Q.44 - Excercises And Problems

Expert-verified
Found in: Page 355

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# The unexplored planet Alpha Centauri III has a radius of . A visiting astronaut drops a rock, from rest, into a -deep crevasse. She records that it takes for the rock to reach the bottom. What is the mass of Alpha Centauri III?

Mass of Alpha Centauri III

See the step by step solution

## Step 1: Given information

height of the stone traveled into crevasse

time taken to for stone reaching through the crevasse

## Step 2: Explanation

The velocity of the stone

The initial mechanical energy of the stone, when it is located at height 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 stone

is the radius of the planet

is the altitude of the stone

When the stone 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 M, we find