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Mommentum and cm
10/10/2016 2
MOMENTUM
10/10/2016 3
The linear momentum of a particle or an object that
can be modeled as a particle of mass (m) moving
with a velocity (v) is defined to be the product of the
mass and velocity:
p=mv
The impulse of the force F acting on a particle equals
the change in the momentum of the particle.
Ft=m
10/10/2016 4
CONSERVATION OF MOMENTUM
Conservation of momentum is a fundamental
law of physics which states that the
momentum of a system is constant if there
are no external forces acting on the system. It
is embodied in Newton's first law (the law of
inertia). SCIENCEWORLD
10/10/2016 5
Conservation of Momentum for a System of Objects
 Internal forces have absolutely no effect on the net
momentum of a system.
 If the net external force acting on a system is zero, its
net momentum is conserved. That is,
10/10/2016 6
10/10/2016 7
10/10/2016 8
COEFFICIENT OF RESTITUTION
How much bounce!
The ration between the relative speeds
 =
 

  

    
Perfectly elastic  = , perfectly inelastic  = ,  

=
10/10/2016 9
A tennis ball dropped on the floor from a height
of 100 cm rebounds to a height of 60 cm. Find
the coefficient of restitution.
10/10/2016 10
Center of Mass
The center of mass of a system of masses is the point where the
system can be balanced in a uniform gravitational field.
10/10/2016 11
10/10/2016 12
Suppose the masses are separated by 0.500 m, and that
m1 = 0.260 kg and m2=0.170 kg. What is the distance from
m1 to the center of mass of the system?
  =
11 + 22
1 + 2
=
0.260 0 + 0.170(.500)
0.260 + 0.170
= 0.198
10/10/2016 13
10/10/2016 14
10/10/2016 15
A persons arm is held with the upper arm vertical, the lower arm and hand horizontal. (a) Find
the center of mass of the arm in this configuration, given the following data: The upper arm has
a mass of 2.5 kg and a center of mass 0.18 m above the elbow; the lower arm has a mass of 1.6
kg and a center of mass 0.12 m to the right of the elbow; the hand has a mass of 0.64 kg and a
center of mass 0.40 m to the right of the elbow. (b) A 0.14-kg baseball is placed on the palm of
the hand. If the diameter of the ball is 7.4 cm, find the center of mass of the armball system.
10/10/2016 16
10/10/2016 17
A 59-kg woman and a 71-kg man sit on a seesaw, 3.5 m
long. Where is their center of mass?
10/10/2016 18
A uniform carpenter's square has the shape of an L, as
shown in the figure. Locate the center of mass relative
to the origin of the coordinate system.
10/10/2016 19

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Mommentum and cm

  • 3. 10/10/2016 3 The linear momentum of a particle or an object that can be modeled as a particle of mass (m) moving with a velocity (v) is defined to be the product of the mass and velocity: p=mv The impulse of the force F acting on a particle equals the change in the momentum of the particle. Ft=m
  • 4. 10/10/2016 4 CONSERVATION OF MOMENTUM Conservation of momentum is a fundamental law of physics which states that the momentum of a system is constant if there are no external forces acting on the system. It is embodied in Newton's first law (the law of inertia). SCIENCEWORLD
  • 5. 10/10/2016 5 Conservation of Momentum for a System of Objects Internal forces have absolutely no effect on the net momentum of a system. If the net external force acting on a system is zero, its net momentum is conserved. That is,
  • 8. 10/10/2016 8 COEFFICIENT OF RESTITUTION How much bounce! The ration between the relative speeds = Perfectly elastic = , perfectly inelastic = , =
  • 9. 10/10/2016 9 A tennis ball dropped on the floor from a height of 100 cm rebounds to a height of 60 cm. Find the coefficient of restitution.
  • 10. 10/10/2016 10 Center of Mass The center of mass of a system of masses is the point where the system can be balanced in a uniform gravitational field.
  • 12. 10/10/2016 12 Suppose the masses are separated by 0.500 m, and that m1 = 0.260 kg and m2=0.170 kg. What is the distance from m1 to the center of mass of the system? = 11 + 22 1 + 2 = 0.260 0 + 0.170(.500) 0.260 + 0.170 = 0.198
  • 15. 10/10/2016 15 A persons arm is held with the upper arm vertical, the lower arm and hand horizontal. (a) Find the center of mass of the arm in this configuration, given the following data: The upper arm has a mass of 2.5 kg and a center of mass 0.18 m above the elbow; the lower arm has a mass of 1.6 kg and a center of mass 0.12 m to the right of the elbow; the hand has a mass of 0.64 kg and a center of mass 0.40 m to the right of the elbow. (b) A 0.14-kg baseball is placed on the palm of the hand. If the diameter of the ball is 7.4 cm, find the center of mass of the armball system.
  • 17. 10/10/2016 17 A 59-kg woman and a 71-kg man sit on a seesaw, 3.5 m long. Where is their center of mass?
  • 18. 10/10/2016 18 A uniform carpenter's square has the shape of an L, as shown in the figure. Locate the center of mass relative to the origin of the coordinate system.