P5 - v k j i i k j i 10 3 6 12 55 10 10 2 4 15 3 = − =...

Discussion 5: Name: solutions
TAM212, Fall, 2003
A 3-kg object A and a 10-kg object B undergo a central impact. Before impact, v
B
= -10 i (m/s), and
v
A
= 15 i (m/s) They stick together after the collision. What is their combined velocity, after the
collision? and, if the collision takes 2ms, what is the average impulsive force experienced by B
during the collision?
No external impulsive forces, so we can write
Bf B Af A Bi B Ai A
m m m m v v v v L + = + ⇒ = ∆ 0
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
f
kg kg s m kg s m kg s m kg v i i i 10 3 / 55 / 10 10 / 15 3 + = − = − + ⇒
i v s m
f
/ 23 . 4 − =
( )
( ) ( ) ( )
N
s x
s m kg
m t dt
ave Bi Bf B B ave
t
t
28850
10 2
/ 10 23 . 4 10
3
2
1
=
− − −
= ⇒ − = ∆ = ∆ =
−
∫
∑
i i
F v v L F F
If time: What is their combined velocity if, instead of the velocity above, A has the velocity v
A
= 15 i + 4 j + 2 k (m/s) before the
collision?
Bf B Af A Bi B Ai A
m m m m v v v v L + = + ⇒ = ∆ 0
( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
f
kg kg s m kg s m kg s m kg v k j i i k j i 10 3