Universal Gravitation Problem (Grade 11)

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Homework Help Overview

The problem involves comparing the height reached by an object thrown vertically upward from the surface of the Moon, where the acceleration due to gravity is 1.6 N/kg, to the height reached from the surface of the Earth, where gravity is 9.81 N/kg. The original poster seeks guidance on how to approach the problem without necessarily looking for a complete solution.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to relate the gravitational accelerations of the Earth and Moon to determine the height ratio. They express uncertainty about the simplicity of their calculation and seek validation.
  • Some participants suggest incorporating kinematic equations to relate distance and velocity, while others question the necessity of additional variables like mass and radius of the celestial bodies involved.
  • There is a discussion about the relevance of the gravitational constant and whether it should be factored into further calculations.

Discussion Status

The discussion is ongoing, with participants exploring various aspects of the problem. Some guidance has been offered regarding the use of kinematic equations, and there is a recognition of the relationship between acceleration and height. However, no consensus has been reached on the best approach or the necessity of additional variables.

Contextual Notes

Participants note the absence of certain variables such as height, acceleration, and initial velocity, which may impact the accuracy of the calculations. There is also a mention of neglecting air resistance on Earth, which is relevant to the problem's constraints.

danielle_54321
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Homework Statement



If you threw something vertically upward from the moon's surface where g=1.6N/kg [down], how many times higher would it reach compared to throwing it from the surface of the Earth with the same force? Neglect the effect of air resistance on the Earth.

Homework Equations


I don't know which equations to use. Without other variables, I don't know where to start. I am not necessarily looking for a solution, I just need help at getting my solution started.
I do know that
g=9.81N/kg on earth.
F=ma is likely a relevant equation, because g is an acceleration and the force and mass are both constants.

The Attempt at a Solution



g(earth)/ gmoon
=9.81/1.6
=6.13125

Does this make sense? The solution seems much too simple. :(
 
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well, sometimes one gets lucky. for more rigor, you might add kinematics expression relating distance and velocity, such as v^2=2*a*h where v is the initial velocity the rock or whatever was thrown upwards.
 
Okay, thank-you.

So, if I do not have any other varables (height, acceleration, force, time, distance, initial velocity or final velocity) is my answer the most accurate possible?

Also, do you think I should factor in:

Fg = (G*m1*m2)/d^2

where G is the gravitational constant (6.67 x 10^-11) and m1 is the mass of the planet and m2 is the mass of the object thrown and d is the distance between the mass' centre and the centre of the object?


In order to do any further calculations, would it profit me to determine the mass and radius of both the moon and the earth?

I don't know if that makes any sense or not?
 
g already is G*m1/d^2. An it is fair to assume that the initial impulse is not powerful enogh to reach an altitude for which you need to consider any variation on d.

If you want, you can calculate the highest point for both situations. You will get that result again. Or using the formula by denverdoc, as you have the same initial speed, it is easy to see that 'a' and 'h' wil be inversely related.
 

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