Fun With the Casio fx-3650P
Previous Entries
5/11/2014:
1. Circular Sectors
2. Stopping Sight Distance
3. Resistors in Parallel
4. Net Present Value
5. Rod Pendulum
6. Vectors: Dot and Cross Products
2. Stopping Sight Distance
3. Resistors in Parallel
4. Net Present Value
5. Rod Pendulum
6. Vectors: Dot and Cross Products
10/27/2015:
1. Combination with Replacement
2. Great Circle (Distance in km)
3. Orbital Speed and Period
4. Eccentricity and Area of an Ellipse
5. Super Factorial
6. Escape Velocity
7. Finance: Payment of a Monthly Mortgage
8. Wind Chill Factor
9. Speed of Sound in Dry Air
7/2/2017:
1. Modulus Function
2. Normal CDF
3. Sum: Σ (AX + B)^C, from X =
0 to X = Y
4. Sun Altitude and Azimuth Based on the
Vernal Equinox
5. Trapezoid: Midsegment, Height, and Area
6. Solar Irradiance
7. General a list of X Random Integers from
0 to Y
Contents for this Blog Entry:
1. kth Derivative of
f(x) = y^n
2. Sight Reduction
Table
3. Distance Off at
Second Bearing by Two Bearings and Run
4. Hydraulic
Cylinder: Force and Flow
5. Mass Held by Two
Strings
6. Atwood Machine:
Tension and Acceleration
kth Derivative of f(x) = x^n
This program calculates
the kth derivative of x^n. Using the variables of the Casio fx-3650p, this
program calculates:
‘d^A/dx^A X^B. A is an integer, where B and X are real
numbers.
Program (47 steps):
?
→ A : ? → B : → X : 1 → C : Lbl 1 : CB → C : B – 1 → B : A – 1 → A : A ≠ 0 ⇒ Goto 1 : CX ^ B
Input order: A = order, B = power, X = x
Examples:
A = 3, B = 2.5, X =
3. Result: 1.08253175473
A = 4, B = 6, X =
1. Result: 360
Sight Reduction Table
The program calculates
altitude and azimuth of a given celestial body.
Inputs:
A: Local Hour Angle
(LHA)
B: The observer’s latitude
on Earth, north is positive, south is negative (L)
D: Declination of
the celestial’s body, north is positive, south is negative (δ)
The latitude is
often entered in degrees/minutes/seconds format.
Do this using the [ °
‘ “ ] key. The calculator is set in Degrees program.
Formulas:
Altitude:
H = asin (sin δ sin
L + cos δ cos L cos LHA)
Zenith:
Z = acos ((sin δ –
sin L sin H) ÷ (cos H cos L))
If sin LHA < 0
then Z = 360° - Z
Output variables:
C = altitude
X = zenith
Program (67 steps):
Deg
: ? → A : ? → B : ? → D : sin^-1 ( sin D sin B + cos D cos B cos A ) → C ◢ cos^-1 ( ( sin D – sin B sin C ) ÷ ( cos C cos B ) ) → X: sin A
> 0 ⇒ 360 – X → X : X
Source: “NAV 1-19A Sight Reduction Table” HP 65
Navigation Pac. Hewlett Packard, 1974.
Distance Off at Second Bearing
by Two Bearings and Run
This program calculates
the distance off between to bearings.
Input variables:
A: first bearing
B: second bearing
C: run (typically in miles, distance will be in
the same length unit)
Distance formula:
D = C * sin A° / sin
|A° - B°|
Since the Casio
fx-3650P does not have an absolute value function, the workaround √(x^2) is used instead.
Program (31 steps):
Deg
: ? → A : ? → B : ? → C : C sin A ÷ sin ( √ (A – B) ^ 2 ) → D
Example:
A = 15°, B = 8 °, C
= 1.5 miles
Result: 3.185613024 miles
(updated 7/1/2018; the result is now correct)
Source: Henry H. Shufeldt and Kenneth E.
Newcomer. The Calculator Afloat: A
Mariner’s Guide to the Electronic Calculator Naval Institute Press: Annapolis, MD. 1980
Hydraulic Cylinders: Force and
Flow
The program calculates
the force and flow.
Input variables:
D: large radius
C: small radius, radius of the cut
X: pressure
Y: speed of the cylinder
Formulas:
Area: A = π (D^2 – C^2)
/ 4
Force: F = pressure
* area = X * A
Flow: q = velocity * area = Y * A
Program (36 steps):
?
→ D : ? → C : π ( D^2 – C^2 ) ÷ 4 → A : ? → X : AX ◢ ? → Y : AY
Example:
Input:
D = 8 in, C = 4
in (8 in cylinder with a 4 in cutout), X
= 68 psi, Y = 3.6 in/sec
Results:
Force: 2563.539605 lb, Flow: 3.6
in^3/sec
Mass Held by Two Strings
The program calculates
the tension of the two strings shown in the diagram above. The tension of both strings are found by
solving the following system of two equations:
cos A° * X – sin B° Y
= 0
sin A° * X – cos B° *
Y = M * g
Where g is Earth’s gravitation
constant, or g = 9.80665 m/s^2 ≈ 32.174 ft/s^2
SI units are used in
this program.
Program (45 steps):
Deg
: ? → A : ? → B : ? → M : 9.80665 M ÷ ( tan A sin B – cos B ) → Y : Y sin B ÷ cos
A → X ◢ Y
Example:
Input:
A = 43°, B = 89°, M
= 16 kg
Results:
X = 234.4572201 N, Y
= 171.4972763 N
Atwood Machine: Tension and Acceleration
The program
calculates the tension in the string of the Atwood Machine and the acceleration
of the system. If the acceleration is
negative, the pulley is turning clockwise, otherwise it is turning
counterclockwise. The following system
of equations is solved, where X is the tension of the strings and Y is the
acceleration of the system.
X + A * Y = g * A
-X + B * Y = -g * B
Where g is Earth’s gravitation
constant, or g = 9.80665 m/s^2 ≈ 32.174 ft/s^2
SI units are used in
this program.
Program (45 steps):
? → A : ? → B : 9.80665 (A – B) ÷ (
A + B ) → Y
: A (9.80665 – Y) → X ◢ Y
Examples:
Input:
A = 11.2 kg, B =
10.3 kg
Results:
X = 105.2367576 N, Y
= 0.41051093 m/s^2
Eddie
All original
content copyright, © 2011-2018. Edward
Shore. Unauthorized use and/or
unauthorized distribution for commercial purposes without express and written
permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial
purposes, provided that full credit is given to the author. Please contact the author if you have
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