A sled and rider have a total mass of 58.4 kg. They are on a snowy hill accelerating at 0.4g. The coefficient of kinetic friction between the sled and the snow is 0.17. What is the angle of the hill's slope measured upward from the horizontal? You may find a spreadsheet program helpful in answering this question. Can somebody shows me how to get to the answer key? The answer key is 32.9degree

Answer 1

Net force down the hill: F=ma and those are given.
force friction:=mg*mu*sinTheta
net force=ma=mg*cosTheta-mg*mu*sinTheta

so you have to solve
acceleration=g*cosTheta-g*mu*sinTheta or
a/g= cosTheta-mu*sinTheta
You can do this with a spreadsheet, or calculator, or iteration until you zero into the solution.
For a spreadsheet, column 1 angle, then for column two, use this for formula:
cosTheta-mu*sinTheta-a/g
as you vary theta, when column two becomes zero, you have a solution. On many calculators, you can also do the same thing. Yes, you know mu, a, and g. If you have a spreadsheet, use that, and you may have to use the Theta in radians, if so, add a third column converting to degrees.