The small piston of a hydraulic lift has an area of 0.10 m2. A car weighing 2.0 x 104 N sits on a rack mounted on the large piston. The large piston has an area of 0.50 m2. How large a force must be applied to the small piston to support the car?

weightlarge/areaLarge=weightsmall/areaSmall

weght small= forcesmall=weightlarge*areaSmall/areaLarge

To find the force needed to support the car, we can use Pascal's law, which states that the pressure applied to a fluid is transmitted equally throughout the entire fluid.

First, let's calculate the pressure applied by the car on the large piston using the formula:

Pressure = Force / Area

Since the force applied by the car is 2.0 x 10^4 N and the area of the large piston is 0.50 m^2, we can plug in these values:

Pressure = 2.0 x 10^4 N / 0.50 m^2 = 4.0 x 10^4 N/m^2

Since the pressure is transmitted equally throughout the fluid, this is also the pressure applied to the small piston.

Now we can find the force needed to support the car on the small piston using the formula:

Force = Pressure x Area

Plugging in the values, we have:

Force = (4.0 x 10^4 N/m^2) x (0.10 m^2)
Force = 4.0 x 10^3 N

Therefore, a force of 4.0 x 10^3 N must be applied to the small piston to support the car.

To determine how large a force must be applied to the small piston to support the car, we can apply Pascal's Law, which states that the pressure exerted on an enclosed fluid is transmitted undiminished in all directions.

Pascal's Law can be stated as:

Pressure (P) = Force (F) / Area (A)

In this case, we have the following information:

Area of the small piston (A1) = 0.10 m^2
Area of the large piston (A2) = 0.50 m^2
Force exerted by the car (F2) = 2.0 x 10^4 N

Since the pressure is transmitted undiminished, the pressure on the small piston (P1) is equal to the pressure on the large piston (P2), which can be expressed as:

P1 = P2

Using Pascal's Law, we can write the following equation:

F1 / A1 = F2 / A2

We can rearrange this equation to solve for F1 (the force applied to the small piston):

F1 = (F2 * A1) / A2

Substituting the given values, we can calculate the force applied to the small piston:

F1 = (2.0 x 10^4 N * 0.10 m^2) / 0.50 m^2

F1 = 2.0 x 10^4 N * (0.10 / 0.50)

F1 = 2.0 x 10^4 N * 0.2

F1 = 4.0 x 10^3 N

Therefore, a force of 4.0 x 10^3 N must be applied to the small piston to support the car.