# Worksheet: Hydraulics

In this worksheet, we will practice applying Pascal's principle to calculate the forces applied to and by fluids from forces exerted on and by various surfaces.

**Q1: **

A host pours the remnants of several bottles of wine into a single large jug after a party, almost completely filling the jug. The body of the jug is in the shape of a cylinder with a 14.0 cm diameter, and it has a thinner cylindrical neck of diameter 2.00 cm. The host inserts a cork with the same diameter as the neck into the jug’s neck, placing it in direct contact with the wine. The host is amazed that the bottom of the jug breaks away when he pounds the cork into place. Calculate how much the magnitude of the force exerted against the bottom of the jug exceeds the N magnitude force applied to the cork when it is struck by the host.

- A N
- B N
- C N
- D N
- E N

**Q2: **

The tires on a bicycle support the bicycle and its rider, which have a combined mass of 80.0 kg. The tires are perfectly flexible and support the weight of the bicycle and the rider by pressure alone. Calculate the total area of the tires in contact with the ground if the gauge pressure in the tires is Pa.

**Q3: **

What magnitude force must be exerted on the master cylinder of a hydraulic lift to support the weight of a car with a mass of kg resting on a second cylinder? The master cylinder’s diameter is 2.50 cm and the second cylinder’s diameter is 25.0 cm.

**Q4: **

A certain hydraulic system is designed to exert an output force 50.0 times as large as its input force. The system consists of two cylinders, the master cylinder and the second cylinder.

What must the ratio of the areas of the second cylinder and master cylinder be?

What must the ratio of the diameters of the second cylinder and master cylinder be?

By what factor is the distance through which the input force moves relative to the distance through which the output force moves? Assume no losses due to friction.