that to figure out the direction of the net force and thus the correct choice.

## 1. What is a free-body diagram?

A free-body diagram is a simplified representation of an object or system that shows all the external forces acting on it. These forces can include gravity, friction, and normal force. It helps to visualize the forces acting on an object and understand how they affect its motion.

## 2. How does a car coasting down a circular hill work?

When a car is coasting down a circular hill, it is subject to two main forces: the force of gravity pulling it towards the center of the circle and the normal force from the road pushing it outwards. These two forces together create a centripetal force that keeps the car moving in a circular path.

## 3. Which free-body diagram is correct for a car coasting down a circular hill?

There may be multiple correct free-body diagrams for a car coasting down a circular hill, depending on the specific situation. However, the most common diagram would show the force of gravity pointing towards the center of the circle and the normal force pointing outwards, perpendicular to the road. Other forces, such as friction or air resistance, may also be included depending on the situation.

## 4. What factors affect a car coasting down a circular hill?

The main factors that affect a car coasting down a circular hill are the mass of the car, the radius of the circle, and the speed at which the car is traveling. The greater the mass and speed, the more force is needed to keep the car moving in a circular path. A smaller radius will also require more force to maintain the circular motion.

## 5. How do we calculate the centripetal force for a car coasting down a circular hill?

The centripetal force can be calculated using the formula Fc = mv^2/r, where m is the mass of the car, v is the speed, and r is the radius of the circle. This formula shows that the centripetal force is directly proportional to the mass and square of the velocity, and inversely proportional to the radius. So, to increase the centripetal force, we can either increase the mass or velocity, or decrease the radius.

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