Physics question?

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

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3 Answers

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  • 3 weeks ago
    Best 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))

    • oldprof
      Lv 7
      3 weeks agoReport

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

  • 3 weeks ago

    Can't be done. That's why the other two answers did not answer the question.

  • 3 weeks ago

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

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