Question

A 6kg object undergoes an acceleration of 2m/s, what is the magnitude of the resultant acting on it . If this same force is applied to a 4kg object, what acceleration is produced

Answer 1

Answer:

$12\; \rm N$.

$3\; \rm m\cdot s^{-2}$.

Explanation:

By Newton's Second Law, the acceleration of an object is proportional to the size of the resultant force on it, and inversely proportional to the mass of this object.

$\displaystyle \text{acceleration} = \frac{\text{resultant force}}{\text{mass}}$.

Rearrange this equation for the resultant force on the object:

$\text{resultant force} = \text{acceleration} \cdot \text{mass}$.

For the $6\; \rm kg$ object in this question:

$\begin{aligned} F &= m \cdot a \\ &= 6\; \rm kg \times 2\; \rm m \cdot s^{-2} \\ &=12\; \rm N\end{aligned}$.

When the resultant force on the $4\; \rm kg$ object is also $12\; \rm N$, the acceleration of that object would be:

$\begin{aligned} a &= \frac{F}{m} \\ &= \frac{12\; \rm N}{4\; \rm kg} = 3\; \rm m \cdot s^{-2}\end{aligned}$.