Forces of 3 N and 4 N act the right angles on a block of mass 5 kg. Show that the resulting acceleration is 1 m/s².
To find the resulting acceleration of the block, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the vector sum of the individual forces acting on the block.
Given that the forces of 3 N and 4 N act at right angles, we can treat them as perpendicular components of a single force vector. Let's denote the force of 3 N as F₁ and the force of 4 N as F₂.
To find the resulting acceleration, we need to determine the net force acting on the block. We can use the Pythagorean theorem to find the magnitude of the resultant force:
Magnitude of the resultant force (F) = √(F₁² + F₂²)
Plugging in the values, we get:
F = √(3² + 4²)
F = √(9 + 16)
F = √25
F = 5 N
Now that we have the magnitude of the resultant force (F = 5 N), we can use Newton's second law to find the acceleration. Rearranging the equation, we have:
Acceleration (a) = F / mass
Plugging in the values, we get:
Acceleration (a) = 5 N / 5 kg
Acceleration (a) = 1 m/s²
Therefore, the resulting acceleration of the block is 1 m/s².