Given the cross-sectional areas of the small and large pistons in a hydraulic lift (0.25 m² and 5 m², respectively) and the mass of a car (1200 kg), calculate the force required to lift the car using Pascal's law.
Answer (2)
Using Pascal's law, the force required to lift a car with a mass of 1200 kg can be calculated as 588.6 N. This is derived by first calculating the car's weight and then applying the principle of pressure across two pistons. The result shows how much force needs to be applied at the smaller piston to lift the car at the larger piston.
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In this problem, we need to use Pascal's Law to find the force required to lift a car using a hydraulic lift. Pascal's Law states that when pressure is applied to a confined fluid, the pressure change occurs throughout the entire fluid.
In a hydraulic lift, the pressure applied at the small piston is transmitted throughout the fluid and is therefore the same as the pressure at the large piston.
Let's begin by summarizing the given information:
The cross-sectional area of the small piston, A s = 0.25 m 2 .
The cross-sectional area of the large piston, A l = 5 m 2 .
The mass of the car, m = 1200 kg .
The force required to lift the car, F l , is related to the weight of the car. First, we calculate the weight of the car using the formula:
F = m ⋅ g
where g = 9.81 m/s 2 is the acceleration due to gravity.
F l = 1200 kg × 9.81 m/s 2 = 11772 N
Now, let's use Pascal's Law, which tells us that the pressure is the same on both sides of the hydraulic system:
Pressure = Area Force
The pressure at the large piston P l and the small piston P s must be equal. Therefore:
A s F s = A l F l
Rearranging the formula to solve for F s , the force needed on the small piston:
F s = A l F l ⋅ A s
Substitute the known values into the equation:
F s = 5 m 2 11772 N ⋅ 0.25 m 2
F s = 5 2943 N
F s = 588.6 N
Therefore, the force required to lift the car using the hydraulic lift on the small piston is approximately 588.6 N .
