Stupid physics problem.

[Gary Dillard]

I don't know what you've already covered in Physics, but before I answer your problems you'll have to indulge me in a story......
I took Physics my freshman year of college, and we had 3 exams which were all worth 33 points. The class average on each one was about 12; the second highest score on each one was 18-19; one kid got a 33 on the first test and a 32 on the second; he didn't have to take the final. I remember looking at the problems in my Physics book with a blank dumb stare - how were we expected to understand this stuff?
Fast forward 3 years. I walked into a room of a freshman, he had the exact same Physics text book and the exact same blank dumb stare on his face. I looked at what he was doing, showed him how to solve the problems in about 5 minutes, and he thought I was some kind of genius. That's when I realized that it just takes alot of practice and exposure to different methods for it to sink in. We covered the same material in Physics, then Statics, then Dynamics, then strength of materials, then machine design, then mechanics - when you use the same stuff in different applications somewhere along the line it sinks in. I'm not sure when it did for me, but it did. So don't give up.

Anyway, for both of these problems you need to draw a free body diagram, which shows all of the forces acting on a system or body. If they equal zero, you have a statics or constant velocity problem. If they don't equal zero, you have a dynamics problem.

Number 1a: constant velocity means forces up equals forces down.
Total force acting down = m*g
Total forces acting up (I'm assuming there's a single pulley at the top) equals F {the tension in the rope pulling on the bucket} + F {the tension in the rope pulling on your hands, which equals the force you are pulling on the rope}. Note that the tension along any point on the rope is equal to F. Therefore, 2*F=mg, F=mg/2 = (64)*9.81/2 = 314 Newtons
Number 1b: I'm guessing you meant increase force by 14%, but it doesn't matter.
Total force acting down = m*g
Total forces acting up = 2*F*1.14 = m*g*1.14
Difference = m*g*(1.14-1) = m*g*.14 = net force
Since F=m*a, m*a=m*g*.14, or a = .14g or 1.373 m/s^2

Number 2: sum forces normal to the plane
F = m*g*cos(34)
sum forces parallel to the plane
m*g*sin(34) - (mu)*(F) = m*a, or
m*g*sin(34) - (mu)*m*g*cos(34) = m*a
The mass term falls out
[9.81*sin(34)-(.03)]/[9.81*cos(34)] = .67 = mu