ok I'll be using a home work problem to ask the question. I'm not asking for help on the question I got the correct answer just need to understand this concept better.
Calculate the acceelration due to gravity on the Moon. The moon's radius is about 1.74 E 6 meters and its mass is 7.35 E 22 kg. For this problem I'll be using m2 as the mass which the moon is orbiting
Ok then...
F [in radial direction acting on m2] = (m2 a [radial direction] = Fg = r^-2 G m m2)m2^-1
divide both sides by m2
a [radial direction] = r^-2 G m
I rember in like inclined planes and such when two forces equal and opposite each other are present you can just cancel them out...
so how is there any net force?
how come like in inclined planes when I find the net force i don't include both masses...
Net force = (net mass) a
I don't use net mass in this problem because of why?
Why do I just use m2 and not m1 + m2
net force = (m1 + m2) a
?????
net mass? You are looking for the acceleration on m2, forceonm2/m2 is the acceleration on m2
To answer your question, let's break down the concepts involved.
In the case of calculating the acceleration due to gravity on the Moon, we are considering a scenario where an object of mass m1 is being attracted towards the Moon, which has a mass of m2. The force of gravity between these two objects can be calculated using Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the force of gravity between the two objects,
G is the gravitational constant,
m1 is the mass of the object,
m2 is the mass of the Moon, and
r is the distance between the center of the object and the center of the Moon (in this case, the radius of the Moon).
Now, in this problem, we are interested in calculating the acceleration experienced by the object due to the force of gravity. This can be done by using Newton's second law of motion:
F = m * a
Where:
F is the net force acting on the object,
m is the mass of the object, and
a is the acceleration of the object.
Here's where the confusion arises. In the context of inclined planes and other similar scenarios, we often deal with systems where multiple objects are involved, and the net force is the sum of forces from all objects acting on a particular object of interest. In those cases, we would indeed consider the sum of masses (m1 + m2) in the net force calculation.
However, when calculating the acceleration due to gravity, we are considering the acceleration of the object of mass m1 caused by the gravitational force exerted by the Moon (mass m2). In this case, the net force acting on the object is solely due to the gravitational force exerted by the Moon, and we do not include m1 in the net force calculation because it is the mass we are interested in calculating the acceleration for.
Therefore, in the formula for calculating the acceleration due to gravity on the Moon, we only use m2 (mass of the Moon) because we are determining the acceleration experienced by an object of mass m1 due to the gravitational force exerted by the Moon. The concept of net mass isn't applicable in this scenario, as we are considering the acceleration of a specific object under the influence of the gravitational force of another object.