Three objects are moving along a straight line as shown in the figure. Taking th

Question

Three objects are moving along a straight line as shown in the figure. Taking the positive direction to be to the right, what is the total momentum of this system ? In a police ballistics test, 2.20-g bullet traveling at 700. m/s suddenly hits and becomes embedded in a stationary 5.00-kg wood block. What is the speed of the block immediately after the bullet has stopped moving relative to the block? A 900-kg car traveling 30.0 degree south of cast at 12.0 m/s suddenly collides with a 730 kg car traveling north at 17.0 m/s. The cars stick together after colliding. What is the velocity of the wreckage just after the collision?

Explanation / Answer

1)

We know that momentum is a vector quantity so it has both magnitude and direction

we take +Ve in +ve x direction and -ve in the -ve x directon
momentum of a body of mass m moving with velocity v is p = m*v kgm/s

given picture

   let p1 = 8*5kgm/s p2 = -15*4 kg m/s, p3 = 3*2 kgm/s

net momentum P = P1+P2+P3

   P = 8*5 -15*4+3*2 = 40-60+6 = -14 kg m/s

2)

   given mass of bullet is m = 2.2 g, moving with velocity v = 700 m/s,

       mass of wooden block M = 5 kg, at rest

conservation of momentum is

   m1u1+m2u2 = (m1+m2)V

   2.2*10^-3*700 + 5*0 = (2.2*10^-3+5) V

   V = 0.307864 m/s

3)

mass of car moving south of east is m1 = 900 kg, angle theta1 = 30 degrees, with velocity u1 = 12 m/s

   car moving north is m2 = 730 kg, at angle theta2 = 270 degrees, with velocity u2 = 17 m/s

stick together the final velocity of the system is V =?

   let the components of momentum of m1 is

  
   P1 = p1 cos i + p1 sin 330 j = (900*12)cos 330 i + (900*12)sin 330 j = 9353 i -5400 j

   P2 = p2 cos 270 i + p2 sin 270 j = (730*17)cos270 i +(730*17)sin270 j = 0 i - -12410 j

net momentum is P = P1+P2 = (9353 i -5400 j)+(0 i -12410 j) = 9353 i -17810 j

   conservation of momentum is

   m1u1+m2u2 = (m1+m2)V

   p1+p2 = (m1+m2) V

   V = P1+p2 /(m1+m2)
  
   V = (9353 i -17810 j)/(900+730)

   v = ((9353)/(900+730)) i -(17810/(900+730)) j)
   v = 5.74 i - 10.93 j

magnitude is sqrt(5.74^2+(-10.93)^2) m/s
      

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