A box has a mass of 90 kg If the box is accelerating upward at 1.0m/s2, what is the tension of the cable?
To find the tension in the cable, we need to 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.
First, let's convert the mass of the box to Newtons. We know that the weight of an object is given by the formula: weight = mass * gravity, where gravity is approximately 9.8 m/s^2 on Earth.
So, weight = 90 kg * 9.8 m/s^2 = 882 N
Next, we can find the net force acting on the box. The net force is equal to the tension in the cable minus the weight of the box in this case, because the box is accelerating upward.
So, net force = tension - weight
We are given that the box is accelerating upward at 1.0 m/s^2, so the acceleration acting on the box is in the upward direction.
Using Newton's second law, we can set up the equation:
net force = mass * acceleration
net force = 90 kg * 1.0 m/s^2 = 90 N
Now we can substitute the values we have into the equation for net force:
90 N = tension - 882 N
Rearranging the equation to solve for tension:
tension = net force + weight
tension = 90 N + 882 N
tension = 972 N
Therefore, the tension in the cable is 972 Newtons.