Write up a solution involving clearly the 4 steps of the problem-solving process

Question

Write up a solution involving clearly the 4 steps of the problem-solving process Identify, Setup, Execute, Evaluate. At your job at a warehouse, you have designed a method to help get heavy packages up a 15 degree ramp. The package is attached to a rope that runs parallel to the ramp and passes over a pulley at the top of the ramp. The other end of the rope is attached to a counterweight that hangs straight down. The mass of the counterweight is always adjusted to be twice the mass of the package. However, your boss is worried that the acceleration of the package will make it too difficult to handle at the top of the ramp and tells you to calculate it. To determine the influence of friction on the package by the ramp, you run some tests and find that using a horizontal force of 250 Newtons, you can push a 50 kg package at a constant speed along a level floor made of the same material as the ramp.

Explanation / Answer

We need to find the coefficient of friction (u) between the box and the surface.
fr = u fn
fr = f
fn = m g

substitute

f = u m g
u=f/(mg)
u = 250/(50 * 9.8) = 0.51

Now lets look at the ramp
f = m a
a = f/m
a = (frope - frict)/m
frope = 2m
frict = u fn
fn = m g cos 15
frict = u m g cos 15
a = (2m - u m g cos 15)/m
a = 2 - u g cos 15
a = 2 - .51*9.8 cos 15
a = 5.798 m/s^2

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