Meriam, Kraige & Bolton — Introduction to Statics: Problem 1_9

⚡ Mecademy AIENG정역학 · ch1  Problem Statement 1/9 Compute the magnitude of the force which the earth exerts on the moon. Perform the calculation first in newtons and then convert your result to pounds. Refer to Table D/2 for necessary physical quantities. Problem 1/9 ● Calculation Process (SI Units) 1. Present Final Formula: The magnitude of the gravitational force between two masses is given by Newton's Law of Universal Gravitation: where: is the universal gravitational constant. is the mass of the Earth. is the mass of the Moon. is the mean distance between the centers of the Earth and the Moon. 2. Substitute Values: According to standard physical data (Table D/2 in engineering textbooks like Meriam & Kraige): Substituting these into the formula: 3. Partial Operations: Calculate the numerator: F F= G r 2 m m em G m e m m r G=6.673×10m/(kg⋅ −113 s) 2 m = e 5.976×10kg 24 m = m 7.350×10kg 22 r=384,398km=3.84398×10m 8 F=(6.673× 10) −11 (3.84398×10) 82 (5.976×10)(7.350×10) 2422 Numerator=(6.673×10)× −11 (5.976×10)× 24 (7.350×10)≈ 22 2.9 Calculate the denominator: 4. Final Calculation: ● Final Conclusion: The magnitude of the force in Newtons is approximately . ● Calculation Process (U.S. Customary Units) 1. Present Final Formula: Use the conversion factor between Newtons (N) and pounds (lb): 2. Substitute Values: The standard conversion factor is . 3. Final Calculation: ● Final Conclusion: The magnitude of the force in pounds is approximately . The magnitude of the gravitational