Newton's 2nd law problem. I have trouble setting up eq. for gravity/weight

[Sentience]

Homework Statement

http://rwdacad01.slcc.edu/academics/dept/physics/tvanausdal/2210/problems/force/force3.htm

A block is given a push up the incline so it has an initial velocity of 5 m/s up the incline. If the incline angle is 30 degrees and the coefficient of kinetic friction is 0.2, what will be the stopping distance of the block?

Homework Equations

F = m * a

Force of friction = mu * Fn

The Attempt at a Solution

I do just fine until I go to set up the equation for the forces acting in the x direction. When this block is pushed it will move up the incline a bit, then come back down the incline because of friction and gravity. Both of these forces are pointing down in the incline right?

If you click on the solution, my instructor has it set up so both forces are negative. It just seems like going to the right would be the positive x direction.

Could I instead write it out so both are positive?

I feel like I understand everything in these problems just fine, I just set get the sign on one of my components wrong. (usually gravity acting in the horizontal direction) Do you have a foolproof way of setting them up consistently so your signs aren't off?

 

[James98765]

You are struggling with a very common problem. Handling positive and negative signs requires a free body diagram (picture of forces), coordinate system, and experience.

First, you could set up a coordinate system where gravity and friction are positive, but I don't recommend it because the situation becomes more confusing. You should understand that a coordinate system can be pointed in any direction. The x-axis doesn't always point to the right. The person solving the problem decides the most convienent orientation for the coordinate system.

Here is what I would do:
1.) Draw the object with all the forces acting on it. Do not include the anything else (such as the ramp) because the picture just gets more complicated.
2.) Draw the coordinate system with the positive x-axis pointing in the direction that the object is moving and the positive y-axis pointing perpendicular to the surface. Do not assume that the x-axis always has to be to the right and the y-axis has to be vertical.
3.) Break all forces into x and y components. (Respond if you aren't familiar with components. I'll describe them in detail.)
4.) Set up an x force equation by adding all x component forces together. Write them as positive if they are pointing in the positive x direction and negative if they are pointing in the negative y direction.
5.) Repeat Step (4.) for the y force equation.

I attached a sample free body diagram for you to see what I'm talking about.

Let me know if this seems too confusing. I can try and simplify it for you. I'm not sure what your current understanding is.