Assignment 5

course Phy 202

Question: query introset plug of water from cylinder given gauge pressure, c-s hole area, length of plug.

Explain how we can determine the velocity of exiting water, given the pressure difference between inside and outside, by considering a plug of known cross-sectional area and length?

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Your Solution:

From what I gathered from one of the practice problems, Velocity is the area* pressure. If the area decreases, the velocity and pressure will increase.

If we know the Length and Area of the plug, A*L= volume and volume*density= mass

I think next we would need to find the Kinetic Energy since we have all the necessary values.

KE= ½ mv^2

Confidence Rating:1

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Given Solution:

** The net force on the plug is P * A, where A is its cross-sectional area and P the pressure difference.

• If L is the length of the plug then the net force F_net = P * A acts thru distance L doing work `dW = F_net * L = P * A * L.

If the initial velocity of the plug is 0 and there are no dissipative forces, this is the kinetic energy attained by the plug.

The volume of the plug is A * L so its mass is rho * A * L.

• Thus we have mass rho * A * L with KE equal to P * A * L.

Setting .5 m v^2 = KE we have

.5 rho A L v^2 = P A L so that

v = sqrt( 2 P / rho).

Your Self-Critique:

Well I left out some of the elements, but I got the same conclusion I believe.

Your Self-Critique Rating:2

You were on the right track.

&#Your response did not agree with the given solution in all details, and you should therefore have addressed the discrepancy with a full self-critique, detailing the discrepancy and demonstrating exactly what you do and do not understand about the parts of the given solution on which your solution didn't agree, and if necessary asking specific questions (to which I will respond).

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Question: prin phy and gen phy 10.25 spherical balloon rad 7.35 m total mass 930 kg, Helium => what buoyant force

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Your Solution:

Buoyant force is the amount of space an object is taking up by the force of gravity on that object.

We first need to find the volume using the equation for the volume of a sphere

V= 4/3 pi r^3

V= (4/3)*pi*(7.35)^3

V= 1663m^3 which we can convert to 2160 kg.

Thus buoyant force is 2160 kg* 9.8 m/s^2= 20,500 N

Confidence Rating:2

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Given Solution:

** The volume of the balloon is about 4/3 pi r^3 = 1660 cubic meters and mass of air displaced is about 1.3 kg / m^3 * 1660 m^3 = 2160 kg.

The buoyant force is equal in magnitude to the force of gravity on the displaced air, or about 2160 kg * 9.8 m/s^2 = 20500 Newtons, approx.. If the total mass of the balloon, including helium, is 930 kg then the net force is about

• Net force = buoyant force - weight = 20,500 N - 9100 N = 11,400 N

If the 930 kg doesn't include the helium we have to account also for the force of gravity on its mass. At about .18 kg/m^3 the 1660 m^3 of helium will have mass about 300 kg on which gravity exerts an approximate force of 2900 N, so the net force on the balloon would be around 11,400 N - 2900 N = 8500 N approx.

The mass that can be supported by this force is m = F / g = 8500 N / (9.8 m/s^2) = 870 kg, approx.. **

Your Self-Critique:

Did I go far enough in my solution? Because I thought that the question was asking for the buoyant force of the balloon. You went on to find the net force. Do I need to do all of that or is my answer fine?

Your Self-Critique Rating:

3

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&#Good work. See my notes and let me know if you have questions. &#