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Q.42 - Excercises And Problems

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 355

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Short Answer

An object of mass is dropped from height above a planet of mass and radius Find an expression for the object’s speed as it hits the ground.

the expression for object's speed is

See the step by step solution

Step by Step Solution

Step 1: Given information

mass of an object is

height of an object to be dropped is

mass of the planet

radius of the planet

Step 2: Explanation

The initial mechanical energy of the object, when it is located at height h above the the planet, is just gravitational potential energy:

where

is the gravitational constant

is the mass of the planet

is the mass of the object

is the radius of the planet

is the altitude of the object

When the object hits the ground, its mechanical energy will sum of potential energy and kinetic energy:

where

is the speed of the object at the ground

Since the mechanical energy is conserved, we can write

and solving for , we find

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