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Earnings per share (continuing operations formula)

Earnings per share is the monetary value of earnings per each outstanding share of a company’s common stock. Shares outstanding are all the shares of a ... more

R-value (insulation) of a multi-layered installation

Formula first contributed by:
zfyl

The R-value is a measure of thermal resistance, or ability of heat to transfer from hot ... more

Specific gravity of solids

Silts, sands and gravels are classified by their size, and hence they may consist of a variety of minerals. Owing to the stability of quartz compared to ... 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

Heinz mean

In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability ... more

Gamma distribution Mean (With a shape parameter k and a scale parameter θ)

In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The parameterization with k ... more

Nut Factor

Bolted joints are one of the most common elements in construction and machine design. They consist of fasteners that capture and join other parts, and are ... more

Estimated Blood Alcohol Concentration - EBAC

Blood alcohol content (BAC), also called blood alcohol concentration, blood ethanol concentration, or blood alcohol level is most ... more

Specific absorption rate - with Electric intensity

Specific absorption rate (SAR) is a measure of the rate at which energy is absorbed by the human body when exposed to a radio ... more

Arithmetic Mean Return

Compound annual growth rate is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the ... more

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