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.
The figure, or a description of which rope goes where, is needed
To determine the tension in each rope, we need to apply 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.
Let's assume that the tension in the rope connected to the box with mass m1 is T1, and the tension in the rope connected to the box with mass m2 is T2.
For the box with mass m1:
The net force acting on m1 is the tension in the rope (T1) pulling the box forward, while the mass of m1 resists the motion. So we have:
T1 - m1 * a = 0
Rearranging the equation, we get:
T1 = m1 * a
Substituting the given values, we have:
T1 = 115 kg * 0.21 m/s^2 = 24.15 N
For the box with mass m2:
The net force acting on m2 is the tension in the rope (T2) pulling the box forward, while the mass of m2 resists the motion. So we have:
T2 - m2 * a = 0
Rearranging the equation, we get:
T2 = m2 * a
Substituting the given values, we have:
T2 = 286 kg * 0.21 m/s^2 = 60.06 N
Therefore, the tension in each rope is approximately:
T1 = 24.15 N
T2 = 60.06 N