Finding the net gravitational force with Vector Notation

In summary: Similarly, in F35, you seem to use only one of the masses instead of the product of the two masses.4. In the resultant calculation, you subtracted the two forces, but shouldn't you add them since they are acting in opposite directions?5. The final horizontal and vertical components seem to be incorrect as well, since you are using only one of the forces instead of the sum of all four forces.In summary, the net gravitational force from the four spheres on the central sphere with mass m5 = 2.90 g can be calculated using the formula F = G * (m1 * m5 / r^2), where G is the gravitational constant, m1 and m5 are the masses of
  • #1
Ella1777
15
0
Information Given: In the figure, a square of edge length 17.0 cm is formed by four spheres of masses m1 = 4.70 g, m2 = 2.90 g, m3 = 0.800 g, and m4 = 4.70 g.

Question: In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.90 g? Attempted Solution:F=k*m1*m2/r^2
r= (sqrt (0.1m)^2 + (0.1m)^2)=0.1414m
F25=(6.67*10^-11)(0.0290)/0.1414m
F25=1.36796322*10^-11

F35=(1.36796322*10^-11)/4=3.14990806*10...

Resultant: F25-F35=(1.36796322*10^-11)-(3.141990806...

Horizontal:( 2.77917256*10^-13) cos(45)= 1.4596046*10^-13 N

Vertical: (2.77917256*10^-13) sin (45)= 1.2422855*10^-13 N
Answer(Incorrect):1.46e-13 i + 1.24e-13 j N
I don't understand I checked this several times yet it's incorrect!
Help is greatly appreciated
Thank You!
 
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  • #2
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Ella1777 said:
Information Given: In the figure, a square of edge length 17.0 cm is formed by four spheres of masses m1 = 4.70 g, m2 = 2.90 g, m3 = 0.800 g, and m4 = 4.70 g.

Question: In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.90 g?Attempted Solution:F=k*m1*m2/r^2
r= (sqrt (0.1m)^2 + (0.1m)^2)=0.1414m
Where did the 0.1m values come from? Did you draw a sketch of the setup?
F25=(6.67*10^-11)(0.0290)/0.1414m
F25=1.36796322*10^-11
Where did the 0.0290 value come from?
F35=(1.36796322*10^-11)/4=3.14990806*10...

Resultant: F25-F35=(1.36796322*10^-11)-(3.141990806...

Horizontal:( 2.77917256*10^-13) cos(45)= 1.4596046*10^-13 N

Vertical: (2.77917256*10^-13) sin (45)= 1.2422855*10^-13 N
Assuming that "F25" means the force of m2 on m5, then what happened to the calculations for the other masses? Shouldn't there be F15, F25, F35, and F45?
 
  • #3
A diagram would reduce the confusion.
1. In calculating F25, why did you use r in the denominator? Should it not be r2?
2. In the numerator, you seem to use only one of the masses, instead of the product of the two masses.
 

1. What is the formula for finding the net gravitational force with vector notation?

The formula for finding the net gravitational force with vector notation is F = G * (m1 * m2) / r^2, where F is the net gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the objects.

2. How do you represent the gravitational force as a vector?

The gravitational force is represented as a vector by using its magnitude and direction. The magnitude is determined by the formula mentioned above, and the direction is determined by the direction of the gravitational force, which is always towards the center of mass of the objects.

3. Can you use vector notation to find the net gravitational force between more than two objects?

Yes, vector notation can be used to find the net gravitational force between more than two objects. The formula for finding the net gravitational force remains the same, but you would need to calculate the force between each pair of objects and then add them together vectorially to get the net force.

4. How does the direction of the gravitational force affect the vector notation calculation?

The direction of the gravitational force affects the vector notation calculation by determining the direction of the vector. As mentioned earlier, the direction of the gravitational force is always towards the center of mass of the objects, so the resulting vector will also point in that direction.

5. Can vector notation be used to find the gravitational force between objects of different masses?

Yes, vector notation can be used to find the gravitational force between objects of different masses. The masses of the objects are taken into account in the formula for finding the net gravitational force, so it can be used for any combination of masses.

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