# Conservative/ Non conservative forces problem

• shaggyace
In summary: So the problem is, when the rock is at the top, where is the rock? Is it at height y=0, or is it at the surface of the water? In summary, the problem involves a 1.8 kg rock being released from rest at the surface of a pond 1.8 m deep, with a constant upward force of 4.3 N exerted on it by water resistance. The goal is to calculate the nonconservative work done by water resistance on the rock, the gravitational potential energy of the system, the kinetic energy of the rock, and the total mechanical energy of the system when the rock is at the top of the pond (y=0). The equations used are W=Fd,
shaggyace
Im kind of struggling with some conservative/nonconservative force problems. Someone please help me.

## Homework Statement

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 .

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

## 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.

shaggyace said:
Im kind of struggling with some conservative/nonconservative force problems. Someone please help me.

## Homework Statement

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 .

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

## 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.
shaggyace said:
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?
shaggyace said:
To find its gravitational potential energy, I used the U=mgd formula but got the wrong answer for some reason.

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?
shaggyace said:
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).

## 1. What is the difference between conservative and non-conservative forces?

Conservative forces are those that do not dissipate energy and can be fully recovered after the completion of a closed path, while non-conservative forces dissipate energy and cannot be fully recovered after a closed path.

## 2. How do conservative and non-conservative forces affect the motion of an object?

Conservative forces do not affect the total mechanical energy of an object, as energy is conserved in a closed path. Non-conservative forces, on the other hand, decrease the total mechanical energy of an object over time.

## 3. What are some examples of conservative and non-conservative forces?

Examples of conservative forces include gravity and spring force, while examples of non-conservative forces include friction and air resistance.

## 4. How can the concept of work be applied to conservative and non-conservative forces?

Work done by conservative forces results in a change in potential energy, while work done by non-conservative forces results in a change in both potential and kinetic energy.

## 5. Can a system have both conservative and non-conservative forces acting on it?

Yes, a system can have both conservative and non-conservative forces acting on it. In such cases, the total work done on the system is equal to the change in its total mechanical energy.

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