1. Dry air is more dense, because a water molecule is lighter than a nitrogen molecule or an oxygen molecule.

2. The windy trip will take more time. d/(v+u) + d/(v-u) is longer than 2d/v.

3. On a clearer night, the earth radiates its energy through the atmosphere, which lowers the temperature of the earth's surface and the air near it. But on a cloudy night, much of the ratiation is absotbed by the clouds and rerdaiated back to the earth.

4. (b) How much a floating object extends below and above the liquid depends on the weight of the object and the weight of the displaced fluid, both of which are proportional to g. Lower g or increase it; the proportion floating above and below is unchanged.

5. (b). Of course, at any moment all cars have the same speed, but the gravitational p.e. of the system of cars is least when the middle car is at the bottom - when the center of mass of the system is lowest.

6. (c) If she barely pushes the book so the vertical component of her push is less than the book's weight, then friction acts upward to keep the book stationary. If she pushes so that the vertical component of her push equals the book's weight, then there's zero wall friction on the book. Or if she pushes harder so the verticlal component of her oush exceeds the book's weight, then friction acts downward.

7. Hold alpha, put the beta in your pocket, eat the gamma.

8. (c) Relative to the swimmer, the speed of both life preservers is zero.

9. (a)

10. (d) Both the weight and the air resistance are downward

11. (c)

12. The image of the candle will be yellow.

13. (c) Because the balls are in free fall and have the same acceleration, the velocity of one changes in exactly the same way as the other --- their relative velocity is constant.

14. (d) Use "KE loss = WD against friction" and assume a constant frictional force.

15. (b). The horizontal compoent of the tensions in both sides must be equal.

16. (b) The ball to win the race is the ball having the greatest average speed. Along each track both balls have identical speeds--except at the dip in Track B. Instantaneous speeds everywhere in the dip are greater than along the flat part of the track. Greater speed in the dip means greater overall average speed and shorter time for a ball to track B.

17.Your eyeglasses are colder than the inside air. what happens to the speed of molecules in the air when they encounter a cold surface? They slow down. And what happens to water molecules in the air when they slow down? they stick to one another. Tis is condensation. So when you go from a cold place to a warm place, water vapour in the air rapidly condenses on your eyeglasses, making then foggy.

18.Block B hits the floor first. Notice that the race isn't between Blocks A and B, but between A and the end part of the B-chain system, which isn't in free fall because one end is fastened to the post. So it doesn't accelerate g like Block A. The B-chain center of mass, initially closer to the floor, accelerates less than g. But acceleration of its "free' end inceases in fall, surpassing g - like the tip of a falling pole accelerates more than g when it rotates to the ground.

19. It's pressure, not force, that's important. Pressure depends not only on force, but on the area of contact. When you lie on a hard floor, the area of your body in contact with the floor is relatively small, so the average pressure is relatively large. On a bed of nails, the area would be even less and the pressure even more. Lying on a sofa supports more of your body. So comparing the sofa with the floor (or the bed of nails), we see that considerably more sofa area meets your body - with less average pressure.

20. 1. The shortest path to the opposite shore occurs for boat a,whose resultant velocity lets it to move directly across the river, perpendicular to the flow. 2. Time wise, the opposite shore is reached first by Boar b, since the velocity provided by the motor i directly across the river. 3. the fastest ride is on Boat c, as it has the greatest resultant speed.

21.With a bit os simple geometry and knowing that light travels in striaght lines, we see that the Sun's diametre is 1/108 the 150,000,000 km distance from the Earth --- 1,390,000 km.

22.(a) As water gains speed, pressure in the water deceases, in accord with Bernoulli'sprinciple. Decreased water pressure squeezes less on air bubbles, allowing them to expand - so that air pressure and surrounding water pressure match. If the flowing water continues its flow into a wider section of pipe, speed decreases, pressure increases, and the bubbles become smaller.

23.(b) The burning candles consume oxygen and expel mainly carbon dioxide, which because of its greater density,would you might guess settle to the bottom of the jar and snuff out the shorter candle. It would if it were't so warm. Because it is warm, the carbon dioxide gas has a density thst is less than that of the surrounding air, which is why it rises to snuff the taller candle first.

24.(a) The end supporting the punctured balloon tips upward as it is lightened by the weight of air that escapes. Although there is a loss of byouant force of the punctured ballloon, that decrease in upward force is less than the weight -of-air loss, since the density of air in the balloon before puncturing was greater than the density of surrounding air.

25.(a). Same amount of potential energy is given to the two darts. The one with a larger mass will have a slower initial speed. The fall in air is independent of mass.

26.(a) Its range is increased. To understand why, think energy conservation. Much of the potential energy of the gunpower is converted into kinetic energy when the gunpower fires. That's both kineic energy of the cannonball and kinetic energy of the recoiling cannon. Because the tree reduces recoil, the cannonball gets a greater share of kinetic energy-hence its increased range.

27.(b) The shaken can rolls slower and loses the race. Why? Suppose friction were practically absent between the contained liquid and the inner can surface. The metal can would then roll down the incline while the liquid inside would essentially all be translational. So what slows the can that is shaken ? Perhaps surface tension between bubbles and the can creates more friction than that of straight fluid-can adhesion. Then the liquid would undergo some rotation, having rotational kinetic energy that diminishes translational kinetic energy.

28. Turn your air conditioner off altogether and save fuel. The amount of heat that leaks into your house depends on the insulation and the difference in inside and outside temperature, DT. In accord with Newton's law of cooling, keeping DT high consumes more fuel. When you turn your conditioner off you minimise both DT and fuel consumption. Will more fuel be required to re-cool the house when you return than would have been consumed to keep it cool while you were away ? Not at all. When you return and turn your conditioner on again, you extract heat at a smaller DT. The amount of fuel consumed to bring room temperature to its original cool setting is less than the amount consumed to keep it at the cool setting continuously.