A net force of magnitude 36N gives an object of mass m1 an acceleration of 6.0m/s2. The same net force gives m1 and another object of mass m2 fastened together an acceleration of 2.0 m/s2. What acceleration will m2 experience if the same net force acts on it alone?

Question

04-11-2015
Physics

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A net force of magnitude 36N gives an object of mass m1 an acceleration of 6.0m/s2. The same net force gives m1 and another object of mass m2 fastened together an acceleration of 2.0 m/s2. What acceleration will m2 experience if the same net force acts on it alone?

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AL2006 AL2006 · Answer 1 · 2015-11-04T19:14:24-05:00

In working toward the complete solution of this problem,
I'm going to use addition, subtraction, multiplication, and
division. Also, I think I'll be using Newtons 2nd law of motion
like at least fifteen times, so I'll write it here for our review:

   Force = (mass) x (acceleration).

-- When 36 N of force acts on m₁ it accelerates at 6 m/s² .

   36 N = (m₁) x (6 m/s²)

Divide each side by 6 m/s² : m₁ = (36 N) / (6 m/s²) = 6 kg .

-- The same force acting on (m₁+m₂) accelerates them at 2 m/s² .

   36 N = (6kg + m₂) x (2 m/s²)

Divide each side by 2 m/s² : 6kg + m₂ = (36N) / (2m/s²) = 18 kg

Subtract 6kg from each side: m₂ = 12 kg .

-- The same net force acts on m₂ alone:

   36 N = (12 kg) x (acceleration)

Divide each side by 12 kg : Acceleration = (36 N) / (12 kg) = 3 m/s² .