Question

One force magnitude 72 acts on an object. Another force of magnitude on the abject is the magnitude of the resultant force on the object?

Answer 1

The magnitude, let us say, of force 1, F₁=72 units

The magnitude of the force that is acting at a right angle, F₂= 52 units

Let us assume that force 1 is acting along the positive x-axis and the second force is acting along the positive y-axis.

In the vector form, we can write,

`\begin{gathered} \vec{F_1}=72\text{ }\hat{\text{i}} \\ \vec{F_2}=52\text{ }\hat{\text{J}} \end{gathered}`

Thus the sum of these two forces will be,

`\begin{gathered} \vec{F}=\vec{F_1}+\vec{F_2} \\ =72\text{ }\hat{\text{i}}+52\text{ }\hat{\text{j}} \end{gathered}`

The magnitude of a vector

`\vec{A}=\vec{B}+\vec{C}`

is given by,

`A=\sqrt[]{B^2+c^2}`

Therefore the magnitude of vectr F is given by,

`\begin{gathered} F=\sqrt[]{F^2_1+F^2_2} \\ \end{gathered}`

On substituting the known values in the above equation,

`\begin{gathered} F=\sqrt[]{72^2+52^2} \\ =88.81\text{ units} \end{gathered}`

Thus the magnitude of the resultant vector is 88.81 units