# Pressure, force, and Area: Calculating the net Force Applied on A dam by Water

• Beginner@Phys
In summary, the problem asks for an expression for the net force of water on a dam of width w and depth d, given the density p and appropriate constants. The attempt at a solution involves using the equation P=F/A or pressure=Force/Area and the hydrostatic pressure equation p=p_0+pgd, but care must be taken to consider if pressure is the same at every depth. The solution also notes that atmospheric pressure cancels out in the final equation.
Beginner@Phys

## Homework Statement

Water stands at depth d behind a dam of width w . Find an expression for the net force of the water on the dam. Express your answer in terms of the variables w,d,p (density), and appropriate constants.

## Homework Equations

P=F/A or pressure=Force/Area
Hydrostatic pressure: p=p_0+pgd

## The Attempt at a Solution

Fnet=P*A=(pgd)*A =pgd*w*d

I guess that p_0 cancels out, because atmospheric pressure is felt both by the dam and the water. Does this make sense?

Beginner@Phys said:

## The Attempt at a Solution

Fnet=P*A=(pgd)*A =pgd*w*d
Careful. Is the pressure the same at every depth?

I guess that p_0 cancels out, because atmospheric pressure is felt both by the dam and the water. Does this make sense?
That part makes sense.

Yes, your solution is correct. The hydrostatic pressure equation, p=p_0+pgd, takes into account the atmospheric pressure (p_0) and the pressure due to the weight of the water (pgd). Since both the dam and the water are exposed to the same atmospheric pressure, it cancels out in the net force calculation. Therefore, the net force on the dam is simply given by pgd*w*d, where p is the density of water, g is the acceleration due to gravity, d is the depth of the water, and w is the width of the dam.

## 1. What is pressure and how is it related to force and area?

Pressure is the amount of force applied per unit area. It is related to force and area through the formula P = F/A, where P is pressure, F is force, and A is area. This means that as the area decreases, the pressure increases, and as the force increases, the pressure also increases.

## 2. How do you calculate the net force applied on a dam by water?

To calculate the net force applied on a dam by water, you need to first determine the pressure of the water on the dam. This can be done by multiplying the density of water (1000 kg/m^3) by the height of the water above the dam and the acceleration due to gravity (9.8 m/s^2). Then, you can use the formula F = P x A to calculate the force, where F is the net force, P is the pressure, and A is the area of the dam.

## 3. How does the shape and size of the dam affect the net force applied by water?

The shape and size of the dam can greatly affect the net force applied by water. A larger dam with a wider base will have a larger area, thus reducing the pressure and resulting in a smaller net force. On the other hand, a smaller and narrower dam will have a smaller area, leading to a higher pressure and a larger net force. The shape of the dam can also affect the direction of the net force, as a curved dam may distribute the force differently compared to a straight dam.

## 4. What other factors can influence the net force on a dam besides the pressure and area?

Besides pressure and area, other factors that can influence the net force on a dam include the height of the water above the dam, the weight of the water, and the strength and stability of the dam itself. The shape and angle of the dam can also play a role in the distribution and direction of the force applied by the water.

## 5. Why is it important to calculate the net force on a dam?

Calculating the net force on a dam is important for ensuring the structural integrity and safety of the dam. If the net force exceeds the strength of the dam, it can lead to structural failure and potential flooding and damage downstream. By calculating the net force, engineers and scientists can make informed decisions about the design and maintenance of the dam to prevent any potential disasters.

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