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?
tension= net force=mg-ma=m(9.8-1.2)
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 the mass of the object multiplied by its acceleration. In this case, the net force is the tension in the rope pulling upward, and the mass of the object is given by the weight divided by the acceleration due to gravity.
Step 1: Find the mass of the object.
The weight is given as 30.9 N, so we need to convert it to kilograms (kg) using the acceleration due to gravity. Let's assume the acceleration due to gravity is 9.8 m/s^2.
Using the formula weight = mass * acceleration due to gravity, we can rearrange it to find the mass: mass = weight / acceleration due to gravity.
mass = 30.9 N / 9.8 m/s^2 = 3.15 kg.
Step 2: Calculate the tension in the rope.
We can use Newton's second law of motion, which states that the net force is equal to mass multiplied by acceleration.
The net force is provided by the tension in the rope, and the acceleration is given as 1.20 m/s^2.
Using the formula net force = mass * acceleration, we can rearrange it to find the tension: tension = net force / mass.
tension = (mass * acceleration) / mass = acceleration.
Therefore, the magnitude of the tension in the rope is equal to the acceleration, which is 1.20 m/s^2.