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1. Consider a 500 kg camel standing on the surface of the Earth. The mass of the Earth is 5.98x1024 kg and the average radius of the Earth is 6.37x106 m. The Universal Gravitation Constant (G) is 6.67x10-11 N.m2/kg2 and the gravitational acceleration (g) at the surface of the Earth is 9.8 m/s2.
a. Determine the weight of the camel.
b. Using Newton’s Law of Universal Gravitation, determine the gravitational force of the Earth acting on the camel.
c. How do your answers to Part A and Part B compare?
d. Based on your answers to the above problems, how does “g” relate to the mass of the Earth, the radius of the Earth, and the Universal Gravitational Constant? Express your answer as a mathematical formula.
e. Concept question: What is the gravitational acceleration at a distance of one Earth radius above the surface of the Earth?
f. Concept question: What is the gravitational acceleration halfway and ¾ of the way to the center of the Earth?
2. The Moon has a mass of 7.44x1022 kg and its average radius is 1.74x106 m. The Universal Gravitation Constant (G) is 6.67x10-11 N.m2/kg2.
a. Use Newton’s Universal Law of Gravitation to calculate the gravitational force (weight) for a 70 kg person standing on the surface of the Moon.
b. What is the gravitational acceleration on the surface of the Moon? Use you answer to Part A to find this value.
c. The average distance between the Moon and the Earth is 3.8 x108 m. Use Newton’s Universal Law of Gravitation to determine the gravitational force acting on the Moon due to the Earth. Note: the mass of the Earth is 5.98x1024 kg.
d. Based on your answer in Part C, determine the gravitational acceleration due to the Earth acting on the Moon.
e. Determine the gravitational force of the Earth on the 70 kg person in Part A.
f. Consider the 70 kg person standing on a typical bathroom scale (on the Moon), when the Earth is directly overhead. Draw the free-body (force vector) diagram for the person and label all forces. Which force in your diagram corresponds to the scale reading?
g. Applying Newton’s 2nd Law to the person, what is the reading on the scale?
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