Two masses and a Gravitational field

[++A++]

A point mass of 3.8kg is on the x-axis at x=8.2 and an equal point mass is on the y-axis at y=5.9. What is the magnitude of the gravitational field from these two masses at the origin?

Well for this problem I tried using the equation F= G m1 m2/ r^2
for r I added 8.2 and 5.9
for G I used the number given in my book 6.67E-11
I am thinking that maybe I am not finding r the right way but then I found this equation in my book
F1,2 =( - G m1 m2 / r^2 (1,2) ) * r1,2
and am now very confused. Please help me sort out this mess!

 

[cepheid]

for r I added 8.2 and 5.9
I am thinking that maybe I am not finding r the right way

Hmm...that's one error right there.

Advice...if you haven't already drawn a diagram...do so. Don't try to visualise it in your head! Once you have the picture...you'll immediately see why you cannot simply add the two distances given. One mass lies 8.2 units to the right of the origin along the x-axis, and the other lies 5.9 units above the origin along the y-axis. So *if* you were trying to find the separation between the two masses, which is diagonal (relative to the axes), what method would you have to use?

I highlighted the 'if' there, because it's not certain that that's what you are really looking for in this question. You seem to be calculating the gravitational force between the two objects. Is that what the question asks for? No...it seems to ask for the gravitational field "felt" at the origin. Here's the strategy I'd recommend:

1. Find out what equation you need to calculate the gravitational field strength at a point (due to a point mass). (don't just look it up...understand what it means based on the relationship between graviational forces and fields)

2. Calculate the graviational field at the origin due to each of the two masses (separately).

3. Note that forces (and therefore fields) add together...so that the total gravitational field at the origin is just the vector sum of the fields due to the two masses. In plainer language, once you have the field at the origin due to each one of the two masses...just combine their effects to find the total graviational field. This is the principle of superposition.

I hope that helps...if you still have trouble, let us know what steps you did take, and where you got stuck.

 

[wais]

It seems like you are on the right track with using the equation F= G m1 m2/ r^2 to find the gravitational force between the two masses. However, instead of adding 8.2 and 5.9 for r, you should be using the distance between the two masses, which is the hypotenuse of a right triangle with sides 8.2 and 5.9. This can be found using the Pythagorean theorem, which gives a distance of approximately 10.2 units.

Also, the equation you found in your book, F1,2 =( - G m1 m2 / r^2 (1,2) ) * r1,2, is the equation for finding the gravitational force between two masses when they are not directly on the x- or y-axis. In this case, since the masses are on the x- and y-axis, we can simply use the equation F= G m1 m2/ r^2.

To find the gravitational field at the origin, we need to find the force between the two masses and then divide by the mass of the object at the origin. So, the magnitude of the gravitational field at the origin would be:

F = (6.67E-11)(3.8)(3.8)/(10.2)^2 = 1.13E-11 N

This is the magnitude of the gravitational force between the two masses. To find the gravitational field, we divide by the mass of the object at the origin, which is 3.8kg. So, the magnitude of the gravitational field at the origin would be:

1.13E-11 N / 3.8kg = 2.97E-12 N/kg

I hope this helps clear things up for you! Just remember to use the correct distance between the masses and to divide by the mass of the object at the origin to find the gravitational field.