# Need help determining F and n in terms of variables

• blazeuofa
In summary, to determine the magnitude of the force (F) necessary to hold a box of mass (m) against a frictionless wall at an angle θ, the equation F=mg/sinθ should be used. Similarly, to determine the magnitude of the normal force (n), the equation n=F should be used. These equations only require the variables m, θ, and g. It is important to resolve the force into horizontal and vertical components and include the appropriate trigonometric function in the equation.
blazeuofa

## Homework Statement

A box of mass (m) is held against a frictionless wall by a force of magnitude F at an angle $$\theta$$ (above right). Determine F in terms of whatever variables are necessary. Similarly, determine the magnitude of the normal force (n) in terms of whatever variables are necessary. (Hint: you can only have m, $$\theta$$, and g in your answers)

## The Attempt at a Solution

F=ma, a=g
F=mg

n=F?

They want you to resolve the Force into the horizontal and vertical components of force necessary to hold the box with no net force.

If you don't have a sinθ or cosθ in your answer you can be certain it isn't correct.

LowlyPion said:
They want you to resolve the Force into the horizontal and vertical components of force necessary to hold the box with no net force.

If you don't have a sinθ or cosθ in your answer you can be certain it isn't correct.

so Fx=Sin$$\theta$$ and Fy=mg

I know the answer is F=mg/sin $$\theta$$, but I thought you divide Fx by Fy? So why is the answer F=mg/sin $$\theta$$?

Not quite, because they defined the angle θ with respect to "rightward" axis. Hence the component that balances the m*g is going to be the vertical sinθ component.

## 1. What does F represent in this equation?

F represents the force that is acting on an object. It is typically measured in Newtons (N).

## 2. How do you determine n?

n represents the number of variables in the equation. To determine n, count the number of distinct variables present in the equation.

## 3. Can F and n be solved for simultaneously?

Yes, it is possible to solve for both F and n simultaneously by using algebraic manipulation and substitution.

## 4. Are there any specific units for n?

No, n represents the number of variables and does not have a specific unit. It is a dimensionless quantity.

## 5. Can F and n change in different situations?

Yes, the values of F and n can change depending on the specific situation and the variables involved. They are not constant values.

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