Tuesday, May 29, 2018

Fun With the Casio fx-3650P: Program Collection 5/29/2018

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

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 questions.

3 comments:

1. Hi Eddie,
The Casio fx-3650P only holds 4 programs correct? In your opinion isn't this a bit cumbersome for a programmable scientific?
/Regards

1. Lonewolf,

Yes, there are only slots for 4 programs and only 360 steps. To use all four slots efficiently, you will need to be selective and efficient with the steps. If you have a collection, you may want to consider buying a small notebook (can be a book of index cards wired together) to have the programs as a reference. I started a few booklets for several calculators.

Eddie

2. Thanks.How can I solve 3 equations with 3 variables using casio fx-3650P ?? Please..

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