Question

. Three newtons are exerted northward on a 10-kg object while 4 newtons are exerted southward. What is the acceleration of the object?

Answer 1

First, find the net force acting on the object by adding the individual forces exerted on it (as vectors):

Take the vectors pointing to the south as negative and those pointing to the north as positive. Then, the magnitude of the net force acting on the object, is:

$F_N_{}=3N-4N=-1N$

Use the magnitude of the net force to find the magnitude of the acceleration using the Newton's Second Law of Motion:

$\vec{F_N}=m\cdot\vec{a}$

Isolate the acceleration from the equation and substitute F_N=-1N and m=10kg:

$\begin{gathered} \Rightarrow\vec{a}=\frac{\vec{F_N}}{m} \\ =\frac{-1N}{10\operatorname{kg}} \\ =-0.1\frac{m}{s^2} \end{gathered}$

The direction of the acceleration is the same as the direction of the net force.

Therefore, the acceleration of the object is:

$0.1\frac{m}{s^2}\text{ southward}$