Problem: The strength of a gravitational field is defined to be the acceleration imparted to an object with mass in that field. The weight of an object is the force exerted by the gravitational field on it. At the surface of the Earth, the strength of the gravitational field is approximately 9.8 m/s ^ 2. Assume that you have a mass of 69 kilograms.
What is your weight on the surface of the Earth? On the surface of the Moon, the strength of the gravitational field is approximately 1.5 m/s ^ 2. How much would you weigh there? On another planet, suppose that you weigh 2000 Newtons. What is the strength of the gravitational field there?
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Solution: Your weight on Earth is equal to the force exerted on your mass by the Earth's gravitational field. Since your mass would be accelerated at 9.8 m/s ^ 2 by this field, the force must by Newton's Second Law be the product of your mass and this acceleration. Thus your weight is (9.8 m/s ^ 2)( 69 kg) = 676.2 Newtons. On the Moon, your weight would give your mass an acceleration of about 1.5 m/s ^ 2. Your weight there would thus be (1.5 m/s ^ 2)( 69 kg) = 103.5 Newtons.
If your weight on a certain planet was 2000 Newtons, then the strength of the gravitational field would be the acceleration that would result from application of this net force to your 69 kilogram mass. This acceleration is 2000 Newtons/ 69 kilograms = 28.98 meters/second ^ 2.