You work for a moving company and are given the job of pulling two large boxes of mass m1 = 115 kg and m2 = 286 kg using ropes as shown in the figure below. You pull very hard, and the boxes are accelerating with a = 0.21 m/s2. What is the tension in each rope? Assume there is no friction between the boxes and the floor.

To find the tension in each rope, we can start by analyzing the forces acting on the boxes.

In this case, there are two forces acting on each box:
1. The force of gravity, which is equal to the weight of the box, calculated as Fg = m * g, where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. The tension force applied by the ropes.

Let's break down the forces acting on each box individually:

For the first box with mass m1 = 115 kg:
The force of gravity acting on the first box is Fg1 = m1 * g.
The tension force applied by the first rope is T1.

For the second box with mass m2 = 286 kg:
The force of gravity acting on the second box is Fg2 = m2 * g.
The tension force applied by the second rope is T2.

Since the boxes are accelerating, we can apply Newton's second law of motion, which states that net force equals mass times acceleration (F = m * a). In this case, the net force acting on each box is provided by the tension force and the force of gravity.

For the first box:
Net force1 = T1 - Fg1 = m1 * a

For the second box:
Net force2 = T2 - Fg2 = m2 * a

We can solve these equations simultaneously to find the tensions in each rope:

T1 - m1 * g = m1 * a
T1 = m1 * a + m1 * g

T2 - m2 * g = m2 * a
T2 = m2 * a + m2 * g

Plugging in the given values:
m1 = 115 kg
m2 = 286 kg
g = 9.8 m/s^2
a = 0.21 m/s^2

T1 = 115 kg * 0.21 m/s^2 + 115 kg * 9.8 m/s^2

T2 = 286 kg * 0.21 m/s^2 + 286 kg * 9.8 m/s^2

Evaluating these equations will give us the tension in each rope.