Universal gravitation 11- determine the gravitational force of attraction

[dani123]

Homework Statement

Two bags of apples, each containing 20 apples of equal mass, experience a gravitational force of attraction of 200 units when separated by a distance of 25.0cm. If 10apples are removed from one bag and placed into the other bag, and the two bags are separated by the same 25.0 cm distance, determine the gravitational force of apples now. Note that the magnitude of the gravitational force should be expressed in units.

Homework Equations

I have made a list of equations that are relevant for this entire module on universal gravitation. So although there are many of them does not mean that they all apply in this circumstance. The ones relevant to this question will be placed in bold.

Kepler's 3rd law: (T_a/T_b)²=(R_a/R_b)³

motion of planets must conform to circular motion equation: F_c=4∏²mR/T²

From Kepler's 3rd law: R³/T²=K or T²=R³/K

Gravitational force of attraction between the sun and its orbiting planets: F=(4∏²K_s)*m/R²=Gm_sm/R²

Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏²K_e)m/R²=Gm_em/R²

Newton's Universal Law of Gravitation: F=Gm₁m₂/d²

value of universal gravitation constant is: G=6.67x10^-11N*m²/kg²

weight of object on or near Earth: weight=F_g=m_og, where g=9.8 N/kg
F_g=Gm_om_e/R_e²

g=Gm_e/(R_e)²

determine the mass of the Earth: m_e=g(R_e)²/G

speed of satellite as it orbits the Earth: v=√GM_e/R, where R=R_e+h

period of the Earth-orbiting satellite: T=2∏√R³/GM_e

Field strength in units N/kg: g=F/m

Determine mass of planet when given orbital period and mean orbital radius: M_p=4∏²R_p³/GT_p²

The Attempt at a Solution

F_g=200N
d=25cm=0.25m

I used F_g=(6.67X10^-11)(30)(10)/(0.25)²=3.2X10^-7N

I have a strong feeling this answer is wrong, but if someone could point me in the right direction it would be greatly appreciated! Thank you so much in advance.

 

[Infinitum]

Your feeling is correct

First off, you do not know the mass of apples in each bag, so your equations are incorrect.

Let the mass of 10 apples be m, the mass of 20 would be 2m. Now set up an equation for both bags,

$$F_{1} = \frac{G\cdot 2m\cdot 2m}{r^2}$$

Try making a similar equation for the 10 apple case. Now without the need to substitute the values of G and r, as they remain same, just divide the equations to get an equation for F₂.

 

[grzz]

You were told that 10 apples were removed from one bag. But you were not told that they were transferred to the other bag.

 

[dani123]

why is it 2m*2m? I am confused

 

[dani123]

grzz the question actually did state that they were transferred into the other bag, I just edited the problem! Thanks for noticing

 

[Infinitum]

why is it 2m*2m? I am confused

I explained why in my previous post... The mass of one 20 apple-bag is 2m, the mass of the other 20 apples bag is 2m. What would the gravitational force between them be(without substituting numerical values)??

 

[dani123]

F=4.2688x10^-9*m²?

 

[Infinitum]

F=4.2688x10^-9*m²?

Uhh I asked without substituting the numerical values, its easier that way

 

[dani123]

I left m for the mass... but I used the value for G and r...

 

[dani123]

so you mean like 4m²=F₁*r²/G?

 

[Infinitum]

so you mean like 4m²=F₁*r²/G?

Yes! Can you make a similar equation for the case with 10 and 30 apple-bags?

 

[dani123]

3m²=F₂*r²/G for the second?

But do I use 200N for the force in both equations to determine the mass?

 

[Infinitum]

3m²=F₂*r²/G for the second?

Yep.

But do I use 200N for the force in both equations to determine the mass?

Nope. You don't need to find the mass. You need to find the force F2, which ofcourse is not equal to 200N(F1). Try dividing the equations and see how you can find F2..

 

[dani123]

dividing the F₁ equation by the F₂ equation?

 

[Infinitum]

dividing the F₁ equation by the F₂ equation?

Yes...

 

[dani123]

F₂=266.67 N? Does this seem right?

 

[Infinitum]

F₂=266.67 N? Does this seem right?

Nope. Recheck your equations. What expression did you get after division?

 

[dani123]

3/4=F₁/F₂... because everything else canceled out

 

[Infinitum]

3/4=F₁/F₂... because everything else canceled out

Umm no. Without much trouble, that should be 4/3=F1/F2, don't you think?

 

[dani123]

ops haha so the answer should be 150 N right?

 

[Infinitum]

ops haha so the answer should be 150 N right?

Aye!

 

[dani123]

Thank you so much!