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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

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

Thrust-to-Weight Ratio - Propeller-driven aircraft

Thrust-to-weight ratio is a dimensionless ratio of thrust to weight of a rocket, jet engine, propeller engine, or a vehicle propelled by such an engine ... 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

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

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

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/

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

Thrust-to-Weight Ratio

Thrust-to-weight ratio is a dimensionless ratio of thrust to weight of a rocket, jet engine, propeller engine, or a vehicle propelled by such an engine ... 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

Thrust to Power

Thrust is a reaction force described quantitatively by Newton’s second and third laws.
The power needed to generate thrust and the force of the ... 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

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

Power-mechanics (Velocity)

Power is the rate at which work is done. It is equivalent to an amount of energy consumed per unit time. Power in mechanical systems is the combination of ... more

Power - rotational systems (torque)

Power is the rate at which work is done. It is equivalent to an amount of energy consumed per unit time. Power in mechanical systems is the combination of ... more

Power in a reference system(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

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

Wing loading - turning radius

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

Glide Ratio

Gliding flight is heavier-than-air flight without the use of thrust; the term volplaning also refers to this mode of flight in animals. It is employed by ... more

Velocity at a distance x (for object following a ballistic trajectory)

A trajectory or flight path is the path that a moving object follows through space as a function of time. A trajectory can be described mathematically ... more

Energy–Maneuverability Theory (aircraft performance)

Energy–maneuverability theory is a model of aircraft performance. It was developed by Col. John Boyd, and is useful in describing an aircraft’s ... more

Time of flight for a projectile following a ballistic trajectory

A trajectory or flight path is the path that a moving object follows through space as a function of time. ballistic trajectory of a projectile is the path ... more

Tractive Force

As used in mechanical engineering, the term tractive force can either refer to the total traction a vehicle exerts on a surface, or the amount of the total ... more

Turbine specific speed

The specific speed value (radian/second) for a turbine is the speed of a geometrically similar turbine which would produce one unit of the specific speed ... more

Wind Energy

Wind power is the conversion of wind energy into a useful form of energy, such as using wind turbines to produce electrical power, windmills for mechanical ... more

Tractive Force - Steam locomotives

As used in mechanical engineering, the term tractive force can either refer to the total traction a vehicle exerts on a surface, or the amount of the total ... more

Karman vortex street formula

In fluid dynamics, a Kármán vortex street is a repeating pattern of swirling vortices caused by the unsteady separation of flow of a fluid around blunt ... 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

Leadscrew Frictional Torque of the Thrust Collar

A leadscrew (or lead screw), also known as a power screw or translation screw, is a screw used as a linkage in a machine, to translate turning motion into ... more

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