A block of weight 30.9 N is hanging from a rope. The tension from the rope is pulling upward on the block. The block is accelerating downward at a rate of 1.20 m/s2. What is the magnitude of the tension in the rope?

I found the mass of the block to be 25.75 kg; however, I'm having a hard time figuring out how to get the magnitude of the rope. Please help! Thanks

Sum of forces = ma, up is positive.

T - 30.9 = 25.75(-1.2)

To find the magnitude of the tension in the rope, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the tension in the rope pulling upward and the weight of the block pulling downward. Since the block is accelerating downward, the tension in the rope must be larger than the weight of the block.

First, let's calculate the mass of the block using the weight given. The weight of an object can be calculated using the formula:

weight = mass x acceleration due to gravity

In this case, the weight is given as 30.9 N and the acceleration due to gravity is approximately 9.8 m/s^2. Rearranging the formula, we have:

mass = weight / acceleration due to gravity

Substituting the values, we get:

mass = 30.9 N / 9.8 m/s^2 = 3.15 kg

Now that we have the mass, we can calculate the tension in the rope using Newton's second law:

net force = mass x acceleration

In this case, the acceleration is given as 1.20 m/s^2. Rearranging the formula, we have:

net force = tension - weight

Substituting the values, we get:

tension - 30.9 N = 3.15 kg x 1.20 m/s^2

tension - 30.9 N = 3.78 N

To solve for the tension, we simply add the weight to both sides of the equation:

tension = 3.78 N + 30.9 N

tension = 34.68 N

Therefore, the magnitude of the tension in the rope is approximately 34.68 N.