# Normal Reaction in the following cases

• Kasul
In summary, the normal reaction is maximum at the highest point on the track where the centripetal force is downward.
Kasul

## Homework Statement

A small block is shot into each of the four tracks as shown below. Each of the tracks rise to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal Reaction is maximum in which track?

2. Homework Equations

At the highest point, N - mg = (mv^2)/r
So, N = (mv^2)/r + mg

## The Attempt at a Solution

I don't understand how the curvature of the track affects the normal reaction. I suppose it can't be option 3 and option 4 because those have greater radius and using the above mentioned formula, the normal reaction will be less. But why is the answer 1 when option 1 and 2 seem to have the same radius?

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Kasul said:
But why is the answer 1 when option 1 and 2 seem to have the same radius?
Fair question. They certainly look like the same radius, the only difference being that 1 continues further along the downward curve. Since that's beyond the highest point, it cannot affect anything at the highest point. The only other possibility is that the radii are not the same, they just look it to the unaided eye, but that would make it a poor question.

I'm sure it must have something to do with one track being extended but I don't know what difference that makes. Either that or the person that framed the question made a mistake.

Kasul said:
I'm sure it must have something to do with one track being extended but I don't know what difference that makes. Either that or the person that framed the question made a mistake.
I'm certain it is a flawed question.

Kasul
Kasul said:

## Homework Statement

A small block is shot into each of the four tracks as shown below. Each of the tracks rise to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal Reaction is maximum in which track?

2. Homework Equations

At the highest point, N - mg = (mv^2)/r
So, N = (mv^2)/r + mg

At the highest point, the direction of the centripetal force is downward, the resultant of gravity and the normal force, both downward. (mv^2)/r=N+mg, so N= (mv^2)/r - mg. So where can be the normal force maximum? At the smallest or greatest radius of curvature?

ehild said:
At the highest point, the direction of the centripetal force is downward, the resultant of gravity and the normal force, both downward. (mv^2)/r=N+mg, so N= (mv^2)/r - mg. So where can be the normal force maximum? At the smallest or greatest radius of curvature?
Are you suggesting that options 1 and 2 have different radii at their highest points? Doesn't look that way to me.

I suggested that the OP's equation for the normal force was wrong .
One peak of curves 1 and 2 looks a bit wider than the other one for me, but not considerably. I agree that it is a poorly presented question.

## 1. What is normal reaction?

Normal reaction, also known as normal force, is the force exerted by a surface on an object that is in contact with it. It is perpendicular to the surface and counteracts the weight of the object.

## 2. How is normal reaction calculated?

The normal reaction force can be calculated using the equation R = mg, where R is the normal force, m is the mass of the object, and g is the acceleration due to gravity.

## 3. What is the significance of normal reaction?

The normal reaction force is important in maintaining the equilibrium of an object on a surface. It prevents objects from falling through surfaces and allows for stability in structures.

## 4. How does normal reaction differ from other types of forces?

Normal reaction is different from other forces, such as friction or tension, because it is always perpendicular to the surface and does not cause any motion. It only prevents an object from penetrating the surface.

## 5. Can normal reaction ever be greater than the weight of an object?

Yes, in certain cases, the normal reaction force can be greater than the weight of an object. This can occur when an object is accelerating or when there are other external forces acting on the object.

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