Some help - I hope enough
There's really too much information there for me to give you any meaningful specific help without actually doing the problems for you. Let me try giving you some general guidelines.
First off, remember Newton's First and Second Laws: basically, forces cause accelerations and accelerations are caused by forces. Any time you see an object accelerating, there are forces involved somewhere. Similarly, any time forces are applied to objects, accelerations will result unless the forces are balanced by others acting in the opposite direction. (That's an oversimplification, but it's close.)
Gravity acts as a force on any object, particularly if you're talking about objects near the surface of the Earth. If you consider an object sitting on a table, for instance, there is a force due to gravity (called the "weight") pulling it down. Since we observe that the object doesn't fall, there must be a force opposing the weight. This is the force exerted by the surface of the table on the surface of the object. This force always acts perpendicular to the surface, so it is called the "normal force" - normal being mathematician-speak for "perpendicular". Any time an object is resting on a surface, you will have two forces (at least) acting - the weight and the normal force. If the surface is parallel to the surface of the Earth, the two will cancel out exactly.
When you try to move an object along a surface, there is a force between the two surfaces that will resist that motion. This force is called friction. Friction is a complicated process, but we can model it with a reasonable degree of accuracy by saying that there is some number, called the "coefficient of friction", that will give us the frictional force if we multiply it by the normal force between the two surfaces. So, for instance, if we're dealing with a 10.0 kg object sliding along a flat table at a constant speed, with a coefficient of sliding friction of .5, we know that:
1) The weight of the object is mg = (10.0 kg)(9.80 m/s^2 = 9.80 N.
2) The normal force between the two objects must cancel out the weight, so it's also 9.80 N.
3) The frictional force is then (.5)(9.80N) = 4.90 N.
4) Sincer the object is not accelerating ("constant speed" and direction), the net force must be 0 - i.e. the frictional force must be canceled out by something.
5) Therefore, someone or something is pushing the object with a force of 4.90 N in the direction of motion, to cancel the 4.90 N frictional force acting in opposition.
If the object is on an incline, then you'll have to decompose the forces acting into those normal to and parallel to the surface in order to determine the normal force and frictional forces. I didn't look through the problems enough to determine if this is something you need to worry about - if you aren't dealing with inclines, then ignore this.
I hope that helps, at least some. In summary, the equations that express the laws you want to use are:
Newton's Second Law: F = ma, F and a being vectors.
Weight: W = mg, W and g being vectors. (Note that this is the same as Newton's Second Law, specifically for gravitational forces.)
Friction (sliding): F = (mu)N, mu = coefficient of sliding friction, N = normal force. Neither F nor N are vectors here, as the directions are perpendicular.
Friction (static): F < (mu)N, where mu is again the coefficient of friction but a different one from above and N is the normal force. Here, static friction acts to keep things from starting to move. It will increase from 0 to its maximum possible value, at which point the thing starts to slide and we move over into the other regime.
Let me know if this is insufficient. Good luck.
here's what I'm looking at, thanks in advance!
