Thinking Mathematically: Explore the quantitative dependencies of the acceleration upon the speed and the radius of curvature. Then answer the following questions. a. For the same speed, the acceleration of the object varies (directly, inversely) with the radius of curvature. b. For the same radius of curvature, the acceleration of the object varies (directly, inversely) with the speed of the object. c. As the speed of an object is doubled, the acceleration is (one-fourth, one-half, two times, four times) the original value. d. As the speed of an object is tripled, the acceleration is (one-third, one-ninth, three times, nine times) the original value. e. As the radius of the circle is doubled, the acceleration is (one-fourth, one-half, two times, four times) the original value. f. As the radius of the circle is tripled, the acceleration is (one-third, one-ninth, three times, nine times) the original value.

In the future, people will only enjoy one sport: electrodisc. in this sport, you gain points when you cause metallic discs hovering on a field to exchange charge. you are an electrodisc player playing the popular four disc variant. the disks have charges of qa = −8.0 µc, qb = −2.0 µc, qc = +5.0 µc, and qd = +12.0 µc. (1) you bring two disks together and then separate them. you measure the resulting charge of these two disks and find that it is +5.0 µc per disk. which two disks did you bring together? (a) a and b (b) a and c (c)a and d (d)b and c(e) b and d (f) c and d. (2) you bring three disks together and then separate them. you measure the resulting charge of these three disks and find that it is +3.0 µc per disk. which three disks did you bring together? a, b, and c (a) a, b, and d (c) a, c, and d (d) b, c, and d. (3) given the resulting charge of each disk measured in (b) is +3.0 µc, how many electrons would you need to add to a disk of this charge to electrically neutralize it? electrons