a 107 KG BOX ON THE RIGHT AND A 43 KG BOX ON THE LEFT ARE TIED TOGETHER BY A HORIZONTAL CABLE. tHE 107 KG BOX IS ACTED UPON BY AN EXTERNAL FORCE OF 598 n TO THE RIGHT. THE FRICTIONAL FORCE EXERTED BY THE FLOOR ON THE 107 KG BOX IS 30 n AND THE FRICTIONAL FORCE EXERTED BY THE FLOOR ON THE 43 KG BOX IS 16 N. wHAT IS THE MAGNITUDE OF THE TENSION ON THE CONNECTING CABLE?
To find the magnitude of the tension on the connecting cable, we need to consider the forces acting on both boxes.
First, let's summarize the given information:
- Mass of the box on the right = 107 kg
- Mass of the box on the left = 43 kg
- External force acting on the box on the right = 598 N (to the right)
- Frictional force on the box on the right = 30 N
- Frictional force on the box on the left = 16 N
Next, we'll analyze the vertical forces acting on both boxes. Since there is no vertical acceleration mentioned and assuming the boxes remain on the ground, we can conclude that the vertical forces are balanced.
Then, let's analyze the horizontal forces acting on both boxes. The box on the right is acted upon by three forces: the external force, the tension in the cable, and the frictional force. The box on the left is acted upon by only the tension in the cable.
The equation for the box on the right is:
Tension - Frictional force - External force = mass * acceleration
Since the box is not accelerating in the horizontal direction, the equation becomes:
Tension - Frictional force - External force = 0
Now, substituting the known values into the equation:
Tension - 30 N - 598 N = 0
Rearranging the equation:
Tension = 30 N + 598 N
Calculating the tension:
Tension = 628 N
Therefore, the magnitude of the tension on the connecting cable is 628 N.