# Solving for Min Speed on Loop-the-Loop Rides

• Anne Armstrong
In summary: The car is trying to push through the top of the loop. Since the car is trying to push through the top of the loop, the normal force is the same as the force of gravity, m*g.
Anne Armstrong

## Homework Statement

In a loop-the-loop ride a car goes around a vertical, circular loop at a constant speed. The car has a mass m = 260 kg and moves with speed v = 15 m/s. The loop-the-loop has a radius of R = 10 m. What is the minimum speed of the car so that it stays in contact with the track at the top of the loop?

ac=v2/r
F=ma

## The Attempt at a Solution

At the top of the loop, the forces acting on the car are Fgravity, FNormal, and Fcentrifugal (I think). So I think the minimum speed would be one that made all the forces cancel to zero (aka, Fc is just strong enough to counteract Fgravity and FNormal). If that's true, then Fc=FN+Fg. Since Fc=m*ac=v2/r , so far I have: m*ac=v2/r = m*g+m*g.
..but I don't think that makes sense... Is FN in this case equal and opposite to Fc?

If the car is only just staying in contact, what will the normal force equal? Remember, this the force the track and car exert on each other.

The normal force will equal the force of gravity, m*g?

Anne Armstrong said:
The normal force will equal the force of gravity, m*g?
Why would it have to be that?
A normal force is the reaction that results when attempting to push an object through something that resists. When you place an object on solid ground, the weight of the object acts to push the object through the floor. The normal force is the reaction necessary from the floor to prevent it. When you place on object on an incline, only part of the weight is trying to push the object into the incline, so the normal force is less. In this case, what is trying to push the object through the top of the loop?

## 1. What is the formula for solving for minimum speed on a loop-the-loop ride?

The formula for solving for minimum speed on a loop-the-loop ride is v = √(rg), where v is the minimum speed, r is the radius of the loop, and g is the acceleration due to gravity.

## 2. How do you determine the radius of the loop on a loop-the-loop ride?

The radius of the loop can be determined by measuring the distance from the center of the loop to the top of the loop.

## 3. What is the minimum speed required for a loop-the-loop ride to be safe?

The minimum speed required for a loop-the-loop ride to be safe depends on the radius of the loop. As a general rule, the minimum speed should be at least 4 times the square root of the radius multiplied by the acceleration due to gravity.

## 4. Can you use the same formula to solve for minimum speed on all loop-the-loop rides?

Yes, the same formula can be used for all loop-the-loop rides as long as the radius and acceleration due to gravity are known.

## 5. What factors can affect the minimum speed required for a loop-the-loop ride?

The minimum speed required for a loop-the-loop ride can be affected by factors such as the radius of the loop, the mass and size of the rider, and friction between the ride and the track. Wind speed and direction can also affect the minimum speed required.

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