What is the Correct Calculation for Force in a Three-Mass System?

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In summary, the conversation discusses a problem with calculating the net force in an equation involving two masses, a distance, and the gravitational constant. After a mistake is pointed out, the correct equation is provided and the conversation discusses the importance of using the correct units for force. It is also noted that the direction of the net force is towards the larger mass.
  • #1
MitsuShai
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I can't find what I'm doing wrong in this problem:


Equation: f= (Gm1m)/r^2

F1= (G*(8.5))/(.2)^2 = 1.417 x 10^-8
F2= (G*(12))/.5^2 = 3.2016x10^-9

Fnet= -1.417 x 10^-8 + 3.2016x10^-9 = -1.1x10^-8m

a= 1.1x10^-8, and this is wrong and I can't figure out where I messed up at.
 
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  • #2
Well firstly, on F2, it should be 0.3^2 not 0.5^2 as the point is released 20cm from the 8.50kg mass which makes it 30cm from the 12.0kg mass.

Secondly, force is measured in Newtons (kg*m / s^2). Not metres (m) as you have it. You don't know the mass of particle m so you can't use it. You need the following.

g = GM / r^2 = (m^3 / kg*s^2)(kg) / m^2 = m/s^2

G = 6.67x10^-11m^3 / kg*s^2
M1 = 8.5kg
M2 = 12.0kg
r1 = 0.2
r2 = 0.3

g1 = GM1/r1^2
g2 = GM2/r2^2

g = g1 - g2

Jared
 
Last edited:
  • #3
jarednjames said:
Well firstly, on F2, it should be 0.3^2 not 0.5^2 as the point is released 20cm from the 8.50kg mass which makes it 30cm from the 12.0kg mass.

Secondly, force is measured in Newtons (kg*m / s^2). Not metres (m) as you have it. You don't know the mass of particle m so you can't use it. You need the following.

g = GM / r^2 = (m^3 / kg*s^2)(kg) / m^2 = m/s^2

G = 6.67x10^-11m^3 / kg*s^2
M1 = 8.5kg
M2 = 12.0kg
r1 = 0.2
r2 = 0.3

g1 = GM1/r1^2
g2 = GM2/r2^2

g = g1 - g2 (in the direction of the larger mass

Jared


oh I didn't think of that, thanks Jared
 

1. What is force with three masses?

Force with three masses is a type of force that occurs when three objects interact with each other. It is a vector quantity that describes the strength and direction of the interaction between the three masses.

2. How is force with three masses calculated?

Force with three masses can be calculated using Newton's Law of Universal Gravitation. This law states that the force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

3. What factors affect force with three masses?

The force with three masses is affected by the masses of the three objects and the distance between them. The greater the masses and the closer the objects are, the greater the force will be.

4. What are some real-life examples of force with three masses?

Some real-life examples of force with three masses include the gravitational force between the Earth, Moon, and Sun, as well as the interaction between three planets in our solar system.

5. How does force with three masses relate to Newton's Third Law of Motion?

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. In the case of force with three masses, each mass exerts a force on the other two masses, and these forces are equal in magnitude and opposite in direction.

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