Learning Measurement #2 Review Question Answers

 
   

Practice Problems

0. Here is a set of old test questions covering these same topics, in multiple-choice format. 1D, 2C, 3A, 4D, 5B, 6B, 7C, 8E, 9C, 10B, 11E

1. Why does the buoyant force happen? Circle one choice in each set of brackets: Pressure {increases, decreases} the deeper down in a fluid. If an object is submerged in the fluid, the pressure pushing {up, down} on the {bottom, top} of the object is {greater, less} than the pressure pressing {up, down} on the {bottom, top} of the object. (Or, you can reverse the choice in every set of brackets, except the first.)

2. Look at the table of desities given on the "Density" notes page. What item or items listed there would float in mercury? All of them, except gold.

3. In about five billion years, the Sun will run out of the hydrogen fueling its nuclear reactions. After going through a "red giant" phase, gravity will cause the Sun to shrink down to about the size of the Earth, forming a dead star known as a "white dwarf". What will be the density of the white dwarf, in g/cm³. Assume the mass of the sun (2x1030 kg) collapses into a sphere 6000 km in radius. 2.2 million g/cm³.

4. A solid steel ball is floating in mercury. What percentage of the ball is sticking up above the surface of the mercury? The ratio of their densities is 7.9/13.6 = 58% below the surface, therefore 42% is above the surface.

5. Most people have a density about the same as water --- let's say your density is the same as water. If your mass is 50 kg, then...
(a) What is your volume? 0.05 cubic meters
(b) What is the buoyant force being exerted on your body by the air. (See density table.) 0.6N

6. The strength of gravity (g) at the surface of Europa, one of Jupiter's moons, is 1.32 N/kg. Europa has a thin water ice crust (perhaps 20km thick) below which lies a liquid water ocean that could be as deep as 200 km. What is the pressure at the bottom of this ocean? (Assume g doesn't vary significantly over that depth.) Calculate density * g * h for both the ice layer and the water layer, then add those pressures together to yield 2.88e8 Pa, which is the same as 2850 atmospheres.

7. A solid ball floats in water, but sinks when immersed in vegetable oil. What can you say about the density of the ball? It must be less dense than water, but more dense than the oil. So the density must be between 925 and 1000 kg/m³

8. A block is 10 centimeters tall. When floating in a bowl of mercury, 4 centimeters is below the surface of the fluid. What is the density of the block? 5.4 g/cm³

9. Is a spherical helium balloon 5.0 meters in diameter big enough to lift a person? The density of air near the ground is 1.25 kg/m³. The density of helium at one atmosphere pressure is 0.18 kg/m³.
            (a) What is the volume of the balloon? 65 m³ (remember, radius is half the diameter)
            (b) What is the buoyant force? 800 N
            (c) What is the weight of the helium in the balloon? 120 N
            (d) What is the net force? Assume the weight of the balloon itself (the plastic bag that holds the helium) is insignificant. 680N
            (e) Is that net force enough to lift a person? Assume the person is 50 kg in mass. Yes, because a 50-kilogram person weighs 490 newtons.

10. A uniform beam of length 1.8 m and mass 55 kg is suspended by two chains hanging vertically. The left chain is attached to the beam 20 cm from the left end, and the right chain is attached 50 cm from the right end. What is the tension in each of the chains? 196 N for the left chain, and 343 N for the right chain

11. If water comes out of a particular garden hose (diameter 5/8") at 1.90 m/sec... Note 5/8" = 15.9 mm = 0.0159 m and that means a cross-sectional area of 1.98x10-4 m2.

(a) What is the volume flow rate? 0.00038 m3/sec
(b) What is the mass flow rate? 0.38 kg/sec
(c) If you put a nozzle on the end with a 1/4" opening, how fast will the water come out then? Note 1/4" = 6.35 mm = 0.00635 m and this corresponds to an area of 3.17x10-5 m2. With that smaller area, the water has to travel faster to maintain the same flow rate. The new speed is now 11.9 m/sec.