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Conservative/ Non conservative forces problem

by shaggyace
Tags: conservative, conservative or, forces
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shaggyace
#1
Mar27-12, 01:54 PM
P: 11
Im kind of struggling with some conservative/nonconservative force problems. Someone please help me.

1. The problem statement, all variables and given/known data

A 1.8 kg rock is released from rest at the surface of a pond 1.8 m deep. As the rock falls, a constant upward force of 4.3 N is exerted on it by water resistance. Let y=0 be at the bottom of the pond.
Calculate the nonconservative work, W nc, done by water resistance on the rock, the gravitational potential energy of the system, U, the kinetic energy of the rock, K , and the total mechanical energy of the system, E , when the depth of the rock below the water's surface is 0 .

2. Relevant equations

W=Fd
K=0.5(mv)^2
U=mgd
E=U+K
Wnc=ΔE=Ef-Ei

3. The attempt at a solution

I've been going at this one for almost an hour now. I tried finding the final velocity of the rock first since it starts from rest so that I can find its kinetic energy. To find its non conservative work done by water resistance, I used the Work =force *distance formula and multiplied the force of the water resistance by 1.8 m, but that doesn't seem right. To find its gravitational potential energy, I used the U=mgd formula but got the wrong answer for some reason. For the kinetic energy, I used K=0.5(mv)^2 and used the velocity from the first calculation. To find the total mechanical energy, I added up the potential and kinetic energies. Did I do something wrong? Someone please help me.
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collinsmark
#2
Mar27-12, 06:27 PM
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Quote Quote by shaggyace View Post
Im kind of struggling with some conservative/nonconservative force problems. Someone please help me.

1. The problem statement, all variables and given/known data

A 1.8 kg rock is released from rest at the surface of a pond 1.8 m deep. As the rock falls, a constant upward force of 4.3 N is exerted on it by water resistance. Let y=0 be at the bottom of the pond.
Calculate the nonconservative work, W nc, done by water resistance on the rock, the gravitational potential energy of the system, U, the kinetic energy of the rock, K , and the total mechanical energy of the system, E , when the depth of the rock below the water's surface is 0 .

2. Relevant equations

W=Fd
K=0.5(mv)^2
U=mgd
E=U+K
Wnc=ΔE=Ef-Ei

3. The attempt at a solution

I've been going at this one for almost an hour now. I tried finding the final velocity of the rock first since it starts from rest so that I can find its kinetic energy.
Starting with the final velocity of the rock is not the easiest way to solve this problem. That said, there's nothing keeping you from starting that way, and it may even be useful later to double check your work. What answer did you get? Please show your work of how you got your answer.
Quote Quote by shaggyace View Post
To find its non conservative work done by water resistance, I used the Work =force *distance formula and multiplied the force of the water resistance by 1.8 m, but that doesn't seem right.
Why not?
Quote Quote by shaggyace View Post
To find its gravitational potential energy, I used the U=mgd formula but got the wrong answer for some reason.
What answer did you get? Please show your work.

I'm not quite sure how to interpret the problem statement on this particular part. Do you know, are you supposed to show the gravitational potential energy when the rock is at the top or bottom?
Quote Quote by shaggyace View Post
For the kinetic energy, I used K=0.5(mv)^2 and used the velocity from the first calculation. To find the total mechanical energy, I added up the potential and kinetic energies. Did I do something wrong? Someone please help me.
That last part of the problem statement says, "the total mechanical energy of the system, E , when the depth of the rock below the water's surface is 0." That's different than the total mechanical energy when the rock hits the bottom, because some of the energy was lost to friction by that point (and by the way, when you calculate the rock's total mechanical energy, you need to choose a height and stick with it -- you can't add the mechanical energy when the rock is at the bottom and the gravitational potential energy when the rock is at the top. (If there were no friction, the total mechanical energy would be the same regardless of height, as long as you are consistent with the height. The total mechanical energy is different with different heights, in the case of friction.) In this particular problem, the problem statement tells you to choose the top).


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