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Future value of a present sum

A time value of money calculation is one which solves for one of several variables in a financial problem. In a typical case, the variables might be: a ... more

Reaction quotient

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

Miller's Rule

In optics, Miller’s rule is an empirical rule which gives an estimate of the order of magnitude of the nonlinear coefficient.

More formally, ... 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


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.


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.


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.
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Magnetic Reynolds number (relationship to eddy current braking)

The dimensionless magnetic Reynolds number, is also used in cases where there is no physical fluid involved.

The magnetic Reynolds number is the ... more

Discharge Coefficient

In a nozzle or other constriction, the discharge coefficient (also known as coefficient of discharge) is the ratio of the actual discharge to the ... more

Little's Law

In queueing theory, a discipline within the mathematical theory of probability, Little’s result, theorem, lemma, law, or formula is a theorem by John ... more

Margin of safety (measure of requirement verification)

Many government agencies and industries (such as aerospace) require the use of a margin of safety (MoS or M.S.) to describe the ratio of the strength of ... more

Population growth rate

In biology or human geography, population growth is the increase in the number of individuals in a population.
The “population growth ... more

Boltzmann distribution in mechanics

In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution, probability measure, or ... more

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