## Statement

difficulty

Two bodies have acceleration 6 m/s2 y 9 m/s2 respectively, if they are under the same force. What is the relationship between masses?

## Solution

Data

• Acceleration of the first body a1 = 6 m/s2
• Acceleration of the second body a2 = 9 m/s2
• Force acting on the first body F1
• Force acting on the second body F2

Resolution

The heading tells us the force acting on the first body and the force acting on the second one is the same, so:

${F}_{1}={F}_{2}$

The relation, m1/m2 we can find it applying Newton´s second law ( F=m·a ), and assuming the mass does not vary while the force is acting, we have:

${m}_{1}·{a}_{1}={m}_{2}·{a}_{2}⇒\frac{{m}_{1}}{{m}_{2}}=\frac{{a}_{2}}{{a}_{1}}⇒\frac{{m}_{1}}{{m}_{2}}=\frac{9}{6}=\frac{3·\overline{)3}}{2·\overline{)3}}=\frac{3}{2}$

In another way, we can say the mass of the first body is one time and a half the mass of the second body ( m1=m2·1.5 ).

Note: Observe that we worked throughout the whole problem by using the magnitudes of forces and acceleration, without taking into account its vector nature. Actually, because ${\stackrel{\to }{F}}_{1}={\stackrel{\to }{F}}_{2}$, the accelerations will have the same direction and we can use their magnitudes to find the relation requested.

## Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
Related sections
$F=m·a$