Question

A body of mass 'm' is acted upon by two perpendicular forces 4N and 3N. Find mass 'm' if acceleration of a body is $2\text{ m/s}^2$

Hint:

Whenever forces are given as perpendicular vectors, they naturally form a right-angled triangle.
Recognizing the classic $3-4-5$ Pythagorean triplet instantly saves you from manually calculating the resultant force!

Answer 1

Step 1: Understanding the Concept:
When multiple forces act simultaneously on a single body, the resulting acceleration is caused by the net vector sum of all forces.
Since the two given forces are perfectly perpendicular to each other, their resultant can be found using the Pythagorean theorem.
Step 2: Key Formula or Approach:
The magnitude of the resultant force $F_{\text{net}}$ of two perpendicular forces $F_1$ and $F_2$ is $F_{\text{net}} = \sqrt{F_1^2 + F_2^2}$.
By Newton's Second Law of Motion, the relationship between force, mass, and acceleration is given by $F_{\text{net}} = m \times a$.
Step 3: Detailed Explanation:
The two applied forces are $F_1 = 4\text{ N}$ and $F_2 = 3\text{ N}$.
Calculating the net force acting on the body:
\[ F_{\text{net}} = \sqrt{4^2 + 3^2} \] \[ F_{\text{net}} = \sqrt{16 + 9} = \sqrt{25} = 5\text{ N} \] We are given that the resulting acceleration is $a = 2\text{ m/s}^2$.
Substituting the net force and acceleration into Newton's Second Law formula:
\[ 5 = m \times 2 \] \[ m = \frac{5}{2} = 2.5\text{ kg} \] Step 4: Final Answer:
The mass of the body is $2.5\text{ kg}$.