Cartesian coordinate system is used to specify any point on a plane.
In two dimensional plane,the two types of axes or coordinates are and axis.
Explanation:
Cartesian coordinate system specifies each point and every point on axes.
A Cartesian Coordinate system in two dimension also named as rectangular coordinate system.
The two types of axes or coordinates are and axis.
The horizontal axis is -axis and vertical axis is named as -axis.
The coordinate system specifies each point as a set of numerical coordinates in a plane which are signed from negative to positive. that is from (,).
In three dimensional plane, , and coordinates are used and in two dimensional plane, and coordinates are used to address any point in the interval (,).
For defining both the coordinates, the two perpendicular directed lines - axis and -axis are drawn.
Now, for example is a point in which indicates that the value of is and is .
It is drawn by moving units right from the origin to positive axis and units upwards from the origin to positive -axis.
For some metal alloy, a true stress of 345 MPa (50040 psi) produces a plastic true strain of 0.02. How much will a specimen of this material elongate when a true stress of 411 MPa (59610 psi) is applied if the original length is 470 mm (18.50 in.)?Assume a value of 0.22 for the strain-hardening exponent, n.
Answer:
The elongation is
Explanation:
In order to gain a good understanding of this solution let define some terms
True Stress
A true stress can be defined as the quotient obtained when instantaneous applied load is divided by instantaneous cross-sectional area of a material it can be denoted as .
True Strain
A true strain can be defined as the value obtained when the natural logarithm quotient of instantaneous gauge length divided by original gauge length of a material is being bend out of shape by a uni-axial force. it can be denoted as .
The mathematical relation between stress to strain on the plastic region of deformation is
Where K is a constant
n is known as the strain hardening exponent
This constant K can be obtained as follows
No substituting from the question we have
Making the subject from the equation above
From the definition we mentioned instantaneous length and this can be obtained mathematically as follows
Where
is the instantaneous length
is the original length
We can also obtain the elongated length mathematically as follows
A woman walks due west on the deck of a ship at 3 miyh.The ship is moving north at a speed of 22 miyh.Find the speed and direction of the woman relative to the surface of the water.
The relationship between power, energy, and time can be described by the following equation : P = Δ E s y s Δ t. P is the average power output, measured in watts (W) ΔEsys is the net change in energy of the system in joules (J) - also known as work. Δt is the duration - how long the energy use takes - measured in seconds (s).