b. Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth.)
c. Use the value of C you found in the previous question to determine how much the object would weigh in:
i. Death Valley (282 feet below sea level)
ii. The top of Mt McKinley (20,320 feet above sea level)
What equation are you talking about and where does the C appear in it?
Weight is inversely proptional to mass and the square of the distance from the center of the Earth.
At the top of Mt McKinley, the elevation is 20,320 ft = 3.85 miles, which is 3966.85 miles from the center of the earth. The sea level weight gets multiplied by a factor
(3963/3966.85)^2 = 0.9981
A 100 lb object (at sea level) will weigh 99.81 lb atop Mt. McKinley.
original problem:
1.Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: where C is a constant and r is the distance that the object is from the center of the earth.
a. Solve the equation for r.
b. Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth.)
c. Use the value of C you found in the previous question to determine how much the object would weigh in:
i. Death Valley (282 feet below sea level)
ii. The top of Mt McKinley (20,320 feet above sea level)
Death Valley (282 feet below sea level)
To find the value of C that makes the equation true, we need to use the formula for the weight of an object at different distances from the center of the Earth:
W = C/r^2
where W is the weight of the object, C is a constant, and r is the distance from the center of the Earth.
For the object weighing 100 pounds at sea level (with a distance from the center of the Earth of 3,963 miles), we can substitute these values into the equation:
100 = C/(3963)^2
To solve for C, we need to rearrange the equation:
C = 100 * (3963)^2
Now we can calculate the value of C:
C = 100 * 15705369
C = 1570536900
So, the value of C that makes the equation true is 1570536900.
Now, let's use this value of C to determine how much the object would weigh in Death Valley (282 feet below sea level) and at the top of Mt McKinley (20,320 feet above sea level).
i. To find the weight in Death Valley, we need to determine the new distance from the center of the Earth. Since Death Valley is 282 feet below sea level, the new distance would be 3,963 miles - (282 feet / 5280 feet/mile) ≈ 3,962.952 miles.
Using the formula W = C/r^2 and the value of C we found earlier:
Weight in Death Valley = (C / (3,962.952)^2) pounds
ii. To find the weight at the top of Mt McKinley, we need to determine the new distance from the center of the Earth. Since the top of Mt McKinley is 20,320 feet above sea level, the new distance would be 3,963 miles + (20,320 feet / 5280 feet/mile) ≈ 3,963.825 miles.
Using the formula W = C/r^2 and the value of C we found earlier:
Weight at the top of Mt McKinley = (C / (3,963.825)^2) pounds
Now you can calculate the weight in Death Valley and at the top of Mt McKinley using the respective formulas.