D. Momentum Part II

**6.3-6.4**

**6.3
****Conservation of Momentum**

**40, 42, 43, 45, 46, 50, 53**

42: Remember the momentum is conserved. Also, after he throws the hammer, his mass becomes 59.5 kg)

46: Resolve P_{x}
direction so that m_{1x}v_{1x} + m_{2x}v_{2x} +
m_{3x}v_{3x} = 0.

NOTE: v_{2x} = 0m/s since it isnt moving
that direction. m_{3} = 1.2
kg.

Next, Resolve P_{y}
direction so that m_{1y}v_{1y} + m_{2y}v_{2y} +
m_{3y}v_{3y} = 0.

NOTE: v_{1y} = 0 m/s since it isnt moving
in the y direction. Again, m_{3}
= 1.2 kg.

50: Momentum is conserved so whatever momentum the bullet loses, the block picks up

53: Remember that velocity of the pendulum before it is hit is zero. The velocity at the top of its swing (after it has been hit) is also zero (but maximum potential mgh). As it comes back to its original position, it has maximum velocity AND maximum KE ! Since momentum is conserved, the initial momentum must equal the final momentum.

**6.4
****Elastic and Inelastic Collisions:**

** **

**54, 55, 56, 58, 62, 64, 66, 71 (note: type-o in the
book! 62 and 66 are both ELASTIC collisions!)**

58: Use equations 6.15 and 6.16 on p. 191

62: mv_{o1}
+ mv_{o2} = mv_{1} + mv_{2}. Solve for v_{2}.
Realize that v_{o2} will be 4.0 m/s because it is heading in
the x direction. Once you solve for v_{2},
use K_{o} = ½ mv_{o1}^{2} + 1/2mv_{o2}^{2 }and
find the difference between K_{o} and K (which is 1/2mv_{1}^{2}
+ 1/2mv_{2}^{2}.)
Remember whenever you find difference, it is FINAL
INITIAL (K K_{o})

64: Solve for resulting velocity in the x direction and in the y direction as follows:

X direction: mv_{x}
+ MV_{x} = (m + M) v^{}_{x} (v^{}_{x} = resulting velocity in x
direction)

Y direction: mv_{y}
+ MV_{y} = (m + M) v^{}_{y}

Realize that mass M has zero velocity in the x direction and mass m has zero velocity in the y direction.

66: Subtract
vectors. DP = P_{final} P _{initial}. Realize ball #1 only has an x velocity. Ball #2 has x and y.)

71: a) V_{oblock} = V_{obullet}/(m+M/m)
where m is for the bullet and M is the mass of the block. PLEASE CONVERT MASSES INTO KG!

b) V_{obullet}
= m+M/m(_{})

**c)
**KE_{lost} = M/m+M

**Even
Answers:**

40.
a

42.
moves
0.083 m/s in the opposite direction

46. 2.0 m/s, 54^{o} above the +x axis

50.
0.33
m/s

54.
c

56.
c

58.
v_{1} = +1.3 m/s; v_{2} = +5.3 m/s

62.
1.1
x 10^{2}J

64.
a) vx = 1.0 m/s; vy = 3.3 m/s

b) 73^{o}

66. 15^{o},
0.57 m/s