Momentum and Energy   
Chapter 3








 Joseph F. Alward, PhD
 Department of Physics
 University of the Pacific

 

 

 

 

 

 

 

   Momentum
Momentum = mass x velocity

                  = m v

If the boulder and the boy
have the same momentum,
will the boulder crush the
boy?

Hint:  Which would have the
larger speed?

 

 

 

  Impulse 
Example:  Wall exerts
a force of 10,000 N.

The contact time is
0.01 s.
------------------------------
Impulse = F t
             = 100 N-s

 

 

 

 

 

  Momentum Change
D(mv) = Change in momentum

D(mv) = final - initial

           = 0 - mv

           = - mv
Ignoring negative sign:

D(mv) = mv

 

 

 

 

   Momentum Change = Impulse
D(mv) = Ft
     mv = Ft

 

 

 

 

     Impulses and Contact Time

 

 

 

 

 

  Rolling with the Punches

  Spreading impulse out over a longer time means that the force will be less; either
  way, the change in momentum of the boxing glove, fist, and arm will be the same.

 

 

 

 

 

  

  Force = Impulse / Time
Contact time is reduced
if arm's deceleration is
kept as small as possible.

This is done by using
"follow-through", which
means to continue to
push during the contact
period.

 

 

 

 

 

  Increasing Impulse
Curved blades
prolong contact
with water:

Impulse = F Dt

Greater impulse
means greater
change in
momentum of
the wheel.

 

 

 

 

 

  Conservation of Momentum
Momentum
Before = 0
-------------
Momentum
After = 0
-------------
After firing,
the opposite
momenta
cancel.

 

 

 

 

 

 Conservation of Momentum
Momenta are equal
but opposite.

M v = m V

4 v  = 0.010 x 300
       =  3

   v = 3 / 4
      = 0.75 m / s

 

 

 

 

 

   Conservation of Momentum in Collisions

 

 

 

 

 

    Elastic Collisions
In elastic collisions
no permanent
deformation occurs;
objects elatically
rebound from each
other.
---------------------------

In head-on elastic
collisions between
equal masses,
velocities are
exchanged.

 

 

 

 

 

 

 

  Inelastic Collisions
Inelastic collisions--as between
the arm and wooden plates--
are characterized by permanent
deformation.

The kinetic energy of the swinging
arm is converted into heat and
chemical energy (to break the
bonds between atoms in the wood).

  

 

 

 

 

 

 

 

   Work 
Work = Force x Distance

F = 500 pounds (2000 N)

D = 8 feet (2.5 meters)
-----------------------------------


W = 2000 N  x  2.5 m

     = 5000 N-m
-----------------------------------
Alternative unit:  Joule

1 N-m = 1 joule (J)

 

 

 

 

 

  Work
Work = Force  x  Distance

If the wall doesn't move,
the prisoner does no work.

 

 

 

 

 

   Energy
Work is done on the bow.

The work done is stored
in the bow and string as
elastic potential energy.

After release, the arrow is
said to have kinetic
energy, 1/2 mv2.

Energy is measured in the
same units (joules) as
work.

 

 

 

 

 

  Work and Potential Energy

 The work done on the ball gives the ball gravitational potential energy.
  Gravitational potential energy = mgh

 

 

 

 

 

 Gravitational Potential Energy
Both blocks acquire the same
gravitational potential energy,
mgh.

The same work is done on
each block.  What matters
is the final elevation, not the
path followed.

 

 

 

 

 

   Energy Transformation
The work done in lifting the mass
gave the mass gravitational
potential energy.

Potential energy then becomes
kinetic energy.

Kinetic energy then does work
to push stake into ground.

 

 

 

 

 

  Energy Tranformation

        E = mgh3            E = mgh2 + 1/2 mv22           E = 1/2 mv12               E = mgh3

 

 

 

 

 

  Energy Conservation
Total energy is the sum
of both types of energy.

 

 

 

 

 

   Energy Transformation

 

 

 

 

 Power

Power = Work/ Time

1 joule / second = 1 watt

 

 

 

 

 

  The Lever
Work Out = Work In

Small force applied over
large distance is the same
as large force applied
over a small distance.

 

 

 

 

 

  Lever Example 

 

 

 

 

 

 

   The Pulley