Understanding Power and Linear Momentum

[darkwolfe5]

So my professor has been kind of lazy lately. he goes through a lot of problems on the chalkboard half way till he says "you can do the rest from here" and a lot of us are raising our hands to ask questions. So there are a number of us not getting the explanations we need to understand what is going on. so here's a couple of questions concerning the current material.

1) When you have a force on an object going either up or down an incline, you have gravity pulling straight down on the object and a function of sin or cos that relates to the force along the incline and the other as a function of your normal force. How can you tell when to use which? I totally messed up a quiz because I got my sin/cos backwards (again).

2) Power is a function of either work$$\frac{}{}time$$, or Force$$\ldots Displacement$$ but I keep having trouble finding the average power required when accelerating an object from rest to a constant speed over a period of time.

for example one of my homework problems is asking me to find the total energy transferred through a motor while pulling an object up a frictionless incline. the object starts at rest and is accelerated to a v and then stays at that speed until it completes the full distance of the incline. I've figured out the power required for keeping it at the constant speed, and the average power needed to get it to that velocity. but I can't figure out how to get the correct energy transferred over the full distance.

Please help me understand since my prof can't seem to be bothered and the tutor center at my school is a joke.

 

[mikelepore]

(1) If the incline is at angle theta from the horizontal, the weight (vector) W of the object will have a component W sin theta = mg sin theta parallel to the incline, which is able to make the object accelerate down the incline, and a component W cos theta = mg cos theta perpendicular to the incline, which the normal force will balance. If the object is free to slide down, instead of the object having acceleration g, as with free fall, it will have acceleration a = F/m = (mg sin theta)/m = g sin theta.

 

[cesiumfrog]

Just imagine that the incline is very slight (that is, theta is nearly zero). Isn't it obvious that the tangential component must be nearly zero, whereas the normal force must be almost one whole of the weight? Then try putting sin and cos of zero in your calculator (or picture the plots of those sinusoidals) to remind you which is which. (Repeat for an incline of nearly 90 degrees, if you need more convincing.)

That was the easy way (which your instructor probably uses), but strictly (for your own understanding) you should be drawing right-angle triangles of the force vector (and its components in a conveniently oriented basis) then apply elementary trig' (recall some mnemonic of sohcahtoa) to solve.

..as for your second question, isn't that just calculus?