Pascal's Law

1). Here is a demonstration Pascal used to show the importance of a fluid's pressure on the fluid's depth.

(See attachment)

An oak barrel with a lid of area 0.20 m^2 is filled with water. A long, thin tube of cross sectional area 5.00 10^-5 m^2 is inserted into a hole at the center of the lid, and water is poured into the tube. When the water reaches 15 m high, the barrel bursts.

(a) What was the weight of the water in the tube?

(b) What was the pressure of the water on the lid of the barrel?

(c) What was the net force on the lid due to the water pressure?

2). A hypodermic syringe has a plunger of area 2.3 cm^2 and a 4.50 x 10^-3 cm^2 needle.

(a) If a 1.4 N force is applied to the plunger, what is the gauge pressure in the syringe's chamber?

(b) If a small obstruction is at the end of the needle, what force does the fluid exert on it?

(c) If the blood pressure in a vein is 50 mm Hg, what force must be applied on the plunger so that fluid can be injected into the vein?

3). A rectangular boat, as illustrated in Fig. 9.32 (see attachment), is overloaded such that the water level is just 1.7 cm below the top of the boat. What is the combined mass of the people and the boat?

4). A block of iron quickly sinks in water, but ships constructed of iron float. A solid cube of iron 8.0 m on each side is made into sheets. To make these sheets into a hollow cube that will not sink, what should be the minimum length of the sides of the sheets?

5). A steel beam 11 m long is installed in a structure at 15°C. What are the beam's changes in length at the temperature extremes of -20°C to 55°C?