Solutions to Week 1 Assignment

 

  1. (a) dactual = dmagnified/600 = 3.0cm/600 = 5.0 x 10-3cm
    (b) A = pr2 = p(d/2)2 = 1/4pd2, so Amagnified/Aactual = (1/4dmagnified)/(1/4dactual) = (3.0cm/5.0 x 10-3cm)2 = 360,000
  2. (a) 250,000,000 people = 2.5 x 108 people
    (b) 0.000 000 000 000 0038m = 3.8 x 10-15 m
  3. (a) 6.85 x 10-5 + 2.7 x 10-7 = 6.85 x 10-5 + 0.027 x 10-5 = 6.88 x 10-5
    (b) 702.35 + 1897.648 = 2600.00
    (c) 5.0 x 4.3 = 22
    (d) 0.04/p = 0.01
    (e) 0.040/p = 0.013
  4. (a) (0.32mi/1min) x (1min/60s) x (5280ft/1mi) x (1m/3.28ft) = 8.6m/s
    (b) (0.32mi/1min) x (60min/1h) = 19mi/h

  5. v = Klpgq
    In dimensions, m/s = mp.mq/s2q = mp+q/s2q.
    So, we have the following restrictions on p and q: p+q = 1 and 2q =1.
    Find q and p
    2q =1
    q = 1/2
    p + q = 1
    p + 1/2 = 1
       p = 1/2
    Thus, v = Kl/12g1/2 = KÖlg.

  6. (1 + x)n = (1 + x)1/3 = 1 + 1/3x for |x|<< 1 and n = 1/3.
    (a) 0.99941/3 = 1 + 1/3(-0.0006) = 0.9998 (0.99979996)
    (b) 0.9941/3 = 1 + 1/3(-0.006) = 0.998 (0.997996)
    (c) 0.921/3 = 1 + 1/3(-0.08) = 0.97 (0.9726)
    (d) 1.31/3 = 1 + (0.3) = 1.1 (1.091)

  7. v = at + v0 , where a = 6.0m/s2 and v0 = 3.0m/s
    (a)     v2 = at2 + v0
           -(v1 = at>1 + v0)
          v2 - v1 = a(t2 - t1)
          v2 - v1 = (6.0m/s2)(6.0s - 4.0s) = 12m/s
    (b) v = (6.0m/s2)(5.0s) + 3.0m/s = 33m/s.

  8. Since area has dimensions [L]2, and circumference has dimensions [L}, the area of a circle will never equal is circumference because they have different dimensions.