# Calculating normal force for wedge

• PhySci83
In summary, the formula for normal force between a block and a wedge is N = m*sqrt(g^2-a^2). The attempt at a solution involved using the Pythagorean theorem and expanding the equation to N^2 = m^2(g^2-a^2) before taking the square root to get the final formula.
PhySci83

## Homework Statement

Prove that normal force between a block and wedge is: N = m*sqrt(g^2-a^2)

## Homework Equations

I used the pythagorean theorem to attempt this.

## The Attempt at a Solution

See attached.

Am I doing this right, or am I making up math here to fit the answer?

#### Attachments

• Scan11-06-28 1823.pdf
34.4 KB · Views: 693
I think that is correct but that is only for the given case when a=gsinθ. (Which is correct as your free body diagram is showing)

$F_{N}=F_{g}sin\theta$

Looks right. I assume you are wondering about pulling the m from the square root. It may be the long way around, but try expanding.

$$N^2 = (mg)^2-(ma)^2$$

can be expanded into:

$$N^2 = mmgg-mmaa$$

factor out the m squared:

$$N^2 = mm(gg-aa)$$
$$N^2 = m^2(g^2-a^2)$$

Take the square root of both sides (raise both sides to the half power):

$$N = \sqrt{m^2(g^2-a^2)}$$
$$N = m\sqrt{g^2-a^2}$$

I know this is a long winded response to a relatively simple question, but I am new to helping on the forums and trying to figure out how to use LaTeX. Sorry I am just a beginner myself, but I hope it may give you some insight into the math involved.

## What is normal force for a wedge?

Normal force for a wedge is the perpendicular force exerted by the surface of the wedge on an object in contact with it. It is also known as the support force or contact force.

## How is normal force calculated for a wedge?

Normal force for a wedge is calculated by multiplying the mass of the object by the acceleration due to gravity and the sine of the angle of the wedge's incline. This can be expressed as F_n = m * g * sin(theta), where F_n is the normal force, m is the mass of the object, g is the acceleration due to gravity, and theta is the angle of the wedge's incline.

## Why is normal force important for a wedge?

Normal force is important for a wedge because it helps to keep an object in place on the inclined surface. It counteracts the force of gravity and prevents the object from sliding down the wedge.

## What factors affect the normal force for a wedge?

The normal force for a wedge is affected by the mass of the object, the angle of the wedge's incline, and the acceleration due to gravity. Additionally, any external forces acting on the object can also affect the normal force.

## Can normal force be greater than the weight of an object?

Yes, in some cases the normal force can be greater than the weight of an object. This typically occurs when the angle of the wedge's incline is less than 90 degrees, causing the normal force to increase in order to counteract the weight of the object and keep it in place.

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