fisica1-youn-e-freedman-exercicios-resolvidos

8.97: Apply conservation of energy to the explosion. Just before the explosion the sheel
is at its maximum height and has zero kinetic energy. Let A be the piece with mass 1.40
kg and B be the piece with mass 0.28 kg. Let v
A
and v
B
be the speeds of the two pieces
immediately after the collision.
1 2 1 2
m + =
2 AvA
m
2 BvB
860 J
Since the two fragments reach the ground at the same time, their velocitues just
after the explosion must be horizontal. The initial momentum of the shell before the
explosion is zero, so after the explosion the pieces must be moving in opposite horizontal
directions and have equal magnitude of momentum: m v = m v .
Use this to eliminate v in the first equation and solve for v :
1
2
m v (1 + m
2
B B
Then v
A
B
= ( m
/ m
B
A
A
) = 860 J and v
m ) v
A
B
= 14.3
B
m/s.
= 71.6
b) Use the vertical motion from the maximum height to the ground to find the time it
takes the pieces to fall to the ground after the explosion. Take + y downward.
v
0 y
y − y
= 0, a
0
y
= v
2
= + 9.80 m/s , y − y
0 y
t +
1
2
a
y
t
2
gives t
0
= 4.04 s.
m/s.
= 80.0 m, t = ?
During this time the horizontal distance each piece moves is
x
A
= v
At
= 57 .8 m and xB
= vBt
= 289.1m.
They move in opposite directions, so they are x x = 347 m apart when they land.
A
A
+ B
A
B
B
B