Question about Applying V^2/r with two different velocities

• MaZnFLiP
In summary, the question asks for a situation where -1g acceleration is needed on a turn, using the equation V^2/r = -1g. The poster proposes a vertical picture as a solution and asks for clarification on which velocity to use. They suggest using the final velocity, which would be the velocity of the car at the bottom after going around the arc.
MaZnFLiP
[SOLVED] Question about Applying V^2/r with two different velocities

Homework Statement

I have a problem where I am using the equation V^2/r = -1g to a problem with centripetal force. Basically the question is designing my own situation where i need to have a -1g acceleration on a turn and i decided on the picture below. It is a vertical picture.

-1g = v^2/r

The Attempt at a Solution

I tried figuring out exactly how to get the velocity but I just don't seem to see which velocity to use.

Last edited:
I know that the equation is V^2/r = -1g. I think the velocity I need to use is the final velocity, which is the velocity at the end of the arc, right? So in this case it would be the velocity of the car at the bottom after it has gone around the arc. So if I use the final velocity, the equation will be: Final Velocity^2/Radius = -1g Is this correct?

I know that the velocity should be different on each side but I'm not sure how to incorporate that into the equation.

When applying the equation V^2/r = -1g, it is important to note that the velocity (V) in this equation is referring to the tangential velocity, or the velocity at any given point on the circular path. In a situation like the one described, where there are two different velocities involved, it is important to consider the velocity at each point on the turn separately.

In the given scenario, the velocity on the left side of the turn would be different from the velocity on the right side. This is because the direction of motion changes at the top of the turn, resulting in a change in velocity. Therefore, the equation V^2/r = -1g should be applied separately for each side of the turn.

To determine the velocities at each point, you can use the equation v = sqrt(gr), where g is the acceleration due to gravity and r is the radius of the circular path. This will give you the tangential velocity at any given point on the turn.

Additionally, it is important to note that the -1g in the equation represents the centripetal acceleration, not just the acceleration due to gravity. This means that the net acceleration at any point on the turn should be equal to -1g, taking into account both the acceleration due to gravity and the centripetal acceleration.

In summary, when dealing with a situation where there are two different velocities involved, it is important to consider the velocity at each point separately and use the equation v = sqrt(gr) to determine the tangential velocity at each point. Additionally, the net acceleration at any point should be equal to -1g, taking into account both the acceleration due to gravity and the centripetal acceleration.

1.

What is the formula for applying V^2/r with two different velocities?

The formula for applying V^2/r with two different velocities is V1^2/V2^2 = r1/r2. This formula is used to calculate the ratio between two velocities and their corresponding radii.

2.

Why is V^2/r used in scientific calculations?

V^2/r is used in scientific calculations because it is a fundamental equation in physics that relates velocity, acceleration, and radius in circular motion. It helps to understand the relationship between these variables and how they affect each other.

3.

Can V^2/r be used for non-circular motion?

No, V^2/r can only be used for circular motion. This is because it is derived from the centripetal acceleration formula, which is only applicable to circular motion where the acceleration is always directed towards the center of the circle.

4.

What are the units of measurement for V^2/r?

The units of measurement for V^2/r depend on the units used for velocity and radius. For example, if the velocity is in meters per second (m/s) and the radius is in meters (m), then the units for V^2/r would be m^2/s^2/m = m/s.

5.

How can I apply V^2/r to real-life situations?

V^2/r can be applied to real-life situations such as calculating the speed of a satellite orbiting around the Earth or determining the force needed to keep a car on a curved track. It is a useful tool in understanding circular motion and its applications in various fields of science and engineering.

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