P15

x-component force: Fx = 400 cos40 - 300 cos50 = 306.5 - 192.8 = 113.7 N

y-component force: Fy = 400 sin40 + 300 sin50 = 257.1 + 229.8 = 486.9 N

Since  Fx = F cosq    and   Fy = F sinq,  

so that tanq = Fy / Fx = 486.9/113.7 = 4.28.

Hence, q = arctan (4.28) = 76.8 degrees from the x axis.

F = (486.9**2 + 113.7**2)**(1/2) = 500 N

P29

length of barrel = 24 cm = 0.24 m,     V = 350 m/s,    m = 0.006 kg

      DV = 350 m/s,

      Dt = Dx / Vav = 0.24 m / [(0 + 350)/2] m/s = 0.00137 s

  aav = DV / Dt = 350 / 0.00137 = 255,474 m/s**2

       F = maav = 1,533 N = 1.53 kN

P41

W = 392.4 N,   m = 392.4/9.8 = 40 kg    F = 40 x 5 =200 N downward.

P103

T on the long rope exerted by the hand = T on each of the other two ropes.

The weight is supported by the other two ropes: 2T = 100 N so that T = 50 N

Force pulling down on the right most ceiling bracket = T + T = 100 N