Given the following 3 equations:
m2 * a2x = T – m2 * gsin(theta), (1)
m1 * a1y = T – m1 * g, (2)
a2x = a1y, (3)
Express a1y in terms of some or all of the variables m1, m2, theta, and g.
The answer is:
a1y = [(m2 * sin(theta) – m1) * g] / (m1 + m2)
The thing is, I am confused as to how that answer was achieved. Can someone please explain to me the steps it takes to get to that answer using the 3 given formulas?
2 Answers

as a2x = a1y, (3)
then from (1) we get
m2*a1y=Tm2*gsin(theta) [substituting the value of a2x by a1y]
………..(4)
and given m1*a1y=Tm1*g…..(2)
now subtracting (4) from (2) we get
(m1+m2)*a1y=m2*gsin(theta)m1*g
or,(m1+m2)*a1y=[m2*sin(theta)m1]*g
[taking g common]
or,a1y=[(m2 * sin(theta) – m1) * g] / (m1 + m2)
[divide both sides by (m1+m2)]
which is the required expression for a1y in terms of m1,m2,
theta and g,
(proved)

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