# Physics question?

How did they eliminate a between equations (1) and (2)? (see photo attached)

### 3 Answers

- 3 weeks agoBest Answer
a)

One step at a time:

T - m₁g = m₁a [1]

rearrange

T = m₁g + m₁a [3]

T - m₂g = -m₂a [2]

rearrange

T = m₂g - m₂a [4]

Equate [3] and [4] to eliminate T

m₁g + m₁a = m₂g - m₂a

gather terms in a and g

m₂a + m₁a = m₂g - m₁g

a(m₂ + m₁) = g(m₂ - m₁)

divide both sides by (m₂ + m₁)

a = g(m₂ - m₁)/(m₂ + m₁)

b)

T - m₁g = m₁a [1]

divide by m₁

T/m₁ - g = a [5]

T - m₂g = -m₂a [2]

-T/m₂ + g = a [6]

equating [5] and [6] to eliminate a

T/m₁ - g = -T/m₂ + g

collect terms in T and g

T/m₁ +T/m₂ = 2g

T(1/m₁ + 1/m₂) = 2g

common denominator m₁m₂

T((m₂ + m₁) / m₁m₂)= 2g

multiply both sides by (m₁m₂ / (m₂ + m₁))

T = 2g(m₁m₂ / (m₂ + m₁))

- MorningfoxLv 73 weeks ago
I would just notice that a = (T - m1g ) / m1 = (T - m2g) / (-m2).

Eh...I still see the "a".

I removed the down thumb when you added the correct solution to your answer.