Two boxes, A and B, are connected to each end of a light vertical rope. A constant upward force 90.0N is applied to box A. Starting from rest, box B descends 11.0m in 3.50s . The tension in the rope connecting the two boxes is 30.0N
a) What is the mass of box A?
b) What is the mass of box B?
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To find the masses of boxes A and B, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, the net force acting on each box is the tension in the rope.
Let's start by calculating the acceleration of box B. We can use the formula:
acceleration = (change in velocity) / (time)
The change in velocity of box B can be calculated using the formula:
change in velocity = (final velocity) - (initial velocity)
Since box B starts from rest, the initial velocity is 0 m/s. The final velocity can be calculated using the formula:
final velocity = (distance) / (time)
In this case, the distance is the downward distance box B descends, which is 11.0 m, and the time is 3.50 s.
Now, let's calculate the acceleration:
change in velocity = (final velocity) - (initial velocity)
= (11.0 m) / (3.50 s)
= 3.14 m/s
acceleration = (change in velocity) / (time)
= (3.14 m/s) / (3.50 s)
= 0.897 m/s²
Since the tension in the rope is the net force acting on each box, we can use it to find the mass of each box.
For box A:
net force = tension in the rope = 30.0 N
mass of box A = net force / acceleration
= 30.0 N / 0.897 m/s²
≈ 33.47 kg
For box B:
net force = tension in the rope = 30.0 N
mass of box B = net force / acceleration
= 30.0 N / 0.897 m/s²
≈ 33.47 kg
Therefore, the mass of box A is approximately 33.47 kg, and the mass of box B is also approximately 33.47 kg.