Meriam, Kraige & Bolton — Introduction to Statics: Problem 1_10

⚡ Mecademy AIENG정역학 · ch1  Problem Statement 1/10 Determine the small gravitational force F which the copper sphere exerts on the steel sphere. Both spheres are homogeneous, and the value of is 50 mm. Express your result as a vector. Problem 1/10 (a) Determination of the Mass of Each Sphere ● Calculation Process 1. Present Final Formula: The mass of a homogeneous sphere is calculated using its volume and its density : From the physical property table (Table D/2), the densities are: Density of Copper: Density of Steel: The radius of the copper sphere is . The radius of the steel sphere is . 2. Substitute Values: 3. Partial Operations: 4. Final Calculation: r m V= πR 3 4 3 ρ m=ρ⋅V=ρ⋅ πR( 3 4 3 ) ρ = Cu 8910 kg/m 3 ρ = St 7830 kg/m 3 r = 1 r=50 mm=0.05 m r = 2 = 2 r 25 mm=0.025 m m = Cu 8910× × 3 4 π×(0.05) 3 m = St 7830× × 3 4 π×(0.025) 3 V = Cu π (0.000125)≈ 3 4 5.23599×10 m −43 V = St π (0.000015625)≈ 3 4 6.54498×10 m −53 m ≈ Cu 8910×5.23599×10= −4 4.665 kg ● Final Conclusion: The masses of the copper and steel spheres are approximately and , respectively. (b) Calculation of Gravitational Force Magnitude ● Calculation Process 1. Present Final Formula: Newton's Law of Universal Gravitation states: where and is the distance between centers. Based on the diagram, the horizontal distance is and the vertical distance is . 2. Substitute Values: 3. Partial Operations: 4. Final Calculation: ● Final Conclusion: The magnitude of the gravitational force is approximately . (c) Expressio