Answer:
the force in the hydraulic cylinder AB is 5311.9 N
the magnitude of the pin reaction at C is 4672.9 N
Step-by-step explanation:
first we calculate the angle made by the triangle ACD from the Image
tan∅ = AB/605
tan∅ = 740 / 605
tan∅ = 1.2231
∅ = tan⁻¹ ( 1.2231 )
∅ = 50.73°
so the second image now shows the diagram of the ramp and the angle, the total weight of all the passengers and the ramp act at point G.
Now we equate the moment at point A to 0
∑MA = 0
Fcy (4115) - Mg(1815) = 0
our M is 750 kg and g is 9.81 m/s²
Fcy (4115) - ((750 × 9.81)(1815)) = 0
Fcy (4115) = 13353862.5
Fcy = 13353862.5 / 4115
Fcy = 3245.2 N
Now force in the hydraulic cylinder will be minimum only when the force Fab is perpendicular to the ramp
We equate the moment about the point C to 0
∑Mc = 0
Fab (4115sin50.73) - Mg(2300) = 0
our M is 750 kg and g is 9.81 m/s²
Fab (4115sin50.73) - ((750 × 9.81)(2300)) = 0
Fab(3185.7167) = 16922250
Fab = 16922250 / 3185.7167
Fab = 5311.9 N
Therefore the force in the hydraulic cylinder AB is 5311.9 N
We equate the forces in the horizontal direction to 0
Fcx - Fab cos50.73° = 0
we substitute
Fcx - 5311.9 × cos50.73° = 0
Fcx = 3362.3 N
Next we calculate the resultant pin reaction force at C from the equ
Fc = √( F²cx + F²cy)
we substitute our values
Fc = √( (3362.3)² + (3245.2)² )
Fc = √ 21836384.33
Fc = 4672.9 N
Therefore the magnitude of the pin reaction at C is 4672.9 N