# Circular motion with forces

• StephenDoty
In summary, at the top of the loop, the car’s speed must be great enough to counteract gravity and the normal force, and can be calculated using the equation v = √[gr/m].
StephenDoty
As a roller coaster car crosses the top of a 50.0 -diameter loop-the-loop, its apparent weight is the same as its true weight.What is the car's speed at the top?

So the car is under the circle at the top. so the forces acting on the car would be mg and the normal force acting down

My question is, is the force f=mv^2/r going down with the rest of the forces or up against the other forces?

I know that since a = 0 and that a goes toward the center, thus Fnet = 0 and going to the center. But does this mean that F=mv^2/r goes down too?

Thank you.

Stephen

No, the force f=mv^2/r is not going down with the rest of the forces. This force is a centripetal force, which is the force that keeps the car moving in a circular path around the top of the loop. At the top of the loop, the car’s speed must be great enough to counteract gravity (mg) and the normal force (N) to keep it moving in a circular path. Thus, the speed of the car at the top can be calculated by equating the centripetal force to the sum of the other two forces: f = mv^2/r = mg + N or v = √[gr/m] where g is the acceleration due to gravity, r is the loop’s radius, and m is the mass of the car. Plugging in the given values gives us the car’s speed at the top of the loop-the-loop as v = 8.94 m/s.

The force F=mv^2/r is a centripetal force, meaning it is directed towards the center of the circular motion. In this case, the center is the bottom of the loop-the-loop. This force is necessary to keep the car moving in a circular motion and to counteract the centrifugal force, which is the force that wants to push the car outwards. So in this case, the force F=mv^2/r is going up against the other forces (mg and the normal force) to keep the car in its circular path. The car's speed at the top can be calculated by using the equation F=mv^2/r, where F is the centripetal force, m is the mass of the car, v is the speed, and r is the radius of the loop. By rearranging the equation, we can solve for v and determine the car's speed at the top.

## What is circular motion?

Circular motion is the movement of an object along a circular path. This means that the object is constantly changing direction as it moves.

## What is centripetal force?

Centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is necessary for circular motion to occur.

## What is the relationship between centripetal force and velocity?

The centripetal force acting on an object is directly proportional to the square of its velocity. This means that as the velocity increases, the centripetal force required to keep the object moving in a circular path also increases.

## How does mass affect circular motion?

Mass has no direct effect on circular motion. However, a larger mass may require a greater centripetal force to maintain circular motion at a given velocity.

## What are some real-life examples of circular motion with forces?

Some examples of circular motion with forces include a satellite orbiting the Earth, a car going around a roundabout, and a child on a swing.

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