A force is applied to a 3.2 kg mass and produces 6.1 m/s2 acceleration. What acceleration would be produced by the same force applied to a 9.5 kg mass?

Answer 1

Let's use the GUESS method.

G is for Given. We know the mass of the first object, which we'll call m₁ = 3.2 kg. We are given the acceleration of the first object, a₁ = 6.1 m/s², and the mass of the second object, m₂ = 9.5 kg.

U is for Unknowns. What are we trying to figure out in this problem? We want to know the amount of force that is applied to object 1 and what acceleration that amount of force would produce for object 2.

E is for Equations. Newton's Second Law says that F = ma. The force is the product of the mass and the acceleration. This is true for both objects.

S is for Substitute. We'll take out givens and plug them into the equation. So, plugging them into the following equation we get:

F = m₁a₁

F = (3.2 kg) * (6.1 m/s²) = 19.52 N

The total force is 19.52 Newtons. Now we just need the last S. Solve for a₂

F = m₂a₂

19.52 N = (9.5 kg) *a₂

a = 2.05 m/s²

And there's our answer! The same force that was applied to object 1 would produce an acceleration of about 2.05 m/s² for object 2.