Download How can we use Work to analyze motion?

How can we use Work
to analyze motion?
No friction!!!!!
A
h
h
B
each ball
has a mass
of m
The ball starts at the top of each
ramp, how can we determine how
fast it will be traveling at the
bottom?
For A, if the angle of the ramp is known,
we could find the acceleration the ball
will have down the ramp. Then using the
length of the ramp the final velocity can
be found.
But for B, the curve represents a
problem since the acceleration will
not be constant down the ramp.
As the ball rolls down the ramp,
What will happen to the Potential NRG of the ball? What will happen to the Kinetic NRG of the ball?
What force caused each of these NRG's to change?
Did the force do Work on the ball?
How can the Work done by Gravity be represented in terms of NRG changes?
How do the NRG changes compare?
The Work done by Gravity on the ball
causes a change in the PE grav and the KE.
-ΔPEgrav = ΔKE
-(PEgravf - PEgravi ) = KEf - KEi
PEgravi - PEgravf = KEf - KEi
A loss of PE is countered by a Gain in
KE and both sides will remain
constant.
The sum of the PE and KE for the ball at the
top will be the same at all other points in the
motion down the ramp.
This sum is called the TME,
Total Mechanical NRG.
TME = KE + PEgrav = ΣKE+ΣPE
The TME is constant at any point in the
motion as long as there are no new forces
introduced during the motion.
TMEi = TMEf
Law of Conservation of NRG
For a closed system, the Total Mechanical NRG of a system
remains constant at any point in time.
All forces acting on a body that do work on the
body will cause a change in it's NRG. These
forces account for losses and gains in KE and PE
for the body.
According to the Law of Conservation NRG, the sum of the PE
and KE at any time for a closed system are the same.
If another force were involved, it would
do Work as well and the NRG would still
be conserved.
But the work done by the new force
only causes a change to the final result
since it does the work over the entire
motion.
A skateboarder is at the top of a half-pipe. He has a mass of
140 kg. The top of the half-pipe is 10 m above the bottom.
Find how fast the skateboarder
will be going at the bottom of the
ramp.
A ballistic Pendulum is one way used to determine the speed of
bullet. The bullet hits the pendulum and causes it to swing
through an arc. The height the pendulum swings to determines
how fast the bullet was traveling.
pendulum is 0.62 m long
h = 0m
Use Conservation of NRG
to determine the speed of
the pendulum at the
lowest point given the
final height it swings to.