What is the difference in the force of gravity on a 1.0-kg mass at the bottom of the deepest ocean trench and that at the top of the highest mountain? Assume that g = 9.8 m/s²at sea level. The radius of Earth at sea level is 6.37 * 10⁶ m. The deepest trench is the Marianas Trench, south of Guam, which has a depth d = 1.103 *10⁴ m below sea level. The highest mountain is Everest in Nepal, which has a height of h = 8.847 * 10³ m above sea level. The difference is A) 0.061 N. B) 0.0067 N. C) 0.027 N. D) 0.034 N. E) 0.0062 N.

Question

Quizplus · Accepted Answer

The force of gravity is given by the formula:

F = G * (m1 * m2)/r^2

where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects attracting each other, and r is the distance between their centers of mass.

In this problem, we are asked to compare the force of gravity on a 1.0-kg mass at the bottom of the Marianas Trench and at the top of Mount Everest.

Let's first calculate the force of gravity on a 1.0-kg mass at sea level. Using g = 9.8 m/s^2 and the radius of the Earth at sea level, we can calculate the distance from the center of the Earth to the surface:

r1 = 6.37 x 10^6 m + 0 m = 6.37 x 10^6 m

Using this distance in the formula, we get:

F1 = G * (m1 * m2)/r1^2
   = 6.67 x 10^-11 * (1.0 kg * 5.97 x 10^24 kg)/ (6.37 x 10^6 m)^2 
   = 9.81 N

Now, let's calculate the force of gravity on a 1.0-kg mass at the bottom of the Marianas Trench. The distance from the center of the Earth is:

r2 = 6.37 x 10^6 m + 1.103 x 10^7 m = 1.237 x 10^7 m

Using this distance in the formula, we get:

F2 = G * (m1 * m2)/r2^2
   = 6.67 x 10^-11 * (1.0 kg * 5.97 x 10^24 kg)/ (1.237 x 10^7 m)^2 
   = 9.87 N

Finally, let's calculate the force of gravity on a 1.0-kg mass at the top of Mount Everest. The distance from the center of the Earth is:

r3 = 6.37 x 10^6 m + 8.847 x 10^3 m = 6.378 x 10^6 m

Using this distance in the formula, we get:

F3 = G * (m1 * m2)/r3^2
   = 6.67 x 10^-11 * (1.0 kg * 5.97 x 10^24 kg)/ (6.378 x 10^6 m)^2 
   = 9.80 N

The difference between the force of gravity at the bottom of the Marianas Trench and at the top of Mount Everest is:

ΔF = F2 - F3
   = 9.87 N - 9.80 N
   = 0.061 N

Therefore, the answer is choice A) 0.061 N.

What Is the Difference in the Force of Gravity on a 1.0-Kg