Fluids (Find the Force Exerted)

In summary, the task is to find the force exerted by the mercury on a circular plug at the bottom of a tank with a diameter of 2.54 cm and located 37.6 cm below the surface. Using the formula p = \frac{F}{A}, we can find the force if we know the pressure (p), which can be calculated using the density (rho) of the mercury and the acceleration due to gravity (g). The correct answer is 25.4 N, assuming that the pressure above the surface of the tank is zero.
  • #1
Bcisewski
11
0
Need some assistance on what I am missing
"A tank contains mercury, whose density is 13 600 kg/m3. Find the force exerted by the mercury on a circular plug at the bottom of the tank. The plug has a diameter of 2.54 cm, and is located 37.6 cm below the surface of the mercury". The answer is 25.4 N

1) I have tried p=F/A ending with A*p=F or 2.54*136000=F (Wrong)
2) and F=phgA and again the number to big
3) Finally I tried P2=P1+pgh with P1=(1.01x10^-5) again too large of an answer

Am I missing something from try #1?

Thanks for any assistance
 
Physics news on Phys.org
  • #2
Your first attempt is wrong because you used the density in the formula for pressure! :eek: (it's ok...an honest mistake).

pressure (letter 'p'): force per unit area

[tex] p = \frac{F}{A} [/tex]

density (letter 'rho'): mass per unit volume

[tex] \rho = \frac{m}{V} [/tex]

I'm curious...where did you get the answer 25.4 N? Is it given in the book? Because it doesn't specify what the pressure is above the surface of the tank. Assuming it was atmospheric pressure, and using the third formula you tried, I got the wrong answer. But assuming it (p1) was zero, I got the following:

[tex] p_2 = 0 + \rho g h [/tex]

[tex] F = pA = (\rho g h)(\pi r^2) [/tex] = (13 600 kg/m3 )(9.81 N/kg)(0.376m)([itex]\pi[/itex])((0.0254m)/2)2 = 25.4 N

That's the right answer, but the method seems a little off...does the problem give more info about the pressure above the tank?
 
  • #3
cepheid said:
Your first attempt is wrong because you used the density in the formula for pressure! :eek: (it's ok...an honest mistake).

pressure (letter 'p'): force per unit area

[tex] p = \frac{F}{A} [/tex]

density (letter 'rho'): mass per unit volume

[tex] \rho = \frac{m}{V} [/tex]

I'm curious...where did you get the answer 25.4 N? Is it given in the book? Because it doesn't specify what the pressure is above the surface of the tank. Assuming it was atmospheric pressure, and using the third formula you tried, I got the wrong answer. But assuming it (p1) was zero, I got the following:

[tex] p_2 = 0 + \rho g h [/tex]

[tex] F = pA = (\rho g h)(\pi r^2) [/tex] = (13 600 kg/m3 )(9.81 N/kg)(0.376m)([itex]\pi[/itex])((0.0254m)/2)2 = 25.4 N

That's the right answer, but the method seems a little off...does the problem give more info about the pressure above the tank?

You solved it right, cepheid. Below the plug, there is atmospheric pressure too. So that, the force exerted by the atmosphere is canceled at the two sides.
 

1. What is the definition of fluids?

Fluids are substances that can flow and conform to the shape of their container. They include liquids and gases, and are characterized by their ability to take the shape of their container and to flow when subjected to an external force.

2. How is the force exerted by fluids calculated?

The force exerted by fluids can be calculated by multiplying the pressure of the fluid by the area of the surface it is pushing against. This equation is known as pressure = force/area.

3. What factors affect the force exerted by fluids?

The force exerted by fluids depends on the density of the fluid, the depth of the fluid, and the gravitational force acting on the fluid. Additionally, the shape and size of the container, as well as any external forces, can also affect the force exerted by fluids.

4. How does the force exerted by fluids differ between liquids and gases?

The force exerted by liquids is typically greater than that of gases due to their higher density. Liquids also have a fixed volume, while gases can expand to fill their container, leading to a larger force exerted by liquids.

5. What is the significance of understanding the force exerted by fluids?

Understanding the force exerted by fluids is important in various fields such as engineering, meteorology, and medicine. It helps in designing structures that can withstand fluid forces, predicting weather patterns, and understanding the behavior of fluids in the human body.

Similar threads

  • Introductory Physics Homework Help
Replies
24
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
13
Views
2K
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
23
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
4K
  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
5
Views
6K
Back
Top