Page 129 - Fisika Terapan for Engineers and Scientists

Questions for Discussion 329

1
CENTER OF MASS x (m x m x m x ) (10.18)
CM M 1 1 2 2 n n
(Using M m m m )
1 2 n y
CM 1
O y CM (m y m y m y ) (10.19)
2 2
1 1
n n
x M
1
z (m z m z m z ) (10.20)
CM 1 1 2 2 n n
M
CENTER OF MASS OF CONTINUOUS 1
DISTRIBUTION OF MASS x CM x dm (10.25)
M
circular plate
where dm dV ( is density and dV is a sphere 1
volume element). y CM y dm (10.26)
M
ring parallelepiped 1
z z dm (10.27)
CM
M

VELOCITY OF THE CENTER OF MASS m v m v m v
n n
1 1
2 2
v (10.37)
CM
M
MOMENTUM OF A SYSTEM OF PARTICLES P Mv CM (10.39)

MOTION OF THE CENTER OF MASS Ma F (10.40)
CM ext

GRAVITATIONAL POTENTIAL ENERGY OF A U Mgy CM (10.33)
SYSTEM OF PARTICLES (near the Earth’s surface)

2
1
KINETIC ENERGY OF A SYSTEM OF PARTICLES K m v m v m v 2 (10.42)
1
1
2
2 1 1 2 2 2 2 n n

QUESTIONS FOR DISCUSSION

1. When the nozzle of a fire hose discharges a large amount of 4. Hollywood movies often show a man being knocked over
water at high speed, several strong firefighters are needed to by the impact of a bullet while the man who shot the
hold the nozzle steady. Explain. bullet remains standing, quite undisturbed. Is this reasonable?
2. When firing a shotgun, a hunter always presses it tightly 5. Where is the center of mass of this book when it is closed?
against his shoulder. Why? Mark the center of mass with a cross.
3. As described in Example 2, guns onboard eighteenth-century 6. Roughly, where is the center of mass of this book when it is
warships were often mounted on carriages (see Fig. 10.3). open, as it is at this moment?
What was the advantage of this arrangement?