Forces of 9.5 N and 5.12 N act at right angles on a reddish-green block of mass 3.19 kg. How much acceleration occurs?

To find the acceleration of the reddish-green block, you can use the principles of vector addition. The acceleration can be determined by applying 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.

First, you need to determine the net force acting on the block. Since the forces are acting at right angles, you can use the Pythagorean theorem to find the magnitude of the net force.

The net force (F_net) can be calculated as:

F_net = √((F1)^2 + (F2)^2)

Substituting the given values, we have:

F_net = √((9.5 N)^2 + (5.12 N)^2)
= √(90.25 N^2 + 26.2144 N^2)
= √116.4644 N^2
= 10.80 N

Next, you can use the equation F_net = m * a, where F_net is the net force, m is the mass of the block, and a is the acceleration.

Solving for acceleration:

a = F_net / m
= 10.80 N / 3.19 kg
≈ 3.39 m/s^2

Therefore, the acceleration of the reddish-green block is approximately 3.39 m/s^2.