Friction and Max accleration, please explain this example.

[Yay]

Homework Statement

I'm trying to develop an expression for the maximum accerlation of a person pushing an object up a slope. I've figured out an expression for acceleration using F = MA based on the forces acting on the person and the object. Now I need to find the max accerlation.

We were given a very similar example and solution (same situation, expect the person and the object are on a flat surface). This is an assignment, so I don't want to ask for help on the actual question (pretty sure the uni calls that cheating :P), just the similar example, and hopefully someone will be able to explain what is going on.

Homework Equations

A = F1 - U2kMG / (M1 + M2) subscripts are in lower case letters.

F1 is the frictional force of the person walking
Uxk is mu the coffiecent of kientic friction for object x.
MG is the mass * Gravity

M1 and M2 is the mass of the person and the object.

The solution is then goes:
The acceleration will be a maximum when f1 has reached it maximum at limiting
friction as specified above, when

a = ( U1M -U2M / (M1 + M2) )g

The Attempt at a Solution

I'm only asking for an explanation for a example question and answer.

 

[Doc Al]

There are two horizontal forces acting on the system. The static (not kinetic) friction on the man which acts in the forward direction and the kinetic friction on the box which acts in the backward direction. What's the maximum value of static friction? Apply Newton's 2nd law to the "man + box" system.

 

[thomate1]

I am not asking for help on the actual question.

As a scientist, it is important to understand the concept of friction and its effects on motion. In this example, we are looking at the maximum acceleration of a person pushing an object up a slope. The first step is to understand the forces acting on the system. In this case, we have the force of the person pushing (F1) and the force of friction (f1) acting in the opposite direction. The force of friction is dependent on the coefficient of kinetic friction (Uxk) and the weight of the object (M2g).

Next, we can use Newton's second law (F=ma) to determine the acceleration of the system. This equation states that the net force on an object is equal to its mass times its acceleration. Therefore, the acceleration (a) can be calculated by dividing the net force (F1-f1) by the total mass of the person and object (M1+M2).

To find the maximum acceleration, we need to consider the maximum value for f1, which occurs at the point of limiting friction. This is when the force of friction is equal to the coefficient of kinetic friction (f1=U1k). Substituting this into our equation, we get:

a = (F1-U2kM2)/(M1+M2)

This means that the maximum acceleration will occur when the force of the person pushing (F1) is equal to the maximum frictional force (f1) acting on the object. Solving for a, we get:

a = (U1M1-U2M2)/(M1+M2)g

This is the final expression for the maximum acceleration of the person pushing an object up a slope. It takes into account the forces of the person pushing, the coefficient of kinetic friction, and the masses of the person and object.

In summary, the maximum acceleration of a person pushing an object up a slope is dependent on the force of the person pushing, the coefficient of kinetic friction, and the masses of the person and object. By understanding these concepts and using Newton's second law, we can determine the maximum acceleration of any system.