A block of mass 3.17 kg is hanging from a rope. The tension in the rope is 12.9 N, pulling upward on the block. What is the magnitude and direction of the acceleration of the block?

To find the magnitude of the 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 acting on the block is the tension in the rope. Therefore, we can write:

Tension = mass * acceleration

Rearranging the equation, we get:

Acceleration = Tension / mass

Plugging in the given values, we have:

Acceleration = 12.9 N / 3.17 kg

Now, let's calculate the magnitude of the acceleration:

Acceleration ≈ 4.07 m/s^2

The direction of the acceleration can be determined by looking at the forces acting on the block. In this case, the tension in the rope is pulling upward on the block, while the force of gravity is pulling downward. Since the tension is greater than the force of gravity, the net force is upward. Therefore, the acceleration is in the upward direction.