# Newton’s 2nd Law Problem, How To?

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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.

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?

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• as a2x = -a1y, (3)

then from (1) we get

-m2*a1y=T-m2*gsin(theta) [substituting the value of a2x by a1y]

………..(4)

and given m1*a1y=T-m1*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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