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Tsiolkovsky rocket equation as function of payload

The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that ... more

Thrust

Thrust is a reaction force described quantitatively by Newton’s second and third laws. When a system expels or accelerates mass in one direction, the ... more

Energy required for a chemical rocket

Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with ... more

Ideal rocket equation (Tsiolkovsky rocket equation)

The Tsiolkovsky rocket equation, or ideal rocket equation describes the motion of vehicles that follow the basic principle of a rocket: a ... more

Time to reach a required delta-v - rocket propulsion

Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with ... more

Minimum required rocket energy

Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with ... more

Specific Impulse by weight - with mass flow rate

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

Specific Impulse by weight

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

Minimum chemical rocket energy required

Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with ... more

Specific Impulse

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

Mass Ratio - Rockets

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

Net Thrust of a Rocket Engine

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

Exhaust Gas Velocity

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

Water Rocket - peak height

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

Worksheet 289

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.

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

Force (Newton's second law)

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.

Subtraction

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:

Division

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/

Delta-v budget

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

Newton's second law (variable-mass system)

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

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

Thrust to Propulsive Power

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

Propellant mass fraction

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

Angle required to hit polar coordinate (x,y) - (projectile following a ballistic trajectory)

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

de Laval nozzle - correlation of Area and Velocity

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

Newton's second law Newton's second law (constant-mass system)

The second law states that the net force on an object is equal to the rate of change of its linear momentum in an inertial reference frame. The second law ... more

Gravitational wave - Binaries (Orbital lifetime)

Gravitational waves are disturbances in the curvature (fabric) of spacetime, generated by accelerated masses, that propagate as waves outward from their ... more

Shock Diamond - distance from the nozzle

Shock diamonds (also known as Mach diamonds, Mach disks, Mach rings, doughnut tails or thrust diamonds) are a formation of standing wave patterns that ... more

Time of Flight

Time of flight (TOF) describes a variety of methods that measure the time that it takes for an object, particle or acoustic, ... more

Angular Acceleration

Torque, moment, or moment of force is the tendency of a force to rotate an object about an axis, fulcrum, or pivot.
Moment of inertia is the mass ... more

Thrust (with cross section area)

Thrust is a reaction force described quantitatively by Newton’s second and third laws. When a system expels or accelerates mass in one direction, the ... more

Wind loading - takeoff speed

In aerodynamics, wing loading is the total weight of an aircraft divided by the area of its wing. The stalling speed of an aircraft in straight, level ... more

Power (aerodynamic drag)

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force ... more

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