Question

Newton's Second Law of Motion is represented by the equation, F=ma, which shows the relationship of force, mass, and acceleration. If the force acting on an object remains the same, but the object's mass is tripled how will the acceleration of that object change? A. Acceleration remains the same. B. Acceleration will be three times the original value. C. Acceleration remains at 9.8 m/s due to gravity. D. Acceleration will be one-third the original value.

Answer 1

Well, we can look at a hypothetical example of the Fnet equation:

1 - the original amount of the variable for object.
3 - the amount the mass is changed

Fnet = ma
1Fnet = 3m(_a)

What will acceleration have to be to equal the initial amount of force, Fnet, after multiplying by 3 times the mass? It would have to be 1/3.

Since:
1Fnet = 3m(1/3a)
1 • Fnet = 3 • 1/3 m • a
Look at the numbers only, do they equal after doing the operation? Yes.

1 = 3 • 1/3
1 = 3/3
1 = 1.

So in order for the force acting on the object to remain the same, but the mass is tripled, the acceleration will be 1/3 the original value of whatever acceleration was.

The solution is D.