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Properties of Matter Study Guide (page 4)

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Updated on Sep 27, 2011

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:

Pascal's Principle

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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