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Answer :
The force required by a person to lift a 1000 kg car using a hydraulic jack with an area ratio of 53 is approximately 185 N. This is calculated using Pascal's principle and the information provided.
We can solve this problem using Pascal's principle which is the underlying principle behind the operation of a hydraulic car jack. The principle states that a change in pressure applied at one point of a fluid is transmitted to all points of the fluid. This means that an external force applied to a small area, because of a piston or otherwise, will result in a larger force over a larger area, allowing for heavy lifting such as a car.
Let's denote the force applied by the person as F1, the force by the car jack on the car as F2. Further, the area of the car jack piston to which the person applies his force is A1, and the area of the car jack piston that lifts the car is A2. The ratio A2/A1 = 53 (given).
The weight of the car is the force exerted by the car on the jack due to gravity which equals to mass_gravity. So F2 = 1000 kg * 9.8 m/s^2 = 9800 N.
Because the fluid in the hydraulic jack is incompressible, the pressure applied by the person must be equal to the pressure that lifts the car. That is, F1/A1 = F2/A2. Substituting A2 = 53 A1 from the given area ratio, we get F1/A1 = 9800 N/(53 A1).
Solving this equation for F1, the force applied by the person, gives us F1 = 9800 N / 53 ≈ 185 N. Therefore the person needs to apply a force of approximately 185 N to lift the car with the hydraulic jack.
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