open qa 26

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course phy 201

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution.

If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

026. More Forces (buoyant)

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Question: `q001. Note that this assignment contains 3 questions.

. Water has a density of 1 g per cm^3. If an object is immersed in water, it experiences a buoyant force which is equal to the weight of the water it displaces.

Suppose that an object of mass 400 grams and volume 300 cm^3 is suspended from a string of negligible mass and volume, and is submerged in water. If the mass is suspended in equilibrium, what will be the tension in the string?

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Your solution:

1 g per cm^3

400 g

volume 300 cm^3

tension is force ?

F = ma

F = 400 g 300 cm^3 = 1200 gcm^3

confidence rating #$&*:

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Given Solution:

The 400 g mass will experience a downward gravitational force of .4 kg * 9.8 meters/second^2 = 3.92 Newtons. It will also experience in upward buoyant force equal to the weight of the 300 cm^3 of water it displaces. This volume of water, at 1 g per cm^3, will have a mass of 300 grams and therefore a weight of .3 kg * 9.8 meters/second^2 = 2.94Newtons.

The forces acting on the mass are therefore the downward 3.92 Newtons of gravity, the upward 2.94 Newtons of the buoyant force and the tension, which we will call T, in the string. Since the system is in equilibrium these forces must add up to 0. We thus have

-3.92 Newtons + 2.94 Newtons + T = 0, which has solution

T = .98 Newtons.

In common sense terms, gravity pulls down with 3.92 Newtons of force and the buoyant force pushes of with 2.94Newtons of force so to keep all forces balanced the string must pull up with a force equal to the .98 Newtondifference.

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Self-critique (if necessary):

weight of .3 kg * 9.8 meters/second^2 = 2.94Newtons.

how do you know -3.92 Newtons is negative? because it’s going opposite?

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Self-critique rating: 2

@& The given solution didn't explicitly declare the downward direction to be negative, but in this situation that was regarded as implicit. It would have been better to declare it explicitly.

In any case the 3.92 N and 2.94 N forces are in opposite directions, so one has to be positive and the other negative. Had the downward direction been positive the equation would have had to be

3.92 N - 2.94 N + T = 0*@

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Question: `q002. A solid cylinder has a cross-sectional area of 8 cm^2. If this cylinder is held with its axis vertical and is immersed in water to a depth of 12 cm, what will be the buoyant force on the cylinder?

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Your solution:

8 cm^2

12 cm

f = m a

find mass? then multiply by 9.8 m/s^2 because that is the acceleration

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Given Solution: 2

At a depth of 12 cm, the volume of the immersed portion will be 12 cm * 8 cm^2 = 96 cm^3. This portion will therefore displace 96 grams of water. The weight of this displace water will be .096 kg * 9.8 meters/second^2 = .94Newtons. This will be the buoyant force on the cylinder.

STUDENT COMMENT: oh so the water above the cylander is displaced. i guess the cylander reaches this distance to the surface and maybe higher.

INSTRUCTOR RESPONSE: The mechanism isn't specified here, but you are told that the cylinder is immersed to depth 12 cm. The cylinder might be held there by some other force, it might be bobbing up or sinking down at a certain instant, etc.. As long as it displaces 96 cm^3 of water, the buoyant force will be as calculated.

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Self-critique (if necessary):

At a depth of 12 cm, the volume of the immersed portion will be 12 cm * 8 cm^2 = 96 cm^3. This portion will therefore displace 96 grams of water. The weight of this displace water will be .096 kg * 9.8 meters/second^2 = .94Newtons. This will be the buoyant force on the cylinder.

Should have thought more. Need more practice. so 1 g = 1 cm^3?

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Self-critique rating: 3

@& Water has a density of 1 gram per cm^3. This should be general knowledge, as should the fact that 1 liter of water is 1000 cm^3 and has a mass of 1 kilogram.

The main point of the physics here is that the buoyant force is the weight of the displaced fluid. The given solution finds the volume of the cylinder, the mass of that volume of water, and then the weight of the water.

*@

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Question: `q003. The solid cylinder in the preceding problem has a total length of 18 cm and a mass of 80 grams. If the cylinder is immersed as before to a depth of 12 cm then released, what will be the net force acting on it at the instant of release?

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Your solution:

18 cm

80 g = .08 kg

f=ma

18 cm - 12 cm = 6 cm

6 cm * 8 cm^2 = 48 cm^3

48 cm^3 = . 048 kg

.08 kg x 9.8 m/s^2 = .784 N

confidence rating #$&*:

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Given Solution:

The buoyant force on the cylinder is still .94 Newtons, directed upward. Gravity exerts a downward force of .080 kg * 9.8 meters/second^2 = .79 Newtons, approximately. The net force on the cylinder is therefore .94 N - .79 N = .15 N, directed upward. This will give its 80 gram mass and acceleration a = F / m = .15 N / .080 kg = 1.875 m/s^2.

Note that as the cylinder rises less and less of its volume is submerged, so the buoyant force will decrease while the weight remains the same. Until the buoyant force has decreased to become equal and opposite to the weight, the net force will continue to be upward and the cylinder will continue to gain velocity. After this instant the cylinder will continue to rise, but the net force will be downward so that the cylinder will begin slowing down. Eventually the cylinder will come to rest and the net downward force will cause it to start descending once more. It will continue descending until the net force is again 0, at which the time it will have a downward velocity that will carry it beyond this point until it again comes to rest and the cycle will start over again.

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Self-critique (if necessary):

what is wrong with my way. I am very confused

how can a net force be 1.875 m/s^2? that’s is an acceleration

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Self-critique rating: 2

@& 1.875 m/s^2 is the acceleration of the object.

The net force is .15 N, as indicated in the given solution.

This force gives the .080 kg mass an acceleration of 1.875 m/s^2.

The acceleration wasn't requested, but having read it in the given solution you would be expected to understand it or to ask, as you did.*@

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Self-critique (if necessary):

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#*&!

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