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Calculating Forces Acting on Two Bodies

Learn how to calculate forces acting on two particles or bodies and compute the magnitude and components of the force using position and mass parameters. Apply trigonometric functions to determine X and Y components of the force.

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Calculating Forces Acting on Two Bodies

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  1. How do we calculate forces acting on two bodies? Forces on two particles/bodies, calculated as acting on P(1) P(2).posX P(2).posY P(1).posX P(1).posY

  2. How do we calculate forces acting on two bodies? Forces on two particles/bodies, calculated as acting on P(1) The Force magnitude equation is given by: F = G * M1 * M2 / R2 P(2).posX P(2).posY We need to compute R. P(1).posX P(1).posY We know body positions

  3. How do we calculate forces acting on two bodies? Forces on two particles/bodies, calculated as acting on P(1) F = G * M1 * M2 / R2 P(2).posX P(2).posY R = sqrt(A2 + B2) B = P(2).posY – P(1).posY P(1).posX P(1).posY A = P(2).posX – P(1).posX

  4. How do we calculate forces acting on two bodies? Forces on two particles/bodies, calculated as acting on P(1) F = G * M1 * M2 / R2 P(2).posX P(2).posY We can now compute magnitude of F R = sqrt(A2 + B2) B = P(2).posY – P(1).posY P(1).posX P(1).posY A = P(2).posX – P(1).posX

  5. How do we calculate forces acting on two bodies? Forces on two particles/bodies, calculated as acting on P(1) F = G * M1 * M2 / R2 P(2).posX P(2).posY How can we compute components of F in X and Y directions? R = sqrt(A2 + B2) B = P(2).posY – P(1).posY theta P(1).posX P(1).posY A = P(2).posX – P(1).posX We will use sin and cosfunctions to compute the X and Y components of force F COS(theta) = A/R SIN(theta) = B/R

  6. How do we calculate forces acting on two bodies? Forces on two particles/bodies, calculated as acting on P(1) F = G * M1 * M2 / R2 P(1).posX P(1).posY R = sqrt(A2 + B2) F_Y = F * SIN(theta) = F * B/R Given magnitude of the F, value of A,B and R we can compute F_X and F_Y P(1).posX P(1).posY F_X = F * COS(theta) = F * A/R COS(theta) = A/R SIN(theta) = B/R

  7. How do we calculate forces acting on two bodies? Forces on two particles/bodies, calculated as acting on P(1) F = G * M1 * M2 / R2 P(1).posX P(1).posY R = sqrt(A2 + B2) F_Y = F * B/R Resulting F_X and F_Y are forces acting on P(1) by P(2), they are signed. P(1).posX P(1).posY F_X = F * A/R COS(theta) = A/R SIN(theta) = B/R

  8. How do we calculate forces of N planets on a planet A? • We perform the steps from previous 7 slides for each of the N planets. • We compute the X and Y components of the forces acting on each planet • We add all of the X components of the forces together.  Then we add all of the Y components of the forces together. These results give us the X and Y forces acting on planet A.

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