Forces of 4.57 N and 4.74 N act at right angles on a reddish-green block of mass 5.76 kg. How much acceleration occurs?
To find the acceleration, we need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
First, let's determine the net force acting on the block. Since the two forces are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the net force.
The formula is given by:
Net Force = √(Force₁² + Force₂²)
Net Force = √(4.57² + 4.74²)
Net Force = √(20.8849 + 22.5076)
Net Force = √43.3925
Net Force ≈ 6.59 N
Now we can calculate the acceleration using Newton's second law. The formula is:
Acceleration = Net Force / Mass
Acceleration = 6.59 N / 5.76 kg
Acceleration ≈ 1.14 m/s²
Therefore, the acceleration of the reddish-green block is approximately 1.14 m/s².