Search results
Gravity gradiometry is the study and measurement of variations in the acceleration due to gravity. The gravity gradient is the spatial rate of change of ... more
Acceleration, in physics, is the rate at which the velocity of an object changes over time. Mathematically, instantaneous acceleration—acceleration over an ... more
In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more
In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more
In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more
In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more
The second law states that the net force on an object is equal to the rate of change of its linear momentum in an inertial reference frame. The second law ... more
In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more
In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more
In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with ... more
In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with ... more
Variable-mass systems, (like a rocket burning fuel and ejecting spent gases), are not closed and cannot be directly treated by making mass a function of ... more
The Larmor formula is used to calculate the total power radiated by a non relativistic point charge as it accelerates or decelerates. This is used in the ... more
A simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. The motion is sinusoidal in ... more
Uniform circular motion, that is constant speed along a circular path, is an example of a body experiencing acceleration resulting in velocity of a ... more
In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more
Uniform circular motion, that is constant speed along a circular path, is an example of a body experiencing acceleration resulting in velocity of a ... more
Damped harmonic motion is a real oscillation, in which an object is hanging on a spring. Because of the existence of internal friction and air resistance, ... more
In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more
In 1954, Miles developed his version of this equation for GRMS as he was researching fatigue failure of aircraft structural ... more
Free fall is any motion of a body where its weight is the only force acting upon it. In Uniform gravitational field with air resistance the air resistance ... more
Acceleration, in physics, is the rate of change of velocity of an object. An object’s acceleration is the net result of any and all forces acting on ... more
The electric field is a component of the electromagnetic field. It is a vector field, and it is generated by electric charges or time-varying magnetic ... more
The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that ... more
Time of flight (TOF) describes a variety of methods that measure the time that it takes for an object, particle or acoustic, ... more
The Black–Scholes /ˌblæk ˈʃoʊlz/ or Black–Scholes–Merton model is a mathematical model of a financial market containing derivative investment instruments. ... more
Flux is two separate simple and ubiquitous concepts throughout physics and applied mathematics. Within a discipline, the term is generally used ... more
In finance, volatility is a measure for variation of price of a financial instrument over time. An implied volatility is derived from the market price of a ... more
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 :
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:
By Archimedes’ principle, the weight of water displaced is m w g , so the buoyant force is:
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:
The maximum buoyant force is the weight of this much water, or
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/
...can't find what you're looking for?
Create a new formula
(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?