Finding the Net Force Exerted by Water (of certain depth) on A Dam

The net force on the dam is equal to the weight of the water above it, which can be found by multiplying the density of water (1000 kg/m^3) by the volume of water (60m * w *200m). In summary, to find the net force on a 200m high dam with a 60m water depth, you need to multiply the density of water by the volume of water above the dam. The width of the dam is not necessary for this calculation.
  • #1
Beginner@Phys
9
0

Homework Statement

Evaluate the net force on a 200 -m high dam with a 60 mwater depth.

Homework Equations


P=F/A
p(hydrostatic pressure)=rhogh+patm

The Attempt at a Solution


The atmospheric pressure acts on both the dam and the water, so it cancels out of the equation. g=9.8m/s^2, rho=1,000 kg/m^3,d=60m

F=P*A => dF= integral(rhogh)*(wdy) = rho*g*d*w (y) Integrated from y=0 to y=200
=(1,000 kg/m^3 *9.8m/s^2*60m*200 w )-0

But, I was not given width, so how else can I find the net force acting on the dam. All I know is that it remains constant.
 
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  • #2
Beginner@Phys said:

Homework Statement

Evaluate the net force on a 200 -m high dam with a 60 mwater depth.
Are you sure that 200 m is not the width of the dam? The only height that matters is the depth of the water.

F=P*A => dF= integral(rhogh)*(wdy) = rho*g*d*w (y) Integrated from y=0 to y=200
=(1,000 kg/m^3 *9.8m/s^2*60m*200 w )-0
Not sure what you're doing here.
 
  • #3


I would approach this problem by first clarifying what exactly is meant by "net force on a dam". Is it the force exerted by the water on the dam, or the force exerted by the dam on the water? Both of these forces are present and equal in magnitude but opposite in direction according to Newton's third law.

Assuming that the problem is asking for the force exerted by the water on the dam, I would use the equation F = P*A, where P is the hydrostatic pressure and A is the area of the dam. As you correctly stated, the atmospheric pressure cancels out because it acts on both the dam and the water. However, in order to find the area A, we need to know the width of the dam.

If the width is not given, we can make some assumptions to estimate it. For example, we could assume that the dam is a rectangular shape and use the given height and depth to calculate the width. Or, we could assume that the dam is a certain shape, such as a trapezoid, and use geometry to find the area.

In addition, it is important to consider the direction of the net force. Since the water is exerting a force on the dam in a downward direction, we could also calculate the force using the equation F = m*a, where m is the mass of the water and a is the acceleration due to gravity. This would give the same result as using the hydrostatic pressure equation, but it may provide a clearer understanding of the physical concept behind the net force.

Overall, in order to accurately calculate the net force exerted by water on a dam, we need to know the dimensions of the dam as well as the density and depth of the water. Making assumptions and approximations may help in finding a solution, but it is important to clearly state and justify these assumptions in order to ensure the accuracy of the result.
 

Related to Finding the Net Force Exerted by Water (of certain depth) on A Dam

1. What is the net force exerted by water on a dam?

The net force exerted by water on a dam is the total force that the water exerts on the structure of the dam. This includes both the force of the water pushing against the dam and the force of the dam resisting the water.

2. How is the net force calculated?

The net force is calculated by adding together all the individual forces acting on the dam. This includes the force of the water pushing against the dam, the force of gravity pulling the water down, and any other external forces such as wind or currents.

3. What factors affect the net force exerted by water on a dam?

The net force exerted by water on a dam can be affected by several factors, including the depth of the water, the velocity of the water, the shape and size of the dam, and the properties of the materials used to construct the dam.

4. Why is it important to determine the net force exerted by water on a dam?

Determining the net force exerted by water on a dam is important for understanding the structural integrity and stability of the dam. This information can help engineers and scientists design and maintain dams to withstand the forces of water and prevent potential failures or disasters.

5. How can the net force exerted by water on a dam be minimized?

The net force exerted by water on a dam can be minimized by designing the dam to have a strong and sturdy structure, selecting materials that can withstand high forces, and carefully considering the depth and velocity of the water that the dam will be facing. Regular maintenance and monitoring can also help identify any potential weaknesses or vulnerabilities in the dam's structure.

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