<h2>
Answer: 1. On Newtonia: 28.846N</h2><h2>
2. On Earth:42.767N</h2>
Explanation:
The weight is the force with which a planet attracts an object with mass , due to the acceleration of gravity of said planet, and is given by the following equation:
(1)
Knowing this, let's find the weight of an object on Newtonia and on Earth:
<h2>1. On Newtonia:</h2>
The weight in this planet is given by (1):
(2)
In addition, we are told that <em>when a certain tool is pushed on a frictionless horizontal surface by a 12.2 N force, it moves 16.1 m in the first 2.40 s , starting from rest </em>(, and ).
By Newton's 2nd law of motion we know the force is given by:
(3) Being the mass of the object and its acceleration.
Isolating : (4)
We already know , we need to find . In order to approach it, we will use the following equations related to the motion in one dimension:
(5)
(6)
From (5):
(7)
Substituting (7) in (6):
(8)
Finding : (9)
Substituting (9) in (4):
(10)
(11)
On the other hand, we are told <em>that if you release this tool from rest </em>( and ) <em>at </em><em> above the ground, it takes </em><em> to reach the ground.</em>
<em />
In this case we will use the following equation:
(12)
(13)
Finding :
(14) Where the negative sign only indicates the acceleration is "downwards", to the center of the planet.
Substituting (14) in (1):
(15)
This is the weight of the tool on Newtonia.
<h2>2. On Earth:</h2>
In the case of our planet, we will use the same weight equation, knowing the acceleration due gravity on Earth is :
(16)
(17)
Finally:
This is the weight of the same tool on Earth.