A crane is lowering two boxes downward at a constant velocity. The cable from the crane is attached directly to the upper box, m1, which has a mass of 95kg and a second cable hanging from the upper box supports the lower box, m2, which has a mass of 140kg.
Determine the tension in the lower cable.
Determine the tension in the upper cable in the above diagram.
tension=m2*g in lower
upeer= (m2+m1)g in upper cable
To determine the tension in the lower cable, we need to consider the forces acting on the lower box (m2).
1. Gravitational force (Weight):
The weight of the lower box can be calculated using the formula: Weight = mass × gravity. The mass of the lower box is 140kg, and the acceleration due to gravity is approximately 9.8 m/s^2. So, the weight of the lower box is:
Weight = 140kg × 9.8 m/s^2 = 1372 N.
2. Tension in the lower cable:
Since the lower cable is supporting the weight of the lower box, the tension in the lower cable is equal to the weight of the lower box. Thus, the tension in the lower cable is:
Tension in the lower cable = 1372 N.
To determine the tension in the upper cable, we need to consider the forces acting on the upper box (m1).
1. Gravitational force (Weight):
Similar to the previous situation, the weight of the upper box can be calculated using the formula: Weight = mass × gravity. The mass of the upper box is 95kg, and the acceleration due to gravity is approximately 9.8 m/s^2. So, the weight of the upper box is:
Weight = 95kg × 9.8 m/s^2 = 931 N.
2. Tension in the upper cable:
The tension in the upper cable is a result of both supporting the weight of the upper box and transmitting that force to the lower cable to support the weight of the lower box.
To calculate the tension in the upper cable, we need to use the concept of equilibrium. Since the system is at a constant velocity, the net force acting on the system is zero (F_net = 0).
Considering the forces acting on the upper box, we have:
- The tension in the upper cable, upward force (Tension in the upper cable).
- The weight of the upper box, downward force (Weight of the upper box).
Since both forces have the same magnitude but act in opposite directions, they cancel each other out, resulting in a net force of zero.
Therefore, the tension in the upper cable is equal to the weight of the upper box:
Tension in the upper cable = 931 N.