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Question

m₁g-m₂g=(m₁+m₂)a

Solve for m₁

Answer 1

m₁g-m₂g=(m₁+m₂)a Distribute the a to get rid of the parenthesis

m₁g-m₂g=am₁+am₂ Need to get the m₁ to one side of the equation and everything else to the other side. Add m₂g to both sides

m₁g-m₂g +m₂g=am₁+am₂ +m₂g Simplify

m₁g=am₁+am₂ +m₂g Subtract am₁ from both sides of the equation

m₁g-am₁=am₁+am₂ +m₂g-am₁ Simplify

m₁g-am₁=am₂ +m₂g Factor out m₁ on the left

m₁₍g-a)=am₂ +m₂g Divide both sides by g-a to isolate m₁

m₁₍g-a)/(g-a)=(am₂ +m₂g)/(g-a) Simplify

m₁=(am₂ +m₂g)/(g-a)

Answer 2

m1g - m2g=(m1 + m2) a Step 1: expand right side

m1g - m2g = m1a + m2a Step 2: subtract m1a from both sides

m1g - m1a - m2g = m1a + m2a Step 3: add m2g to both sides

m1g -m1a = m2g + m2a Step 4: factor out m1 on left side

m1 (g - a) = m2g + m2a Step 5: divide both sides by (g - a)

Answer:

m1= (m2g + m2a)/(g - a)