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Newton’s Second Law Solution

Summary Description

Programs:

NEWT

Version:

1.0, 22 January 2006

Description:

The NEWT program computes the unknown quantity in the equation F = ma, given any two of the quantities.

Compatibility:

Is compatible CFX-9850G

Compatible with CFX-9850G

Is compatible FX-7400G

Compatible with FX-7400G

Detailed Description

The NEWT program computes the unknown quantity in the equation F = ma, given any two of the quantities.

Newton’s second law of motion is that the instantaneous force applied to a body is equal to the instantaneous change in momentum of the body, or

vector F = d vector p / dt

This equation reduces to the familiar F = ma when (i) scalars are used, rather than vectors, and (ii) the body’s mass is fixed, which is not the case in rocketry and when relativistic velocities are involved. The F = dp/dt form is accurate even for relativistic mechanics and rocketry, and is often regarded as an “correction” of Newton’s second law F = ma. Although both rocketry and relativity were in the future, what Newton actually wrote was the accurate differential equation form, not the simpler form. Conspiracy theorists and UFO believers may start speculating now.

The equation F = ma has three variables: F, the net force applied to the body; m, the body’s mass; and a, the acceleration experienced by the body. Specifying any two of these allows the third to be computed. The NEWT program determines which variable is missing and solves for it.

Note that not every combination of values has a solution. If both F and a are zero, m can have any value. If F is non-zero and a is zero, there is no possible value of m. The program will produce a mathematics error (the error message “Ma error”) in such cases.

Usage

Enter the NEWT program into the calculator, using either the calculator data cable or entering the program directly.

Choose a system of measurement (mKs, cgs, English, etc.), and convert all known values into this system. The result in the solution will also be expressed in this system.

Run the program.

Screen shot The program will display the prompt “0:Done 1:F 2:m 3:a?” and pause for you to input a code. Enter the known factors of the equation by first entering the appropriate code (1 for net force, 2 for mass, 3 acceleration), then entering the factor’s value. The program displays one of the prompts “Force,” “Mass,” or “Accel” after you enter the code for the value and before you enter the value itself. This two-step process of identifying the data to be entered, then entering the data, is indicated in the screen shot to the right.

If you enter an incorrect value for a factor, you can enter the factor again with the correct value. The most recently entered factor value is the value that is used. If you enter an incorrect factor code, you must restart the program. There is no way to “erase” a factor once it has been entered.

Screen shot When you have entered all the known factor values, use the code 0 to indicate that entry of the factor values is complete. The program will then compute and display the factor value that was not entered. The display of values is shown in the screen shot to the right.

Screen shot If you have not entered enough information for the program to determine the unknown factors of the equation, the program will display the message “Not enough information.” This message is shown in the screen shot to the left.

Program

Source Code

The program is available in a ZIP file, or may be entered as shown below. Remember that this program is copyrighted; see the copyright issues page for limitations on redistribution.

Program NEWT (242 bytes):

'NEWT 1.0End of line operator
0→A~GEnd of line operator
DoEnd of line operator
"0:Done"End of line operator
"1:F 2:m 3:a"?→AEnd of line operator
If A=1End of line operator
Then "Force"?→CEnd of line operator
1→BEnd of line operator
IfEndEnd of line operator
If A=2End of line operator
Then "Mass"?→EEnd of line operator
1→DEnd of line operator
IfEndEnd of line operator
If A=3End of line operator
Then "Accel"?→GEnd of line operator
1→FEnd of line operator
IfEndEnd of line operator
LpWhile A≠0End of line operator
If B+D+F<2End of line operator
Then "Not enough information"End of line operator
Else If F=0End of line operator
Then "a"End of line operator
C/EEnd of line operator
IfEndEnd of line operator
If D=0End of line operator
Then "m"End of line operator
C/GEnd of line operator
IfEndEnd of line operator
If B=0End of line operator
Then "F"End of line operator
EGEnd of line operator
IfEndEnd of line operator
IfEnd

Programming Notes

The display operator is not used; the value to be displayed is simply computed and left in Ans, where the calculator displays it when the program ceases execution.

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Copyright © 2006 Brian Hetrick
Page last updated 22 January 2006.

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