Honors Physics Chapter 5 End-Of-Chapter Discussion Questions Page 199

1. Honors PhysicsChapter 5End-Of-ChapterDiscussion QuestionsPage 199 28 November 2K + 4

2. Directions • Most of the questions have the answer following the question. • Read the question, give it some thought and then read the answer. • The questions will not be discussed in class unless you ask for further clarification.

3. 1. How would you find the mass of an object in interstellar space, where the force of gravity approaches zero? P 199

4. 1A. You could not use a balance or spring scale to find the mass of the object since both depend on gravity to operate (gravitational mass). You would have to measure the inertial mass of the object. That is, you would have to measure the mass using the relationship F = ma. If a known force is applied to the object, it will accelerate. By measuring the resulting acceleration and substituting into F = ma, the mass could be determined.

5. 2. Why is it usually incorrect to say that an astronaut is “weightless” as he moves in orbit above the Earth? P 199

6. 2A. Weight is defined as the force of gravity on a mass. The astronaut is still in the earth's gravitational field while in orbit. That is, the force of gravity is acting on the astronaut and there must be a weight. As explained in the text, the astronaut's mass may not be supported by the space capsule and an apparent weightless condition exists but this does not mean that the astronaut has no weight.

7. 3. A girl hopes to meet her boyfriend by sliding down a rope, made of nylon stockings, from her second story bedroom window. The stockings will break if the tension in them exceeds 400 N. The mass of the girl is 60 kg. Describe how she should slide down the rope so that she will land in the arms of her beloved at a minimum velocity. a = -3.1 m/s2 P 199

8. 3A. Draw a free body diagram of the girl. Two forces act on her: gravity down with a force of (60 kg)(9.8 N/kg) = 588 N and the stocking pulls up with a tension T. If she had no acceleration, then T would be 588 N. which is greater than the breaking strength of the stocking. So she must decrease the tension to 400 N by climbing down the stocking or letting it slide through her hands. Her minimum downward acceleration would be given by:

9. 4. What effect does the rotation of the Earth have on the apparent force of gravity on a man standing (a) at the equator and (b) at the North Pole? P 199

10. 4A. At the equator the force of gravity is both attracting the man to the earth and keeping him moving in a circular path at approximately 1670 km/h. As a result, the force holding him away from the earth, as measured on a bathroom scale, would be slightly less than that at the pole where there is no centripetal acceleration. Again, a free body diagram of the man at the equator and at the pole will illustrate the difference. Approx 0.3%

11. 5. A baseball is thrown vertically into the air. If there were no air resistance to be considered, it should return to its original position with the same speed as it had when thrown. But, given that air resistance is a factor, how will this affect its speed? Explain your reasoning. P 199

12. 5A. Frictional forces always act in the opposite direction to that of the motion. At every point on the way up, the forces of gravity and air resistance both act downwards. However, at every point on the way down, the direction of the air resistance is up, opposite to the force of gravity. Hence, the acceleration for the downwards section of the motion is smaller in magnitude than for the upwards section and the final speed will be less than the initial speed.

13. 6. In a disaster film, an elevator full of people falls freely when the cable snaps. In the film, the people are shown pressed upward against the ceiling. Is this good physics? Explain. P 199

14. 6A. This is bad physics. The people should be shown in random positions much like astronauts in an orbiting space capsule. The only way they could all be at the top of the elevator is if they pushed up from the floor when the cable snapped. Otherwise, the elevator would have to be accelerating downward with an acceleration greater than g, which is nearly impossible.

15. 7. Future space stations may be designed like a giant wheel rotating about a central axis. The astronauts would live along the circumference of this structure. How would such a structure simulate gravity? P 199

16. 7A. On the inside rim of the rotating space station, the surface would exert a centripetal force on any object. This force would act on the object producing an apparent weight much the same as is produced by gravity on the earth. The period of rotation would determine the value of g. It would be set lower than that of earth (9‑8 N/kg) to make movement easier. Note that the larger the diameter of the space station, the slower it must turn to achieve the same artificial gravity.

17. 8. You wish to shoot a rocket to a point due north of your present position. In what direction should you aim the rocket if you are in the Northern Hemisphere? In the Southern Hemisphere? P 199

18. 8A. In the northern hemisphere, the target moves cast more slowly than the launch site, so one must aim west. In the southern hemisphere, the target moves east more quickly than the launch site, so one must aim east.

19. 9. A car being driven along a mountain road proceeds through an “S” curve. The first part of the curve has twice the radius of the second (reverse) part. How does the centripetal force acting on the car in the first part compare with that acting on the car in the second part? If the car doubles its speed, what changes occur in the size of the centripetal force acting on the car as it traverses each part of the curve? P 199

20. 9A. The centripetal force is inversely proportional to the radius and directly proportional to the square of the speed. Thus, the centripetal force in the second part of the curve will be twice that of the first if the speed remains constant. If the speed of the car doubles the centripetal force must be four times greater in the first section and eight times greater in the second compared to the first section at, the original speed. The centripetal force is provided by the friction between the tire and the road so it is quite likely that the car will not complete the second part of the "S" turn.

21. 10. A ball rolls off a horizontal table with a horizontal speed of 2 m/s. Stroboscopic photographs of the motion of the ball are taken from the three positions A, B, and C. In position A, the camera is in front of the table with the ball rolling towards it. In position B, the camera is above the edge of the table. in position C, the camera is to one side of the table at right angles to the plane of the ball's path. Sketch the picture you would expect to obtain in each of the three positions. P 199

22. 11. A white disc is placed near the outside edge of a phonograph turntable that is rotating at 33 ⅓ rev/min. The turntable is on a cart moving at a constant velocity. The disc is illuminated by a strobe light flashing at a constant frequency. Draw a sketch showing the white disc as viewed from a fixed point above the path of the moving cart. Assume several strobe flashes per turntable rotation. Consider various speeds for the cart.

23. 11. F o r Va = vr where va is the speed of the axle and vr is the linear speed at a point on the rim, with respect to the axle. P 200

24. 12. Very rapid circular motion, particularly of machinery near human beings, presents a serious safety hazard. Describe in three examples ‑ one each from your home, the family automobile, and a family member's place of work ‑ the hazard itself, the related physics, and the precautions and/or protection required. P 200

25. 13. Centrifuges assist analysts in determining the components of many substances and separating them out. Describe two applications in the following areas: blood analysis, research into DNA or proteins, dairy products, and minerals. P 200