Section 7: Circles and Ellipses
In the last section, we saw that the equation of a line \[
y = y_A + m(x  x_A)
\] can be obtained by considering a fixed point \(A(x_A,y_A)\) on the line and another general point \
(P(x,y)\). This equation restricts \(P\)
Section 5: Introduction to Analytic Geometry
5.1: What is analytic geometry?
Analytic geometry is the study of geometry by placing plane geometric figures (points, lines, circles, etc)
on coordinate axes. For example, we can analyze a triangle like the on
Section 6: Lines
6.1: Slope of a line
The slope of a line is defined as the change in the \(y\)direction (rise) divided by the change in the \(x\)direction. It is a measure of the steepness of a line. The following gives the formula for finding the slope
Section 3: Angles and Triangles
3.1: Angular measurement
Consider a pair of parallel lines crossed by a straight line.
As we know, right angles are \(90^\circ\). The sum of all angles on a straight line is \(180^\circ\), e.g, \(a
+ c = 180^\circ\). We als
Section 2: Length, Area and Volume
2.1: Perimeter, Area and Volume
The perimeter of a plane geometric figure is the total distance around the boundary of the figure. The
perimeter of a circle is also called the circumference.
The following table lists the
Section 1: Ratios and rates
5.1: Ratio
The quotient \(\dfraccfw_acfw_b\) is called the ratio of \(a\) to \(b\). This ratio is sometimes written as \(a:b\).
Example 1
A paint that has a specific tone of blue color can be made by mixing 3 parts of normal bl
Sunday, September 27, 2015
22:17
Find the length of a rod that is required to make the following frame.
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Friday, September 25, 2015
12:30
A ball bearing sits between two metal grooves as shown below. If the distance between the
vertices of the grooves is 5 mm, what must the radius of the ball bearing be?
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Wednesday, September 23, 2015
08:24
A truss structure is shown on the right.
Find the length x.
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A piston and rod assembly is shown below. Find the maximum angle between the cylinder and
the piston rod.
20150923 Trigonome
Monday, September 21, 2015
10:32
Find the area of this shape.
How about
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etc
A cylinder is supported by a cable and a smooth incline plane shown on the left with a freebody diagram on the right.
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A cylinder is sup
Thursday, September 17, 2015
22:33
If an alloy containing 30% silver by mass (called a 30%
alloy) is mixed with a 55% alloy to get 800 kg of 40%
alloy, how much of each of the alloys must be added?
20150918 Ratios and Rates Page 1
An athlete ran for 4 k
Hydraulic Piping
 Schedule 40 is standard.
P. L. = P.L units are in PSI/ft
Fluid Velocity = Q/A
Hydraulic Tubing
 Normally made from annealed steel w/ low carbon content. Materials with good
bending and flaring properties.
 Nominal size is measured by
Load Sensing PRV
Load sensing PRVs senses the magnitude of the pressure through the circuit and
determines which valves should open. If only much lower pressure is required, a load
sensing PRV minimizes the power loss due to heat by friction in valves.
E
Proportional Valves
a valve that produces an output (pressure,flow,direction) that is proportional to an
electronic control input.
proportional valves stop at intermediates positions, controlled by associated electronics
and a max frequency response of
Charge Pump
 During normal operation, oil losses occur due to slippage.
Slippage may cause cavitation so a charge pump is required.
 Charge pump accounts for slippage by keeping the loop full of oil by supplying a
sufficient flow to make up for slippag
Hydrostatic Transmissions
function: transmit energy received from a prime mover (eg. Internal combustion engine)
to a load having its own operating characteristics. Regulate torque and speed.
A typical hydrostatic transmission closed loop drive consists