Game Development Reference
In-Depth Information
and the relative velocity v
rel
as
cos 115
o
sin 115
o
−1
0
−7.505
−58.890
v
rel
= v
1
−v
2
= (35 km/hr)
−(65 km/hr)
≈
km/hr.
Now we plug these values, along with masses and coe
cient of restitution, into Equa-
tion (12.23), to determine k, the magnitude of the collision impulse. (Note that we also
assume n is a unit vector, so nn = 1.)
−7.505
−58.890
−0.342
−0.940
(1 + 0.1)
km/hr
(e + 1)v
rel
n
(1/m
1
+ 1/m
2
) nn
=
k =
(1/1, 500 kg + 1/2, 500 kg)
=
63.716 km/hr
0.00107 kg
−1
= 59, 533 kg km/hr
The vector impulse received by Kari (who is m
2
) is
−0.342
−0.940
−20, 360
−55, 961
kn = (59, 533 kg km/hr)
=
kg km/hr.
Finally, computing the velocities after the impact, we have
−20, 360
−55, 961
−52, 500
0
−
kg km/hr
1
=
P
′
m
1
=
P
1
−kn
−21.43
37.31
v
′
1
=
=
km/hr
m
1
1, 500 kg
−20, 360
−55, 961
−68, 700
147, 000
+
kg km/hr
2
=
P
′
m
2
=
P
2
+ kn
−35.62
36.42
v
′
2
=
=
km/hr
m
2
2, 500 kg
10. Because the force of gravity is always directly downwards, the bend in the balance bar
causes the lever arm of each side to change depending on the angle of the monkey. For
example, if the monkey begins to lean to the left, this rotates the weight on the right end
of the pole upwards. In this situation, the force of gravity acts more perpendicular to the
bar on the right (the lever arm), and the torque is increased. At the same time, the mass
on the opposite end rotates downwards, causing the bar to become more parallel with the
force of gravity, thus decreasing the torque. In other words, the restorative torque is always
greater than the torque that would tend to tip him over, and when he is upright, they are
in equilibrium.
11. The hollow cylinder will be harder to roll, because the moment of inertia will be larger.
Imagine that the cylinders are made of a compressible substance. Now imagine taking an
individual mass element from the center of the solid center and pushing it outwards. As
the radius increases, the moment of inertia of this element will increase. This is essentially
the difference between the two cylinders, the hollow one has a denser outer ring, with more
of its mass pushed outwards.
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