Answers to posted final exam:

1. (a) 2.4 X 10^-3 kg-m/s
   (b) For the raindrop, v_f - v_i = 0-(-12) = +12. Dp (change in momentum) = +, force on the raindrop is +, force is UP. By Newton's Third Law, force on the roof is down.
   (c) number = 1.8 X 10⁴ADt
   (d) Force = Dmomentum/Dt; pressure = force/area, pressure = 43.2 Pa.

2. (a) Q and U_int; Q = ND[(1/2)mv²]
   (b) Q = CnDT
   (c) C = (3/2)R = 12.5 J/mole-deg

3. (a)c_neon = 617 J/kg-deg; c_argon = 312 J/kg-deg
   (b) 15.2 g

4. (a) 30 J
   (b) 20 J
   (c) 0.025 deg. C

5. (a) F_f = 10.8 N; W_f = -4.31 J
   (b) -7.84 J
   (c) 0.839 m/s

6. (a)3.33 rad/s
   (b) 0.751 J
   (c) 0.038 m, down

7. (a) x: -0.193 kg-m/s; y: +0.052 kg-m/s
   (b) x: 0.493 kg-m/s; y: -0.052 kg-m/s
   (c) 0.450 m/s
   (d) 5.99 deg.

8. (a) -5.39 X 10⁷ J
   (b) -0.84 X 10⁷ J
   (c) 4.1 X 10³ m/s

9. (a) 2.67 X 10⁴ m/s
   (b) 3.96 m/s²
   (c) 0.727 m/s²

10. (a) 4.56 kg-m²/s
    (b) 2.22 rad/s
    (c) Positive; he exerts inward force as masses move inward.

11. (a) F_x = Fsin30^o; F_y = Fcos30^o
    (b) F_y = mg
    (c) F_x = mv²/r
    (d) tan30^o = v²/rg, v = 1.064 m/s