- #1
Madcat
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Homework Statement
I drew up a little diagram to illustrate the problem.
The goal of this lab report is to find the h value (in cm) for each of the possible masses at B. (one problem for 500g, one for 700g and one for 900g. The only thing that should change is the h value. The leftmost mass never changes)
θ and a are unknown. The pulley on the left is considered to be frictionless and the cords masses are negligible.
Point B is "tied" so the cord does not slide and thus BC is fixed at 60 cm. Length AB however is variable due to the pulley.
Homework Equations
Sin(θ) = opposite/hypotenuses
Cos(θ) = adjacent/hypotenuses
Tan(θ) = opposite/adjacent
The Attempt at a Solution
Here are the equations I've come up with thus far.
Cos(a) = ABx/4.9N
Sin(a) = ABy/4.9N
ABx/Cos(a) = ABy/ Sin(a)
cos(θ) = (105-d)/60 (d being the top side of the left-most triangle, separated at h)
tan(a) = h/d
h = sqrt( (60^2) - ((105-d)^2) )
I can also say that:
BCx = ABx (as this is a static question. B is at rest, thus all resulting forces acting on it are equal to 0)
BCy + ABy - W = 0
or alternatively
BCy + ABy = W
(where W is the current mass of the object at point B)
I "know" the solution lies in the angles, but for the life of me I just can't fit my equations together in order to draw a definite conclusion. I'd love a push in the right direction if anyone can contribute something to this. I keep trying to break down the forces but without an angle it is difficult and I can't find the proper substitution.
First time post here, I hope I did it right, thanks in advance for any help.