Lecture Notes Updated Friday, 06-Jan-2006 19:34:59 EST

Propulsion

• Newton's Laws of Mechanical Motion (usually just called Newton's Laws)
• Apply to the motion of all objects in our everyday experience (exceptions are very large objects, such as massive stars, and very small objects, such as atoms)
• Can use these to understand fundamentals of propulsion
• Newton's First Law -- Object at rest remains at rest, or object with some velocity maintains this, unless an external force acts upon the object
• Velocity refers to both the speed and direction of motion
• Force is the amount of push or pull exerted against an object
• Internal forces (i.e., forces between atoms that hold the object together) do not affect overall motion of the object
• Examples
• Object sitting motionless on a surface doesn't begin to move until an external force pushes it
• Baseball thrown horizontally would continue moving in a straight horizontal line, except that the force of gravity changes its velocity (both direction and speed)
• Satellite moving in deep space (very far from any significant gravitational sources) moves on a straight path and with constant speed until it approaches a star and experiences a gravitational force
• Newton's Second Law -- relationship between an external force, the mass of an object, and the change in the object's velocity is given by
where F = external force, m = object's mass, a = object's acceleration (rate at which velocity changes)
• Mass (m) is the amount of matter in an object (i.e. a measure of the number and type of atoms contained)
• Weight (w) is the force that gravity exerts on an object
where g = 9.8 meters/sec2 if w is in Newtons (N) and m is in kilograms (kg) -- metric system of units
• Example
If F = 10 N and m = 2 kg, then

• Newton's Third Law -- when two objects exert forces on each other, the forces are equal in magnitude (strength) and opposite in direction. This law is also stated as "for every action, there is an equal and opposite reaction."
• Example -- rubber-band cart (shown in class)
• (A rubber band is stretched between two nails on the top of a cart that can roll easily on top of flat table. A wooden block is placed against the rubber band and pulled so that the rubber band elongates. When the block is released, it flies to the left, while the cart rolls to the right.)
• Apply Newton's laws
• 3rd law: the action is the motion of the block and the reaction is the motion of the cart. These motions are caused by forces that the block and cart exert on each other, through the rubber band.
• 2nd law: rubber band exerts a force F against the block of mass mb ; block accelerates at rate a = F/mbF is the same as the tension in the rubber band. Also, rubber band exerts force F (but in opposite direction) against the cart (mass of mc), so cart accelerates with a = F/mc
• Rockets operate also by ejecting objects, only in that case, the objects are the molecules that form the exhaust gases
• Example -- balloon (shown in class)
• An inflated balloon is released and the air inside rushes out, causing the balloon to fly around.
• What makes the balloon move? NOT the escaping air pushing against the outside air!
 Air molecules inside balloon collide with each other and with balloon walls. For each molecule striking the left side, another strikes the right; for each one that strikes the upper left, one strikes the lower right, etc. -- the forces exerted against the balloon then cancel in pairs. But for molecules striking the upper end (shown as blue molecules here), there are no counterparts striking the lower end since it is open. The net force on the balloon is then in the upward direction in this figure.

 In a rocket engine, combustion (high-temperature chemical reaction) generates energetic particles that collide with engine walls and exert forces. As with the balloon, these forces cancel out pair-wise, except for those particles colliding with the top of the rocket (as shown here). Forces acting upward are not balanced by forces acting downward because opening (the exit nozzle) allows particles to escape as exhaust gases. Engine is attached to main rocket, so engine exerts upward force on rocket and entire vehicle accelerates upward.

• If rocket launched vertically from Earth's surface, what is its upward acceleration (i.e., how fast does its speed increase?)
• Apply Newton's 2nd law: F = ma. Here, F is the net force, which will be the difference between the rocket's weight and the thrust (force generated by the rocket engine). F = T - W.
• Example
• rocket weighs 1200 N and engine produces thrust T = 2700 N., so
F = T - W = 2700 - 1200 N = 1500 N
• mass of rocket m = W/g = 1200 N. / 9.8 m/sec2 = 122.4 kg.
• a = F/m = 1500 N./122.4 kg = 12.2 m/sec2
• upward speed at end of 1st second = 12.2 m/sec
upward speed at end of 2nd second = 24.4 m/sec

upward speed at end of 3rd second = 36.6 m/sec

Copyright Ó 1998, Robert G. Melton

Updated Friday, 06-Jan-2006 19:34:59 EST