You have landed on an unknown planet, newtonia, and want to know what objects will weigh there. you find that 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. you next observe that if you release this tool from rest at 11.0 m above the ground, it takes 2.58 s to reach the ground. what does the tool weigh on newtonia? what would it weigh on earth?

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:

The weight in this planet is given by (1):

(2)    

In addition, we are told that 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 (, 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 that if you release this tool from rest ( and ) at above the ground, it takes to reach the ground.

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.

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.

the area between the graph and the t axis