Homework SourseThe weight w of an object on or above the surface of a plane
The weight w of an object on or above the surface of a planet varies inversely as the square of the distance d between the object and the center of the planet. If you weigh 120 pounds on the surface of Venus(radius 3800 miles), how much will you weigh 400 miles above the surface of Venus.
Solution
A person weigh 120 pounds on the surface of Venus (radius 3800 miles). Since the weight of an object ( including a person) on or above the surface of a planet varies inversely as the square of the distance d between the object and the center of the planet, therefore, the weight of the person is a /( 3800)2 , where a is an arbitrary constant. Thus 120 = a / ( 3800)2 or, a = 120 * ( 3800)2 . When the person is 400 miles above the surfaceof Venus, his/her distance from the centre of the planet is 3800 + 400 = 4200 miles. Then, the weight of this person, when he/she is 400 miles above the surface of Venus = a /( 4200)2 = 120 * (3800)2 / ( 4200)2 = 120 * (38)2 / (42)2 = 120 * 1444/1764 = 98.23 pounds.
