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 out the acceleration of the block, we need to apply 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 the acceleration of the object. In this case, we have two forces acting on the block, each at right angles to each other.
Let's break down the given information:
Force 1 = 4.57 N (let's say this force is acting horizontally)
Force 2 = 4.74 N (let's say this force is acting vertically)
Mass of the block (m) = 5.76 kg
To find the net force, we need to find the resultant of the two given forces. Since the forces are acting at right angles, we can use the Pythagorean theorem to find the magnitude of the net force.
Using the Pythagorean theorem:
Net force = sqrt((Force 1)^2 + (Force 2)^2)
Net force = sqrt((4.57 N)^2 + (4.74 N)^2)
Calculating the net force:
Net force = sqrt((20.8849 N^2) + (22.4676 N^2))
Net force = sqrt(43.3525 N^2)
Net force = 6.59 N (approximately)
Now, we can use Newton's second law of motion to find the acceleration:
Net force = mass * acceleration
6.59 N = (5.76 kg) * acceleration
Solving for acceleration:
acceleration = 6.59 N / 5.76 kg
acceleration ≈ 1.14 m/s²
Therefore, the acceleration of the block is approximately 1.14 m/s².