Answer :
A force of 95.14 N must be exerted on 0.072 m² piston to lift the heavy machine
We can use the principle of Pascal's law to solve this problem. According to Pascal's law, pressure applied to a confined fluid is transmitted uniformly in all directions.
Let's assume that the hydraulic lift consists of two pistons - one with an area of 2.8 m² (the platform), and the other with an area of 0.072 m² (the piston used to lift the heavy machine). The force exerted on each piston is equal to the pressure multiplied by the area of the piston.
The pressure applied to the fluid in the hydraulic lift is the same for both pistons, so we can set up the following equation:
Pressure × Area of platform = Pressure × Area of piston
We can rearrange this equation to solve for the force required to lift the heavy machine:
Force on piston = Force on platform × (Area of piston / Area of platform)
Substituting the given values, we get:
Force on piston = 3700 N × (0.072 m²/ 2.8 m²)
Force on piston = 95.14 N
Therefore, a force of 95.14 N must be exerted on the piston to lift the heavy machine.
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To lift a heavy machine using a hydraulic lift, a force of approximately 95 Newtons must be exerted on the smaller piston, based on the ratio of the areas of the pistons and the force exerted on the larger piston.
The question revolves around a hydraulic lift system which is utilized to lift a heavy object. According to Pascal's Principle, the pressure exerted on a confined fluid is transmitted undiminished in all directions throughout the fluid; thus, the pressure exerted on one piston is equal to the pressure on the other. To calculate the force F1 needed on the smaller piston, we use the formula:
P = F/A
Where P is the pressure, F is the force, and A is the area. The pressure on both pistons is the same, so:
P1 = F1/A1 = F2/A2
Which rearranges to:
F1 = (A1 / A2) * F2
Substituting the given values:
F1 = (0.072 m2 / 2.8 m2) * 3,700 N
Calculating this yields:
F1 = 95 N approximately
Thus, a force of approximately 95 Newtons must be exerted on the smaller piston to lift the heavy machine.
