Energy Diagrams, Momentum, Impulse, Conservation of Momentum, Rocket Propulsion, Center of Mass
Energy Diagrams
A plot of the potential energy of a system. Total energy (constant if there are no non
‐
conservative forces) is also plotted as a horizontal line. Note the stable and unstable equilibrium points.
Be able to plot the forces acting on an object based on its potential energy curve [pg 235
‐
6].
Impulse and Linear Momentum
Momentum is a vector quantity defined by:
Ԧൌ݉ݒ
Ԧ
It is a vector quantity, so it has
ݔ,ݕ,
and
ݖ
components. Momentum is very useful for describing
collisions (billiard balls, explosions, car crashes, recoil, rocket burning fuel, and the like…).
Momentum is important enough that we define a new term for the change in momentum –
impulse – given by
ܬ
ሬԦ
ൌ∆
Ԧൌ
Ԧ
ଶ
െ
Ԧ
ଵ
. More generally, impulse can be described as the net force acting
on an object during a time interval.
ܬ
Ԧ
ൌ
ܨ
Ԧ
݀ݐ
௧
మ
௧
భ
. Impulse relates the net force applied to an object to its
change in momentum. Note that impulse is also a vector.
Example (Impulse) – 8.9
A hockey puck with mass
݉
is moving on an icy, frictionless, horizontal surface. At
ݐ ൌ 0
, the puck is
moving to the right with speed
ݒ
. a) Calculate the velocity of the puck (magnitude and direction) after a
force of
ܨ
Ԧ
ଵ
directed to the right has been applied for
ݐ
ଵ
seconds. b) If, instead, a force of
ܨ
Ԧ
ଶ
directed to
the left is applied from
ݐൌ0
to
ݐ ൌ ݐ
ଶ
, what is the final velocity of the puck?
U(x)
U(x)
E
U(x)
E
U(x)
E
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentEnergy Diagrams, Momentum, Impulse, Conservation of Momentum, Rocket Propulsion, Center of Mass
Example (Impulse) – 8.12
A bat strikes a baseball with mass
݉
. Just before impact, the ball is traveling horizontally to the right
with speed
ݒ
ଵ
, and it leaves the bat traveling to the left at an angle of
ߠ
above horizontal with a
speed
ݒ
ଶ
. If the ball and bat are in contact for
ݐ
seconds, find the horizontal and vertical components of
the average force on the ball.
Solution:
ܨ
௫
ൌ
௧
ሺെݒ
ଶ
cos ߠ െ ݒ
ଵ
ሻ ܨ
௬
ൌ
௧
ሺݒ
ଶ
sin ߠሻ
Conservation of Momentum
Momentum is also conserved, as long as there are no external forces applied to the system.
Sound familiar? Since energy and momentum are both conserved, they can be used in combination to
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Musumeci
 Physics, Center Of Mass, Energy, Force, Kinetic Energy, Mass, Momentum, Potential Energy, Center of Mass The center of mass, Center of Mass Example

Click to edit the document details