Meriam, Kraige & Bolton — Introduction to Statics: Problem 1_6

⚡ Mecademy AIENG정역학 · ch1  Problem Statement 1/6 From the gravitational law calculate the weight W (gravitational force with respect to the earth) of an 85-kg man in a spacecraft traveling in a circular orbit 250 km above the earth’s surface. Express W in both newtons and pounds. Problem 1/6 1. Identify Known Parameters and Physical Constants To calculate the weight using the law of universal gravitation, we need the mass of the man, the distance from the center of the Earth, and the Earth's physical constants (typically found in the reference tables of the textbook, such as Table D/2). Mass of the man: Altitude above the surface: Gravitational constant: Mass of the Earth: Mean radius of the Earth: 2. Calculate the Weight in Newtons ● Calculation Process 1. Present Final Formula: The gravitational force (weight) is given by Newton's law of universal gravitation: where is the distance from the center of the Earth. 2. Substitute Values: First, calculate the total distance : m=85 kg h=250 km=250×10 m 3 G=6.673×10 m/(kg⋅ −113 s) 2 M=5.976×10 kg 24 R=6371 km=6.371×10 m 6 W= r 2 GMm r=R+h r r=6.371×10 m+ 6 0.250×10 m= 6 6.621×10 m 6 Now, substitute all values into the weight formula: 3. Partial Operations: Calculate the numerator: Calculate the denominator: 4. Final Calculation: ● Final Conclusion: The weight of the man in Newtons is approximately . 3. Convert the Weight to Pounds ● Calculation Process 1. Present Final Formula: Using the conversion factor : 2. Substitute Values: 3