Fluid mechanics cork in water

In summary, a cork with a density of 157 kg/m3 and a volume of 3 cm3 is held at a depth of 0.713786 m in a bucket of water. Using the equations d=m/v and Fb=weight of displaced fluid, the tension in the string is calculated to be 247.842 N. However, there is a mistake in the units used for the volume of the cork, as 3 cm3 is not equal to 0.03 m3. This results in an incorrect answer and highlights the importance of using correct units in calculations.
  • #1
DLH112
20
0

Homework Statement


A cork is held at the bottom of a bucket of
water by a piece of string. The actual depth
of the cork is 0.713786 m below the surface of
the water.

If the density of the cork is 157 kg/m3
and the volume of the cork is 3 cm3
, then what is the tension in the string? The acceleration
of gravity is 9.8 m/s
2
. Assume the density of
water is 1000 kg/m3
.


Homework Equations


d= m/v Fb= weight of displaced fluid


The Attempt at a Solution


The tension should be the force required to keep it in equilibrium...
using d=m/v, into dv = m (1000)(0.03) = 30 kg (mass of displaced water)(9.8)
weight of displaced water = Fb = 294 N
using dv = m again for the cork. (157)(0.03) = 4.71 kg (9.8) = 46.158 N

294 - 46.158 = 247.842 N .
Its a multiple choice answer and the choices are either that number but the decimals in the wrong place (all the answers are smaller), or 0.0123921 N.
maybe I'm supposed to use the depth and P=pgh somehow if that other numbers right, but I'm not sure how it would apply to this problem.
 
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  • #2
Units, Units, Units!

3 cm^3 is not the same as 0.03 m^3

You are essentially saying that 3 cc of water has a mass of 30 kg!
 
  • #3
that makes sense... so it would be like (0.03)^3 then i guess
 
  • #4
Looks like the problem setter didn't think of this particular mistake, or there would have been a choice to match.
 
  • #5




Based on the given information, the tension in the string can be calculated using the equation Fb = mg, where Fb is the buoyant force, m is the mass of the displaced water, and g is the acceleration of gravity. The buoyant force is equal to the weight of the displaced water, which can be calculated using the density of water and the volume of the cork.

First, we can calculate the mass of the displaced water using the density of water and the volume of the cork. This gives us a value of 0.03 kg. Next, we can calculate the weight of the displaced water by multiplying the mass by the acceleration of gravity, giving us a value of 0.294 N.

Next, we can calculate the weight of the cork using the density and volume given. This gives us a value of 0.00471 N. To find the tension in the string, we can subtract the weight of the cork from the weight of the displaced water, giving us a final value of 0.28929 N.

It is possible that the decimals in the given answer choices are incorrect. Additionally, it is important to note that the depth of the cork in the water may affect the tension in the string, as the pressure at different depths can vary and affect the buoyant force. However, without knowing the specific shape and dimensions of the cork, it is not possible to accurately calculate this effect.
 

1. What is the purpose of using a cork in water in fluid mechanics experiments?

The use of a cork in water allows for the visualization of fluid flow and the measurement of various properties such as velocity and pressure. It also helps in understanding the behavior of fluids in different situations.

2. How does the cork behave in water under different flow conditions?

The behavior of the cork in water is dependent on the flow conditions, such as the velocity and density of the fluid. At low velocities, the cork will float on the surface of the water. However, at higher velocities, the cork may sink due to the increased pressure exerted by the fluid.

3. How does the shape and size of the cork affect its behavior in water?

The shape and size of the cork can significantly impact its behavior in water. A larger cork will have a greater buoyant force, making it more likely to float. The shape of the cork also affects its drag coefficient, which determines its resistance to flow.

4. What is the relationship between the cork's position in water and the velocity of the fluid?

The position of the cork in water is directly related to the velocity of the fluid. As the fluid velocity increases, the cork will move further downstream due to the increased pressure exerted on it. This can be seen in the formation of a wake behind the cork.

5. How can the use of a cork in water be applied in real-world situations?

The understanding of fluid mechanics and the behavior of objects, such as a cork, in water can be applied in various real-world situations. For example, it can be used in designing efficient watercraft, predicting the flow of river currents, and understanding the effects of water flow on structures such as dams and bridges.

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