## Saturday, April 10, 2021

### Fun with the HP 20S (April 10, 2021 Edition)

Fun with the HP 20S (April 10, 2021 Edition)

In all the programs presented on the blog, all inputs are stored in the appropriate registers before the program is run.

The Power of a Windmill

This program calculates the power generated by a windmill, given the diameter and velocity of the windmill’s fans.   SI units (meters, kilograms, seconds) are used.   The general equations used are:

Area of the swept by the windmill’s fans (in m^2):

A = ( π * diameter^2 ) / 4

Power generated (in W (Watts), J/s, m^2 kg/s^3):

P = ½ * area * density * velocity^3

Density of air = 1.225 kg/m^3

Input:

R1 = diameter of the fans, m

R2 = velocity of the fans, m/s

Output:

R3 = area that the fans cover, m^2;  press [ R/S ]

R4 = power of the fan, W

Program:

01 LBL A         61,41, A

02 RCL 1         22, 1

03 51, 11

04 × 55

05 π 61, 22

06 ÷ 45

07 4 4

08 = 74

09 STO 3         21, 3

10 R/S 26

11 × 55

12 RCL 2         22, 2

13 y^x 14

14 3 3

15 × 55

16 . 73

17 6 6

18 1 1

19 2 2

20 5 5

21 = 74

22 STO 4         21, 4

23 RTN 61, 26

Example:

Inputs:

diameter = R1 = 6.65 m

velocity = R2 = 10 m/s

Results:

R3 = area = 34.7322702808 m^2

R4 = power = 21,273.515547 W

Source:

Sharp Electronics Corporation.  Conquering The Sciences: Applications for the SHARP Scientific Calculators EL-506P, EL-510S, EL-515S  Japan. 1984

Depth of a Well

This program calculates the depth of a well, which is determined by the time between a person drops a rock and the person hears the rock hit the bottom of the well.  The program uses SI units (meters, kilograms, seconds) with the following constants:

Earth’s Gravitational Acceleration:  g = 9.80665 m/s^2

g/2 = 4.903325 m/s^2

Speed of Sound, in dry air, 20°C temperature: s = 343.21 m/s

Equations:

X = (-B + √(B^2 + 4*A*B)) / 2

Y = g/2 * a^2

where:

B = s / (g/2) (see the above constants)

A = amount of time, in seconds, between the person drops the rock and hears the rock hit the bottom (input)

X = amount of time, in seconds, that it actually takes the rock from the time it was dropped until the rock hits the bottom of the well (output)

Y = depth of the well, in meters (output)

Input:

R1 = time until you hear the rock hit the bottom of the well (sec)

Output:

R2 = time until the rock actually hits the bottom of the well (sec), [ R/S ]

R3 = depth of the well (m)

Program:

01 LBL B         61, 41, B

02 3 3

03 4 4

04 3 3

05 . 73

06 2 2

07 1 1

08 ÷ 45

09 4 4

10 . 73

11 9 9

12 0 0

13 3 3

14 3 3

15 2 2

16 5 5

17 STO 0         21, 0

18 = 74

19 STO 4         21, 4

20 +/- 32

21 + 75

22 ( 33

23 RCL 4         22, 4

24 51, 11

25 + 75

26 4 4

27 × 55

28 RCL 4         22, 4

29 × 55

30 RCL 1         22, 1

31 ) 34

32 11

33 = 74

34 ÷ 45

35 2 2

36 = 74

37 STO 2         21, 2

38 R/S 26

39 51, 11

40 × 55

41 RCL 0         22, 0

42 = 74

43 STO 3         21, 3

44 RTN 61, 26

Example:

Input:

time until you hear the rock hit the ground = R1 = 3 sec

Results:

R2 = time the rock travels to the bottom of the well = 2.8813865 sec

R3 = depth of the well = 40.70930098622 m

Source:

Saul, Ken.  The Physics Collection:  Ten HP-41C Programs for First-Year Physics Class   Corvallis, OR.  1986

Thevenin’s Theorem

This program calculated the equivalent resistance and voltage of a linear network of two resistors and a capacitor.

Formulas:

R_TH = (R1 * R2) / (R1 + R2)

V_TH = V * R2 / (R1 + R2)

Inputs:

R1 = resistor 1 ( Ω )

R2 = resistor 2 ( Ω )

R3 = capacitor ( V )

Output:

R4 = equivalent resistor, R_TH, [ R/S ]

R5 = equivalent capacitor, V_TH

Program:

01 LBL C         61, 41, C

02 RCL 1         22, 1

03 × 55

04 RCL 2         22, 2

05 ÷ 45

06 ( 33

07 RCL 1         22, 1

08 + 75

09 RCL 2         22, 2

10 ) 34

11 = 74

12 STO 4         21, 4

13 R/S 26

14 RCL 3         22, 3

15 × 55

16 RCL 2     22, 2

17 ÷ 45

18 ( 33

19 RCL 1     22, 1

20 + 75

21 RCL 2         22, 2

22 ) 34

23 = 74

24 STO 5     21, 5

25 RTN 61, 26

Example:

Input:

R1 = 8 Ω

R2 = 9 Ω

R3 = 11 V

Results:

R4 = 4.23529411765 Ω

R5 = 5.82352941176 V

Source:

Gussow, Milton and William T. Smith  Schaum’s Easy Outlines: Basic Electricity  New York. 2012  ISBN 978-0-07-178068-1

Norton’s Theorem

This program calculates an equivalent resistance and current when any network connected to a positive and a negative terminal.

Formulas:

R_N = (R1 * R2) / (R1 + R2)

I_N = V / R1

Inputs:

R1 = resistor 1 ( Ω )

R2 = resistor 2 ( Ω )

R3 = capacitor ( V )

Output:

R4 = equivalent resistor, R_N, [ R/S ]

R5 = equivalent current, I_N

Program:

01 LBL D         61, 41, D

02 RCL 1         22, 1

03 × 55

04 RCL 2         22, 2

05 ÷ 45

06 ( 33

07 RCL 1         22, 1

08 + 75

09 RCL 2         22, 2

10 ) 34

11 = 74

12 STO 4         21, 4

13 R/S 26

14 RCL 3         22, 3

15 ÷ 45

16 RCL 1         22, 1

17 = 74

18 STO 5         21, 5

19 RTN 61, 26

Example:

Input:

R1 = 8 Ω

R2 = 9 Ω

R3 = 11 V

Results:

R4 = 4.23529411765 Ω

R5 = 1.375 A

Source:

Gussow, Milton and William T. Smith  Schaum’s Easy Outlines: Basic Electricity  New York. 2012  ISBN 978-0-07-178068-1

Eddie

All original content copyright, © 2011-2021.  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.

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