2.95 a gate having the cross section shown in fig. 2.95 closes an opening 1.5 m wide and 1.2 m high in a water reservoir. the gate weighs 2224 n, and its center of gravity is 0.3 m to the left of ac and 0.6 m above bc. determine the horizontal reaction that is developed on the gate at c.
What is the horizontal reaction developed on the gate at point C?
Answer: To determine the horizontal reaction at point C, we need to consider the forces acting on the gate.
First, let’s calculate the weight of the gate. The weight of the gate is given as 2224 N.
Next, we need to find the center of gravity of the gate, which is specified as 0.3 m to the left of AC and 0.6 m above BC.
Since the gate is symmetrical about its vertical axis, the center of gravity lies on the vertical line passing through point C.
We can split the gate into two rectangular components: one above the center of gravity and one below it.
The component above the center of gravity has a weight of (2224 N) x (0.6 m) / (1.5 m), which is equal to 887.73 N. This component acts downward, causing a force on point C.
The component below the center of gravity has a weight of (2224 N) x (0.6 m) / (1.5 m), which is also equal to 887.73 N. This component acts upward, opposing the force caused by the upper component.
Therefore, the net force acting on point C is the difference between the downward force and the upward force: 887.73 N - 887.73 N = 0 N.
Since there is no vertical force acting on point C, the horizontal reaction developed on the gate at point C is zero.