fisica1-youn-e-freedman-exercicios-resolvidos

8.101: a) If the objects stick together, their relative speed is zero and ∈= 0 . b) From Eq.
(8.27), the relative speeds are the same, and ∈= 1. c) Neglecting air resistance, the
speeds before and after the collision are
From part (c), = ∈
2 h = ( 0.85) 2
( 1.2 m)
H
n
1
=
2 gh and 2gH
1
, and
H 0.87 m. e) H
16
=
2n
= ∈ h.
f) ( 1.2 m)( 0.85) 8.9 cm.
2
k+ 1
= H
k
∈
2gH1
2gh
∈ = = H 1
h . d)
, and by induction
− means that the kinetic energy
increases. In the center of mass frame of two hydrogen atoms, the net momentum is
necessarily zero and after the atoms combine and have a common velocity, that velocity
must have zero magnitude, a situation precluded by the necessarily positive kinetic
8.102: a) The decrease in potential energy ( ∆ < 0)
energy. b) The initial momentum is zero before the collision, and must be zero after the
collision. Denote the common initial speed as v
0
, the final speed of the hydrogen atom as
v , the final speed of the hydrogen molecule as V , the common mass of the hydrogen
atoms as m and the mass of the hydrogen molecules as 2 m . After the collision, the two
particles must be moving in opposite directions, and so to conserve momentum,
From conservation of energy,
from which
speed is
1
2
1
2
2
2
2 3
mV − ∆ + 2mV
= mv
2
2 1 2
( 2m ) V − ∆ + mv = 3 mv
V
2
v0
= + ,
2 3m
2 ∆
4
V = 1.203×
10 m/s, or 1.20 ×
4
v = 2.41×10 m/s.
2
2
0
0
v = 2V
.
4
10 m/s to two figures and the hydrogen atom
8.103: a) The wagon, after coming down the hill, will have speed 2gL sin α = 10 m/s.
300 kg
After the “collision”, the speed is ( )( 10 m/s) 6.9 m/s,
435 kg
= and in the 5.0 s, the wagon
will not reach the edge. b) The “collision” is completely inelastic, and kinetic energy is
not conserved. The change in kinetic energy is
1 2 1
2
435 kg 6.9 m/s − 300 kg 10 m/s = − 4769 so about 4800 J is lost.
2
( )( ) ( )( ) J,
2