a rope 26 ft long is attached to two points A and B, 20 ft apart at the same level. A load of 250lb is carried at the middle of the rope. what force is exerted on A.
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I answered it yesterday. Is that soon enough?
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To find the force exerted on point A, we can calculate the force using the principle of equilibrium.
To start, let's write down what we know:
- The rope is 26ft long and attached to points A and B, which are 20ft apart.
- The load of 250lb is carried at the midpoint of the rope.
The diagram of the situation can be imagined as follows:
```
A ----------- C ------------------- B
Force on A Load (250lb) Force on B
```
In this equilibrium situation, the total force on both sides must balance for there to be no net force.
Since the load is positioned in the middle of the rope, the distance from A to the load (C) is 13ft (half of 26ft).
Now let's calculate the force exerted on point A.
Using the principle of equilibrium, we can say that the force exerted on A plus the force exerted on B should equal zero since there is no net force:
Force on A + Force on B = 0
Since the points A and B are equidistant from the load, the force exerted on A and B should be equal in magnitude but in opposite directions.
Let's assume the force exerted on A is F (which we want to find), and the force exerted on B is -F (negative because it acts in the opposite direction).
Thus, we can write the equation:
F + (-F) = 0
Simplifying, we get:
0 = 0
Since 0 is equal to 0, it confirms that our assumption was correct. The forces on points A and B are equal in magnitude but opposite in direction.
Therefore, the force exerted on point A is 0 lb.