Final answer:
The magnitude of the acceleration of a 20 kg body acted upon by two perpendicular forces of 3 N and 4 N is 0.25 m/s², calculated using vector addition and Newton's second law of motion.
Step-by-step explanation:
To determine the magnitude of the acceleration of a body caused by forces acting at right angles, we use the principles of Newton's second law of motion (F = ma), where F is the net force acting on the mass m producing an acceleration a. In this case, the net force must be calculated using vector addition since the forces are perpendicular to each other.
First, we find the resultant force using the Pythagorean theorem:
- Resultant force (FR) = √(F1² + F2²) = √(3² + 4²) N = √(9 + 16) N = √25 N = 5 N
Next, we apply Newton's second law to find the acceleration:
- Acceleration (a) = FR / m = 5 N / 20 kg = 0.25 m/s²
The magnitude of the acceleration of the body is 0.25 m/s².