Work and conservative forces

In summary, the conversation discusses the concept of work done by a force and how to show that a force is conservative. The discussion includes equations and an attempt at a solution, but it is suggested to start with definitions for a better understanding.
  • #1
zoner7
90
0

Homework Statement


none...

Suppose a force acts on an object. the force does not vary with time, nor with the position or velocity of the object. Start with the general definition of work done by force, and show that the force is conservative

Homework Equations


W = FX
Wnonconservative = KE final PE final - KE initial - KE final

The Attempt at a Solution


I started with W = FX
W = E final - E initial
E = KE f + PE f - KE i - PE i
W = 0 + PE f - O - PE i Since KE is a non-conservation force and there is only a conservative force.
W = PE f - PEi Since PE f = PE i if PE is a conservative force
w = 0

The answer doesn't make any sense... Any suggestions?
 
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  • #2
Hi zoner7,

zoner7 said:

Homework Statement


none...

Suppose a force acts on an object. the force does not vary with time, nor with the position or velocity of the object. Start with the general definition of work done by force, and show that the force is conversation.

Homework Equations


W = FX
Wnonconservative = KE final PE final - KE initial - KE final


The Attempt at a Solution


I started with W = FX
W = E final - E initial
E = KE f + PE f - KE i - PE i
W = 0 + PE f - O - PE i Since KE is a non-conservation force and there is only a conservative force.

This line not true. Saying that KE is a non-conservative force is not true.


I would suggest you start with some definitions. What is the general formula for the work done by a force? And also, what is the definition of a conservative force?
 
  • #3


Your attempt at a solution is on the right track, but there are a few mistakes. Here is a corrected solution:

Starting with the definition of work done by a force, we have:

W = ∫ Fdx

Since the force is not dependent on time, position, or velocity, we can write it as:

F = F(x)

Therefore, we can rewrite the integral as:

W = ∫ F(x)dx

Now, by the fundamental theorem of calculus, we know that the integral of a function is equal to the difference in its values at the endpoints. Therefore, we can write:

W = F(x2) - F(x1)

Since the force does not vary with position, we can write:

F(x2) = F(x1) = F

Substituting this into the equation for work, we get:

W = F - F = 0

This shows that the work done by the force is equal to 0, which means that the force is conservative.

To further prove that the force is conservative, we can also use the work-energy theorem, which states that the work done by all forces on an object is equal to the change in its kinetic energy. Since the work done by the conservative force is 0, the change in kinetic energy must also be 0. This means that the object's kinetic energy remains constant, which is a characteristic of conservative forces.

In conclusion, we have shown that the force is conservative by using the definition of work and the work-energy theorem.
 

1. What is "work" in the context of physics?

Work is a measure of the energy transferred to an object by a force acting on that object. It is calculated by multiplying the magnitude of the force by the distance the object moves in the direction of the force.

2. What are conservative forces?

Conservative forces are forces that do not depend on the path taken by an object, but rather only on its initial and final positions. Examples include gravity, electrostatic forces, and elastic forces.

3. How is work related to conservative forces?

Work done by a conservative force is independent of the path taken by an object. This means that the total work done by a conservative force on an object is the same regardless of the path the object takes from its initial to final position.

4. What is the relationship between work and energy?

Work is directly related to the change in an object's energy. When work is done on an object, it gains energy, and when work is done by an object, it loses energy. This is known as the work-energy theorem.

5. Can work be negative?

Yes, work can be negative. This occurs when the force and displacement are in opposite directions, resulting in the object losing energy. For example, when a person lifts an object and then sets it back down, the work done by gravity is negative because the force of gravity is acting in the opposite direction of the displacement.

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