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True Airspeed - High-speed flight

The true airspeed (TAS; also KTAS, for knots true airspeed) of an aircraft is the speed of the aircraft relative to the airmass ... more

Rydberg formula for any hydrogen-like element

The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements.Rydberg worked on a formula ... more

Vertical Wind Profile - Power Law

The design of buildings must account for wind loads, and these are affected by wind shear. For engineering purposes, a power law wind speed profile may be ... 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

Wave shoaling height

In fluid dynamics, wave shoaling is the effect by which surface waves entering shallower water change in wave height. It is caused by the fact that the ... more

Hydraulic conductivity (Constant-head method)

Hydraulic conductivity is a property of vascular plants, soils and rocks, that describes the ease with which a fluid (usually water) can move through pore ... 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/

Jounce

In physics, jounce or snap is the fourth derivative of the position vector with respect to time, with the first, second, and third derivatives being ... more

Radiant Exitance (real surface)

In radiometry, radiant exitance is the radiant flux emitted by a surface per unit area, and spectral exitance is the radiant exitance of a surface per unit ... more

Sherwood Number for a single sphere

The Sherwood number (Sh) is a dimensionless number used in mass-transfer operation. It can be further defined as a function of the Reynolds and Schmidt ... more

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