Physics Demystified, 2nd edition

Stan Gibilisco

Explanations for Quiz Answers in Chapter 2

1. A vector quantity always possesses two independent characteristics: magnitude and direction. Of the four choices given here, only velocity (the composite of speed and direction) qualifies. Temperature, visible-light intensity, and mass all need only the expression of magnitude to be fully defined. The correct choice is C.

2. Our ship isn't accelerating, and the mass that we see isn't accelerating relative to us. From our point of view, therefore, no force whatsoever acts on the external object. It's coasting through space freely, just as we are. The correct choice is D.

3. In effect, the earth is in a perpetual state of free fall, constantly "pulled" on by the sun's gravitation. As the earth orbits the sun, its acceleration vector points straight toward the sun at all times, and maintains a magnitude equal to the gravitational acceleration of the sun at the earth's distance. If the earth suddenly stopped revolving around the sun, the sun's gravitation would continue to act, "pulling" the earth straight toward the sun at an ever-increasing speed equal to the sun's gravitational acceleration. The correct choice is C.

4. Newton's first law tells us that an object moving at a specific velocity will keep moving at that velocity unless an outside force acts on it. When you power-down the boat's motor, the only force acting on the boat is its own friction with the water, which will eventually bring the boat to a stop. Unfortunately for you, this friction has a negligible effect over the short distance between you and the dock; your boat might as well be sliding along a frictionless surface! You've just seen a vivid demonstration of Newton's first law in action. The correct choice is A.

5. At any given instant in time, a velocity vector comprises instantaneous speed and instantaneous direction. Those are the only two parameters that we must specify; nothing else has any relevance. The correct choice is C.

6. In three-dimensional (3D) space, we can define the magnitude of a vector in terms of the length of the line segment representing it. The type of coordinate system makes no difference. The correct choice is D.

7. A kilogram-meter per second squared (1 kg · m · s-2) equals one newton (1 N) by definition. A gram is 1/1000 of a kilogram. Therefore, a gram-meter per second squared (1 g · m · s-2) equals 1/1000 of a newton (0.001 N). The correct choice is C.

8. On the planet we're visiting, the gravitational acceleration is 5.67 m · s-2 (which we can also denote as 5.67 m/s2). If we drop an object and let it fall freely, and assuming that the atmosphere has no effect on the object's acceleration, then the object will accelerate downward at a rate of 5.67 m/s2 regardless of its mass. After one second (1.00 s) of time, the object will have attained an instantaneous speed of 5.67 m/s. After 2.00 s, it will have gained another 5.67 m/s of speed, so it will be falling at 5.67 + 5.67 = 11.34 m/s. We should round this value off to three significant figures, getting 11.3 11.3 m/s. The correct choice is D.

9. Assuming that the atmosphere has no effect on the second brick, it will accelerate downward at exactly the same rate as the first brick did, even though the second brick has twice the mass of the first one. If we had dropped both bricks side by side, they'd have fallen right along with each other at identical instantaneous speeds all the way down until impact (conducting an extraterrestrial rerun of Galileo's famous 17th-century experiment in Pisa). The correct choice is A.

10. If you hit the brakes while driving a vehicle along a straight, level highway, the vehicle will (if the brakes work properly) lose speed but keep going in the same direction. The velocity vector will therefore maintain the same direction but grow smaller in magnitude. The correct choice is B. (Don't get fooled by the wording of this question. It asks what happens to the velocity vector, not the acceleration vector!)