Three very small spheres are located along a straight line in space far away from everything else. The first one (with a mass of 2.43 kg) is at a point between the other two, 10.60 cm to the right of the second one (with a mass of 5.17 kg), and 20.70 cm to the left of the third one (with a mass of 6.20 kg). Calculate the magnitude of the net gravitational force it experiences.
I'm not sure how to solve these types of problems, given only mass and distance. Plus, the "in space" part sort of throws me off...
The "in space" part means there are no other objects around exerting forces on any of the spheres. I assume you know how to calculate the gravitational force between two bodies, with masses M1 and M2, using the Newtonian equation
F = G M1*M2/R^2
where 6.67 × 10^−11 N m2 kg-2 is the universal constant of gravity.
In this case, object 1 is pulled one way by object 2 and pulled other way by object 2. Compute the two forces and take the difference.
change that to "and pulled other way by object 3".
The ïn space"means that the total gravitation effect is dependent on the spheres only.
Do this as vectors. Gravity is a vector, so the net force (to the right) is
Fnet= G*M1 ( - ml/.1060^2 + mr/.2070^2)
where M1 is 2.43kg, ml is 5.17kg, mr is 6.20 kg)
I tried both of the ways and got the same answer. However, the answer I got using bobpursley's equation got me -5.11E-8, when it was really positive. Was there an error in that equation, or did I just mess up with the math somewhere along the way?
Positive means the force is to the right, but looking at the numbers, it should be to the left (negative).
Yes, it is negative, I just put the numbers in the Google calculator, and it is definitely negative (to the left).
Oh ok I see. Well, my online homework site would only accept it as postive, but it has been known to make errors before.
To solve this problem, you can use Newton's Law of Universal Gravitation which states that the force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.
The formula for gravitational force is:
F = G * (m1 * m2) / r^2
Where:
F is the magnitude of the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the two objects
In this case, we need to find the magnitude of the net gravitational force experienced by the first sphere. To do so, we need to calculate the gravitational forces between the first sphere and the second and third spheres, and then sum them up.
Let's calculate the gravitational force between the first and second spheres:
m1 = 2.43 kg
m2 = 5.17 kg
r1 = 10.60 cm = 0.1060 m
Using the formula, we can calculate F1 (the gravitational force between the first and second spheres):
F1 = G * (m1 * m2) / r1^2
Now, let's calculate the gravitational force between the first and third spheres:
m1 = 2.43 kg
m3 = 6.20 kg
r2 = 20.70 cm = 0.2070 m
Using the formula, we can calculate F2 (the gravitational force between the first and third spheres):
F2 = G * (m1 * m3) / r2^2
Finally, the net gravitational force experienced by the first sphere is the sum of F1 and F2:
F_net = F1 + F2
By plugging in the values for G, m1, m2, m3, r1, and r2, you can calculate the net gravitational force experienced by the first sphere.