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?

One post is enough.

The "following figure" is missing.

Mass of a is 6.7

Mass of b is 2.2

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To find the mass of Box B, we can use the equations of motion and consider the forces acting on the system.

Let's start by analyzing the forces on Box B:
1. Gravitational force (weight): The weight is acting downwards and can be calculated using the formula: weight = mass * gravitational acceleration. Since gravitational acceleration is a constant of approximately 9.8 m/s^2, we can write the weight of Box B as W = mB * 9.8 N, where mB is the mass of Box B.

2. Tension in the rope: The tension in the rope is acting upwards and is equal to 30.0 N. This force is transmitted to Box B.

3. Applied force on Box A: A constant upward force of 78.0 N is applied to Box A. This force is also transmitted to Box B.

Considering the downward direction as positive, we can write the net force on Box B as:
Net force = Weight - Tension in rope - Applied force on Box A
Net force = mB * 9.8 N - 30.0 N - 78.0 N

Now, using Newton's second law of motion, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration, we can set up the following equation:

mB * acceleration = mB * 9.8 N - 30.0 N - 78.0 N

Since the initial velocity is zero (starting from rest), we can use the equation of motion to find the acceleration:
acceleration = (final velocity - initial velocity) / time
acceleration = (12.3 m - 0 m) / 3.80 s

Now, replace the acceleration in the equation:
mB * (12.3 m / 3.80 s) = mB * 9.8 N - 30.0 N - 78.0 N

Simplifying the equation, we have:
12.3 m * mB / 3.80 s = 9.8 N * mB - 30.0 N - 78.0 N

To isolate the mB term and solve for the mass of Box B, we need to rearrange the equation:
12.3 m * mB / 3.80 s + 30.0 N + 78.0 N = 9.8 N * mB

Next, we can solve for mB:
12.3 m * mB / 3.80 s + 108.0 N = 9.8 N * mB

Now, multiply both sides of the equation by 3.80 s to eliminate the denominator:
12.3 m * mB + 410.4 N * s = 9.8 N * mB * 3.80 s

Finally, we can solve for mB by isolating the mB term:
12.3 m * mB - 9.8 N * mB * 3.80 s = -410.4 N * s
(12.3 m - 9.8 N * 3.80 s) * mB = -410.4 N * s

Divide both sides by (12.3 m - 9.8 N * 3.80 s):
mB = (-410.4 N * s) / (12.3 m - 9.8 N * 3.80 s)