A sketch shows a painting staging in mechanical equilibrium. The person in the middle weighs 215 N, and the tensions in each rope are 200 N. What is the weight of the staging?
To find the weight of the staging, we need to consider the concept of mechanical equilibrium. In mechanical equilibrium, the sum of all the forces acting on an object is zero. In this case, we have three forces: the weight of the person in the middle and the tensions in each rope.
Let's break down the forces:
1. Weight of the person in the middle: The weight of the person is given as 215 N, which means there is a downward force acting on the staging.
2. Tension in the left rope: The tension in the left rope is given as 200 N. Since the rope is attached to the staging, there is an upward force exerted by the rope.
3. Tension in the right rope: The tension in the right rope is also given as 200 N. Like the left rope, it exerts an upward force on the staging.
Since the staging is in mechanical equilibrium, the sum of these three forces is zero. Mathematically, we can represent this equilibrium as:
(Weight of person) - (Tension in left rope) - (Tension in right rope) = 0
Substituting the given values:
215 N - 200 N - 200 N = 0
Simplifying the equation, we get:
215 N - 400 N = 0
-185 N = 0
Since -185 N is not equal to zero, it means there must be an additional force acting on the staging to balance the forces. This additional force is the weight of the staging.
Therefore, we can conclude that the weight of the staging is 185 N.