Why Does Friction Work Appear Negative in Dynamics Problems?

[xzibition8612]

Homework Statement

See attachments.

Homework Equations

The Attempt at a Solution

In Example 2.11, why is the work for friction -6(10+Δ)? Why is it negative 6?

In Example 2.12, again why is the friction -6, and then where did (Δ-d) come from? I thought Δ is the distance the spring is initially compressed, and d is the distance of its maximum extension? So why minus? And also in this example why is there a negative sign in front of the work for weight? Totally confused about orientations in this problem.

 

[rude man]

Too hard to read your attachments.

 

[xzibition8612]

you sure do live up to your moniker. mods please ban this guy

 

[LawrenceC]

I can see where the way the solution is laid out that it might be confusing.


I always look at it from the first law of thermodynamics. With this problem, consider energy at the start and then at the end of the process. Put the terms on opposite sides of the equals sign.

Remember that if the system is doing work (such as overcoming friction) it will subtract from the FINAL energy of the system so it should be a negative sign if on that side of the equation.

If work is done on the system, it will add to the final energy of the system so it will add to the FINAL energy in the system. Therefore if you wish to place it on the INITIAL energy side of the equation, it must be negative.

If you think about it in these terms, you'll keep your signs correct.

 

[DeeNos]

In dynamics, work refers to the amount of energy transferred to or from a system as a result of a force acting on it. The work done by a force is calculated by multiplying the magnitude of the force by the distance over which it acts. In the context of Example 2.11, the work for friction is negative because the force of friction is acting in the opposite direction of the displacement, resulting in a negative displacement. The value of -6 represents the magnitude of the force of friction multiplied by the distance over which it acts.

In Example 2.12, the friction force is again negative because it is acting in the opposite direction of the displacement. The value of (Δ-d) represents the distance over which the friction force acts, which is the difference between the initial compression distance (Δ) and the maximum extension distance (d). The negative sign in front of the work for weight is because the weight force is acting in the opposite direction of the displacement, resulting in a negative displacement.

In both examples, the negative signs represent the direction of the forces and their corresponding displacements. It is important to pay attention to the orientation of the forces and their corresponding displacements in order to accurately calculate work in dynamics problems.