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# Properties of Matter Study Guide (page 4)

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#### Example

The diagram in Figure 10.5 shows a hydraulic press used in a car shop to lift cars. An automobile is placed on the large area of the press. The automobile has a mass of 1,540 kg, and the two sides of the press have a diameter of 25 and 15 cm, respectively. Find how much force will need to be applied on the right piston to counteract the weight of the car.

#### Solution

First, we convert the data into S1 units. Next, complete the diagram with the forces and pressure acting on the liquid, and then solve the problem.

25 cm = 25 cm · 1 m/l00 cm = 0.25 m

15 cm = 15 cm · 1 m/100 cm = 0.15 cm

m = 1,540 kg

F = ?

According to Pascal's principle, the pressure exerted by the automobile spreads equally in the liquid, and it will reach the piston on the left-hand side of the press.

p1 = p2

The pressure exerted by the car is:

The platform on which the car rests pushes down on a cylindrical piston of radius 0.25 m:

Al = π · r2 = π · (0.25 m)2 = 0.196 m2

The piston on which the counteraction is applied is also a cylindrical piston of radius 0.15 m:

A2 = π · r2 = π · (0.15 m)2 = 0.071m2

The pressures exerted on the pistons are:

And now we can solve for the unknown force.

Compare this force with the weight of the car:

W = 1,540 kg · 9.8 m/s2 = 15,092 N

W = 1,540 kg · 9.8 m/s2 = 15,092 N

Practice problems of this concept can be found at: Properties of Matter Practice Questions

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