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Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with ... more
Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with ... more
Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with ... more
The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that ... more
The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that ... more
The Tsiolkovsky rocket equation, or ideal rocket equation describes the motion of vehicles that follow the basic principle of a rocket: a ... more
Specific impulse (usually abbreviated Isp) is a measure of the efficiency of rocket and jet engines. By definition, it is the impulse delivered per unit of ... more
Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with ... more
Specific impulse (usually abbreviated Isp) is a measure of the efficiency of rocket and jet engines. By definition, it is the impulse delivered per unit of ... more
In aerospace engineering, mass ratio is a measure of the efficiency of a rocket. It describes how much more massive the vehicle is with propellant than ... more
A rocket engine, or simply “rocket”, is a jet engine that uses only stored propellant mass for forming its high speed propulsive jet. Rocket ... more
Specific impulse (usually abbreviated Isp) is a way to describe the efficiency of rocket and jet engines. It represents the force with respect to the ... more
A rocket engine nozzle is a propelling nozzle (usually of the de Laval type) used in a rocket engine to expand and accelerate the combustion gases produced ... more
A water rocket is a type of model rocket using water as its reaction mass. Such a rocket is typically made from a used plastic soft drink bottle. The water ... more
In astrodynamics and aerospace, a delta-v budget is an estimate of the total delta-v required for a space mission. It is calculated as the sum of the ... more
Thrust is a reaction force described quantitatively by Newton’s second and third laws.
A very common question is how to contrast the thrust
... more
Thrust-to-weight ratio (TWR) is a dimensionless ratio of thrust to weight of a rocket, jet engine, propeller engine, or a vehicle ... more
In aerospace engineering, the propellant mass fraction is the portion of a vehicle’s mass which does not reach the destination, usually used as a ... more
Collision theory is a theory proposed independently by Max Trautz in 1916 and William Lewis in 1918, that qualitatively explains how chemical reactions ... more
A sled experiences a rocket thrust that accelerates it to the right.Each rocket creates an identical thrust T . As in other situations where there is only horizontal acceleration, the vertical forces cancel. The ground exerts an upward force N on the system that is equal in magnitude and opposite in direction to its weight,w.The system here is the sled, its rockets, and rider, so none of the forces between these objects are considered. The arrow representing friction ( f ) is drawn larger than scale.
Assumptions: The mass of the Sled remains steady throughout the operation
Strategy
Although there are forces acting vertically and horizontally, we assume the vertical forces cancel since there is no vertical acceleration. This leaves us with only horizontal forces and a simpler one-dimensional problem. Directions are indicated with plus or minus signs, with right taken as the positive direction. See the free-body diagram in the figure.
Solution
Since acceleration, mass, and the force of friction are given, we start with Newton’s second law and look for ways to find the thrust of the engines. Since we have defined the direction of the force and acceleration as acting “to the right,” we need to consider only the magnitudes of these quantities in the calculations. Hence we begin with
Fnet is the net force along the horizontal direction, m is the rocket’s mass and a the acceleration.
We can see from the Figure at the top, that the engine thrusts add, while friction opposes the thrust.
Tt is the total thrust from the 4 rockets, Fnet the net force along the horizontal direction and Ff the force of friction.
Finally, since there are 4 rockets, we calculate the thrust that each one provides:
T is the individual Thrust of each engine, b is the number of rocket engines
Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/
Variable-mass systems, (like a rocket burning fuel and ejecting spent gases), are not closed and cannot be directly treated by making mass a function of ... more
Characteristic velocity or c*, or C-star is a measure of the combustion performance of a rocket engine independent of nozzle performance, and is used to ... more
In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is the work needed to accelerate a body of a given mass ... more
A de Laval nozzle (or convergent-divergent nozzle, CD nozzle or con-di nozzle) is a tube that is pinched in the middle, making a carefully balanced, ... more
In physics, the ballistic trajectory of a projectile is the path that a thrown or launched projectile or missile without propulsion will take under the ... more
Thrust-to-weight ratio (TWR) is a dimensionless ratio of thrust to weight of a rocket, jet engine, propeller engine, or a vehicle ... more
A typical small rescue helicopter, like the one in the Figure below, has four blades, each is 4.00 m long and has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length. The helicopter has a total loaded mass of 1000 kg. (a) Calculate the rotational kinetic energy in the blades when they rotate at 300 rpm. (b) Calculate the translational kinetic energy of the helicopter when it flies at 20.0 m/s, and compare it with the rotational energy in the blades. (c) To what height could the helicopter be raised if all of the rotational kinetic energy could be used to lift it?
The first image shows how helicopters store large amounts of rotational kinetic energy in their blades. This energy must be put into the blades before takeoff and maintained until the end of the flight. The engines do not have enough power to simultaneously provide lift and put significant rotational energy into the blades.
The second image shows a helicopter from the Auckland Westpac Rescue Helicopter Service. Over 50,000 lives have been saved since its operations beginning in 1973. Here, a water rescue operation is shown. (credit: 111 Emergency, Flickr)
Strategy
Rotational and translational kinetic energies can be calculated from their definitions. The last part of the problem relates to the idea that energy can change form, in this case from rotational kinetic energy to gravitational potential energy.
Solution for (a)
We must convert the angular velocity to radians per second and calculate the moment of inertia before we can find Er . The angular velocity ω for 1 r.p.m is
and for 300 r.p.m
The moment of inertia of one blade will be that of a thin rod rotated about its end.
The total I is four times this moment of inertia, because there are four blades. Thus,
and so The rotational kinetic energy is
Solution for (b)
Translational kinetic energy is defined as
To compare kinetic energies, we take the ratio of translational kinetic energy to rotational kinetic energy. This ratio is
Solution for (c)
At the maximum height, all rotational kinetic energy will have been converted to gravitational energy. To find this height, we equate those two energies:
Discussion
The ratio of translational energy to rotational kinetic energy is only 0.380. This ratio tells us that most of the kinetic energy of the helicopter is in its spinning blades—something you probably would not suspect. The 53.7 m height to which the helicopter could be raised with the rotational kinetic energy is also impressive, again emphasizing the amount of rotational kinetic energy in the blades.
Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/
In chemistry, a reaction quotient: Qr is a function of the activities or concentrations of the chemical species involved in a chemical reaction. In the ... more
Escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero. It is the speed needed to ... more
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Prior to manned space flights, rocket sleds were used to test aircraft, missile equipment, and physiological effects on human subjects at high speeds. They consisted of a platform that was mounted on one or two rails and propelled by several rockets. Calculate the magnitude of force exerted by each rocket, called its thrust T , for the four-rocket propulsion system shown in the Figure below. The sled’s initial acceleration is 49 m/s 2, the mass of the system is 2100 kg, and the force of friction opposing the motion is known to be 650 N.