Transcript thrust, impulse

PH 201
Dr. Cecilia Vogel
Lecture 17
REVIEW
CM
OUTLINE
CM with holes
Thrust
CM of object with hole
How do you find the center of mass of an
object with a hole – if you know where its
cm would be if it didn’t have the hole?
let mi=mass before hole, mf = mass after it has a
hole, mh = mass of stuff
x  cut out of the hole
xi = where cm would be if there were no
hole, xh = center of mass of hole
CM
xCM
mi xi  mh xh

mi  mh
treat a mass taken away
as negative mass added!
Recall
In Car Talk puzzler, man throws a
toolkit
he moves the opposite direction
the CM of the two keeps moving the
way it was
This is how jets and rockets work:
exhaust gases are ejected backward,
and rocket goes forward
Thrust is the force the gases exert on the
rocket
Expelling Gas
Consider one moment in time:
the rocket and its current load of fuel
 mass m
 velocity v
In a short time, Dt, a small amount of
exhaust gas is expelled
Dm
moves at speed vrel RELATIVE to
the rocket,
Force on Gas
What force does the rocket have to exert
on the gas to expel it
Use: Force = ma
mass = Dm
ave acceleration = Dv /Dt
Dv = vf - vi = -vrel-0
so aave = -vrel/Dt
Force exerted by rocket on expelled gas
 ave force = - Dmvrel/ Dt
 OR instantaneous force = -(dm/dt) vrel
Thrust
But the thrust is the force exerted by the
gas on the rocket.
this is the reaction force
 equal and opposite
The thrust force on the rocket is
dm
T  vrel
dt
where vrel = speed of exhaust gas
relative to rocket
and dm/dt is rate at which mass is
expelled (mass per unit time)
Please Note:
This applies not only to rockets expelling
exhaust gases,
but also to anything continuously losing or
gaining mass
Equation in text is misleading
T = ma is only true if T is the only force!


Generally,
SF  ma
SF=ma
and T is one of the forces you sum
Direction of thrust is always opposite
direction of mass expelled (or in the
direction of mass impinging)
Varying Acceleration
Can you have varying acceleration
with constant force??
 if m variese
like a rocket
mass is lost at a rate of dm/dt
and mass is decreasing
Suppose constant thrust is the only
force,
T  m( t )a ( t )
as m decreases, a increases
Velocity of Rocket
Acceleration is decreasing
If thrust is the only force, then a=T/m
velocity does not increase linearly
it increases logarithmically
 m0 
v  v0  vrel ln  
m
where m0 and v0 are initial values
and m and v are values at a later time
Thrust Example
At one instant in time, a balloon filled with air
has a mass of 3.1 g. The balloon is moving at
1.1 m/s and expelling air at a rate of 150
cm3/s at that instant. The expelled air travels
at a speed of 2.7 m/s relative to the balloon.
Pretend there is no drag.
Find the speed of the balloon 0.25 s later, if the
balloon continues to expel air at
approximately constant rate and speed
during that time.