An object with a mass m1 accelerates at 8.0 m/s2 when a force F is applied. A second object with a mass m2 accelerates at 4.0 m/s2 when the same force F is applied to it.

Answer 1

This is a question over Newton's 2nd law of motion (F_net = ma).

a) To find the ratio of m₂ / m₁ , write Newton's second law for each mass:

Object 1: F_net = F = m₁*(8 m/s²) - eq. 1

Object 2: F_net = F = m₂*(4 m/s²) - eq. 2

Now, set the two equations equal to each other using F:

m₁*(8 m/s²) = m₂*(4 m/s²)

m₂ / m₁ = 2 .

Intuitively, this means that the object that accelerates at half the speed has twice the resistance to motion, or twice the inertia.

b) Write Newton's second law for the combined mass system:

F_net = F = (m₁ + m₂)a - eq. 3

Now solve for m₁ and m₂ in equation 1 and 2 (from part a), and plug into equation 3 for the combined mass system:

F = (F/8 + F/4)a

Simplifying, we get:

F = (3F/8)a

Solving, we get:

a = 8/3 m/s² = 2.67 m/s²