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Concentration of a substance (first order reaction)

The concentration of a substance at time “t”, of a first-order reaction, depends only on the initial concentration and the properties of the ... more

First-order rate constant ( Arrhenius equation)

Arrhenius’ equation gives the dependence of the rate constant “k” of a chemical reaction on the absolute temperature (in kelvin), by the ... more

Michaelis–Menten enzyme kinetics (reaction rate)

Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics.The model takes the form of an equation describing the rate of enzymatic ... more

Michaelis–Menten enzyme kinetics (maximum reaction rate)

Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics.The model takes the form of an equation describing the rate of enzymatic ... more

Collision Frequency

Collision theory is a theory proposed independently by Max Trautz in 1916 and William Lewis in 1918, that qualitatively explains how chemical reactions ... more

Released energy of exergonic reaction

A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Classically, chemical reactions encompass ... more

Hole change in Gibbs free energy

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

Van 't Hoff equation

The Van 't Hoff equation in chemical thermodynamics relates the change in the equilibrium constant, Keq, of a chemical equilibrium to the change in ... more

Rate constant (collisions in chemical reactions)

Collision theory qualitatively explains how chemical reactions occur and why reaction rates differ for different reactions. The collision theory states ... 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

Hick's Law

Hick’s law, or the Hick–Hyman law, named after British and American psychologists William Edmund Hick and Ray Hyman, describes the time it takes for ... more

Nernst Equation - total cell potential

In electrochemistry, the Nernst equation is an equation that relates the reduction potential of an electrochemical reaction (half-cell or full cell ... more

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

Diffusion Coefficient - related to Fick's laws of diffusion

Diffusion is the net movement of a substance (e.g., an atom, ion or molecule) from a region of high concentration to a region of low concentration. This is ... 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

Nernst Equation - electrochemical half cell

In electrochemistry, the Nernst equation is an equation that relates the reduction potential of an electrochemical reaction (half-cell or full cell ... more

Fick principle (calculation of cardiac output)

The essence of the Fick principle is that blood flow to an organ can be calculated using a marker substance if the following information is known:
... more

Cell voltage

A galvanic cell, or voltaic cell, named after Luigi Galvani, or Alessandro Volta respectively, is an electrochemical cell that derives electrical energy ... more

Stark–Einstein Law

he Stark–Einstein law is named after German-born physicists Johannes Stark and Albert Einstein, who independently formulated the law between 1908 and 1913. ... more

Time Constant in RC electrical circuits

In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of ... more

Time Constant in RL electrical circuits

In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of ... more

Time Constant in digital electronic circuits

In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of ... more

Molar concentration

In chemistry, the molar concentration, is defined as the amount of a constituent divided by the volume of the mixture. It is also called molarity, ... more

Density

The density of a material is defined as its mass per unit volume. For a pure substance the density has the same numerical value as its mass concentration. ... more

Diffusion Coefficient for two different gases (related to Fick's laws)

Diffusion is the net movement of a substance (e.g., an atom, ion or molecule) from a region of high concentration to a region of low concentration. For two ... more

Kelvin–Helmholtz mechanism

The Kelvin–Helmholtz mechanism is an astronomical process that occurs when the surface of a star or a planet cools. The cooling causes the pressure to ... more

Magnetic Prandtl number (with Reynolds number)

The Magnetic Prandtl number is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) ... more

Worksheet 296

(a) Calculate the buoyant force on 10,000 metric tons (1.00×10 7 kg) of solid steel completely submerged in water, and compare this with the steel’s weight.

(b) What is the maximum buoyant force that water could exert on this same steel if it were shaped into a boat that could displace 1.00×10 5 m 3 of water?

Strategy for (a)

To find the buoyant force, we must find the weight of water displaced. We can do this by using the densities of water and steel given in Table [insert table #] We note that, since the steel is completely submerged, its volume and the water’s volume are the same. Once we know the volume of water, we can find its mass and weight

First, we use the definition of density to find the steel’s volume, and then we substitute values for mass and density. This gives :

Density

Because the steel is completely submerged, this is also the volume of water displaced, Vw. We can now find the mass of water displaced from the relationship between its volume and density, both of which are known. This gives:

Density

By Archimedes’ principle, the weight of water displaced is m w g , so the buoyant force is:

Force (Newton's second law)

The steel’s weight is 9.80×10 7 N , which is much greater than the buoyant force, so the steel will remain submerged.

Strategy for (b)

Here we are given the maximum volume of water the steel boat can displace. The buoyant force is the weight of this volume of water.

The mass of water displaced is found from its relationship to density and volume, both of which are known. That is:

Density

The maximum buoyant force is the weight of this much water, or

Force (Newton's second law)

Discussion

The maximum buoyant force is ten times the weight of the steel, meaning the ship can carry a load nine times its own weight without sinking.

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/

Cross Section

The cross section is an effective area that quantifies the intrinsic likelihood of a scattering event when an incident beam strikes a target object, made ... more

Magnetic Prandtl number (diffusion rate)

The Magnetic Prandtl number is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) ... more

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