Two boxes, A and B, are connected to each end of a light vertical rope, as shown in the following figure. A constant upward force 78.0N is applied to box A . Starting from rest, box B descends 12.3 m in 3.80s . The tension in the rope connecting the two boxes is 30.0 N
What is the mass of box B?
To find the mass of box B, we need to use Newton's second law of motion.
Newton's second law states that the net force acting on an object is equal to the product of its mass and acceleration:
F = ma
In this case, the net force acting on box B is the difference between the gravitational force (downward) and the tension force (upward):
net force on B = gravitational force - tension force
The gravitational force acting on box B is given by:
gravitational force = mass of B * acceleration due to gravity
We can rearrange the equation to solve for the mass of box B:
mass of B = (net force on B + tension force) / acceleration due to gravity
Given:
net force on B = 78.0 N (upward force applied to box A)
tension force = 30.0 N
acceleration due to gravity = 9.8 m/s^2
Substituting the values into the equation:
mass of B = (78.0 N - 30.0 N) / 9.8 m/s^2
mass of B = 48.0 N / 9.8 m/s^2
mass of B ≈ 4.90 kg
Therefore, the mass of box B is approximately 4.90 kg.