A 107 kg bix on the right and a 50 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.
Let's analyze the forces acting on the 107 kg box first. Here are the forces acting horizontally on the 107 kg box:
1. External force to the right: 598 N
2. Frictional force: 30 N
3. Tension force from the cable: unknown (let's call it T1)
Since the box is not accelerating horizontally, the net force acting on it must be zero. Therefore, we can write the equation:
Net force = External force - Frictional force - T1 = 0
Rewriting the equation:
598 N - 30 N - T1 = 0
Now let's analyze the forces acting on the 50 kg box. Here are the forces acting horizontally on the 50 kg box:
1. Frictional force: 16 N
2. Tension force from the cable: unknown (let's call it T2)
Again, since the box is not accelerating horizontally, the net force acting on it must be zero. Therefore, we can write the equation:
Net force = T2 - Frictional force = 0
Rewriting the equation:
T2 - 16 N = 0
Now, we know that the tension in the cable between the two boxes is the same (T1 = T2). So, we can set up a system of equations:
598 N - 30 N - T1 = 0
T1 - 16 N = 0
Solving this system of equations will give us the value of T1, which represents the tension in the connecting cable.
By rearranging the second equation, we can find the value of T1:
T1 = 16 N
Therefore, the magnitude of the tension on the connecting cable is 16 N.