take a satalite going around the earth...
what allows us to say
net force (radial) = Fg = Fr = ma
were the Fg is the force of gravity exerted on the satalite
were Fr is radial force
and ma is the mass and acceleration of the satalite
ok I understand newtons second law but what I don't understand is what allows us to say Fg = Fr
I thought in problems were the force were along the same direction... you added them together to obtain the net force...
i thought the net force would be
Fg + Fr
sense the Fg is points downwards towards the earth and the radial force (sometimes called centripetal) is also pointing along this direction...
this lead me to believe that the net force was
Fg + Fr...
please explain this to me
Thanks!
Fg (the gravity force) and Fr (the raqdial force) are the same thing. You don't add them.
Assuming the satellite is in a circular orbit, the gravity force is perpendicular to the direction of motion, which is tangent to the crcular orbit.
The radial (gravity) force equals mass times centripetal acceleration, m V^2/R
ok why are they the same thing???
Because the gravity force acts radially
I can understand why you may find it confusing, but let me help clarify it for you.
In this case, we are considering a satellite going around the Earth, which means it is in a circular orbit. In circular motion, there is a force called the centripetal force that acts towards the center of the circle and keeps the satellite moving in its path. In this situation, the centripetal force is provided by the gravitational force between the satellite and the Earth.
Now, let's break it down step by step:
1. We start by considering the gravitational force acting on the satellite. This force, Fg, is the force of gravity exerted on the satellite by the Earth. It is directed towards the center of the Earth.
2. Since the satellite is in a circular orbit, it is accelerating towards the center of the orbit. This acceleration is due to the centripetal force, which is provided by the gravitational force. In other words, the satellite is constantly changing its direction as it moves along its circular path.
3. By Newton's second law, force equals mass times acceleration (F = ma). In this case, the net force acting on the satellite is equal to the centripetal force (Fr). Therefore, we can write Fr = ma.
4. Since the centripetal force is provided by the gravitational force (Fg), we can substitute Fr with Fg. So, we have Fg = ma.
It is important to note that the gravitational force (Fg) and the centripetal force (Fr) are not independent forces acting on the satellite. The gravitational force is the source of the centripetal force in this scenario. They are different aspects of the same force acting on the satellite.
Therefore, we can say that Fg = Fr because the gravitational force is the centripetal force required to keep the satellite in its circular path. We do not add Fg and Fr together because they are essentially the same force.
I hope this explanation helps clear up your confusion. If you have any more questions, feel free to ask!