Determining Forces of Moon & Sun on Mass m

In summary, using the equation Fg = GMm/r^2, the forces exerted by the moon and sun on a mass of water on Earth can be calculated as (6.67e-11)(7.3 x 10^22)(m) / (3.9 x 10^5)^2 and (6.67e-11)(1.99 x 10^30)(m) / (1.5 x 10^11)^2, respectively. The distance between the objects should be in meters and the mass can be any value.
  • #1
Trizz
41
0

Homework Statement


(a) Determine the forces that the moon and the sun exert on a mass, m, of water on Earth. Your answer will be in terms of m with units of N. (Use data from table 8-1 in your textbook for this question. The mass of the moon is 7.3 x 10 ^22 kg, and it can be assumed to be 3.9 x 10^5 km from the Earth's center.)

______ m N (force exerted by moon)

______ m N (force exerted by sun)


Homework Equations



Fgr = G M1m2 / r^2

mass of Earth = 5.98 x 10^24



The Attempt at a Solution



I thought that I had everything for the equation, but I still can't seem to get it. Check out my work and see if there's something I'm missing. I'm not sure on what to use for the radius.

Fgr = (6.67e-11)(7.3 x 10^22)(5.98 x 10^24) / (3.9 x 10^5)^2
 
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  • #2
Say the Earth is not there but replaced by a bit of water of mass "m". Then?
 
  • #3
Thanks for the response Bright Wang.

So I replaced my equation with m, and this is what I got

Fgr = (6.67e-11)(7.3 x 10^22)(m) / (3.9 x 10^5)^2

then

Fgr = (4.860e12)(m) / (3.9 x 10^5)^2

then

(3.9 x 10^5)^2 = 4.869e12m

does that look right?
 
  • #4
The given data for radius is in KM.
 
  • #5
Alright I multiplied the radius side by 1000 to make up for the KM units. But one more question. Is that number supposed to be divided by 2 since I want radius, and isn't that diameter? Anyways, i got .03 for an answer, does that seem too small?
 
  • #6
Which number? There's no diameters in this question.
 
  • #7
i need r^2 for the Force of gravity equation. The statement said that the moon is 3.9 x 10^5 km from the earth. Is that not diameter? or is that the radius? Regardless, i still got .03 for the answer, which doesn't seem to make sense to me
 
  • #8
Actually, I am not sure what i got was .03. But here's my equation anyway.

(3.9 x 10^5)^2 = 1.521e11 x 1000 (for km) = 1.521e14

(6.67e-11)(7.3 x 10 ^22)(m) = 4.8691e12(m)

so...

4.8691e12(m) / 1.521e14 = m?
 
  • #9
Distance is radius. It doesn't even matter, r represents the distance between the objects.

"
4.8691e12(m) / 1.521e14 = m? "

What? Your just using the equation.

You want to find Fg. Fg = GMm/r^2... Why do you have mass on both sides? You trying to find force not acceleration.

Its just plug and chug. I didn't get 0.3m N.
 
  • #10
I thought you said to use "m" for a variable ?



"Say the Earth is not there but replaced by a bit of water of mass "m". Then? "

or do i just ignore that number
 
  • #11
m can be whatever.

Fg = GMm/r^2 = G*(Mass of the moon)*m / distance{in meters}^2 = {some number}*m
 
  • #12
wasnt able to get it in time. Thanks for the help though. Hopefully my teacher will explain it better
 

Related to Determining Forces of Moon & Sun on Mass m

1. How do the Moon and Sun exert forces on mass m?

The Moon and Sun exert forces on mass m through gravitational attraction. Both objects have mass and therefore, according to Newton's Law of Universal Gravitation, they exert a force on any other object with mass.

2. What is the equation for determining the force of the Moon and Sun on mass m?

The equation for determining the force of the Moon and Sun on mass m is F = G * (m1 * m2)/d^2, where F is the force, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

3. How does the distance between the Moon and Sun affect the force on mass m?

The force on mass m is inversely proportional to the distance between the Moon and Sun. This means that as the distance between them increases, the force decreases and vice versa.

4. How does the mass of the Moon and Sun affect the force on mass m?

The force on mass m is directly proportional to the mass of both the Moon and Sun. This means that as the mass of either object increases, the force also increases.

5. What is the significance of determining the forces of the Moon and Sun on mass m?

Determining the forces of the Moon and Sun on mass m is important for understanding the movement and behavior of objects in our solar system. It also helps us predict and explain phenomena such as tides and eclipses.

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