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Sears–Haack body (Wave Drag related to the Volume)

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical ... more

Vis-Viva Equation

In astrodynamics, the vis viva equation, also referred to as orbital energy conservation equation, is one of the fundamental equations that govern the ... more

Terminal velocity (creeping flow conditions)

The terminal velocity of a falling object is the velocity of the object when the sum of the drag force and buoyancy equals the downward force of gravity ... more

Precession - (Torque-induced - Classical Newtonian)

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the ... more

Force (Newton's second law)

In physics, a force is any influence which tends to change the motion of an object.In other words, a force can cause an object with mass to change its ... 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

Friction velocity (shear velocity)

Friction velocity, is a form by which a shear stress may be re-written in units of velocity. It is useful as a method in fluid mechanics to compare true ... 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/

Apsidal precession

In celestial mechanics, apsidal precession is the precession (gradual rotation) of the line connecting the apsides (line of apsides) of an astronomical ... more

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