Okay I’m having a little problem with non conservative forces, why are their signs different? Aren’t they basically the same equations?
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First, let’s talk about “mgh”. “m” stands for mass, “g” stands for the acceleration due to gravity, and “h” stands for the height above some reference point. This equation represents the potential energy an object has due to its position relative to a reference point. For example, if you lift an object of mass “m” to a height “h” above the ground, the potential energy it gains is given by “mgh”.
Now, let’s talk about “-MmG/R”. This equation represents the potential energy an object has due to its position relative to a central force, such as the force of gravity. “M” stands for the mass of the central object (e.g. the planet), “G” stands for the gravitational constant, “R” stands for the distance between the two objects, and the negative sign indicates that the force is attractive (i.e. it pulls objects together). This equation applies to situations where the object is in orbit around the central object, and it represents the potential energy an object has due to its position relative to the central object.
So, while both of these equations represent potential energy due to position, they are different because they apply to different situations. “mgh” applies to objects near the surface of the Earth, where the only significant force acting on them is gravity, whereas “-MmG/R” applies to objects in orbit around a central object, where there is a central force (like gravity) that is pulling the objects towards the center. The negative sign in “-MmG/R” indicates that the force is attractive, whereas there is no negative sign in “mgh” because gravity is always pulling objects towards the ground.
First, let’s talk about “mgh”. “m” stands for mass, “g” stands for the acceleration due to gravity, and “h” stands for the height above some reference point. This equation represents the potential energy an object has due to its position relative to a reference point. For example, if you lift an object of mass “m” to a height “h” above the ground, the potential energy it gains is given by “mgh”.
Now, let’s talk about “-MmG/R”. This equation represents the potential energy an object has due to its position relative to a central force, such as the force of gravity. “M” stands for the mass of the central object (e.g. the planet), “G” stands for the gravitational constant, “R” stands for the distance between the two objects, and the negative sign indicates that the force is attractive (i.e. it pulls objects together). This equation applies to situations where the object is in orbit around the central object, and it represents the potential energy an object has due to its position relative to the central object.
So, while both of these equations represent potential energy due to position, they are different because they apply to different situations. “mgh” applies to objects near the surface of the Earth, where the only significant force acting on them is gravity, whereas “-MmG/R” applies to objects in orbit around a central object, where there is a central force (like gravity) that is pulling the objects towards the center. The negative sign in “-MmG/R” indicates that the force is attractive, whereas there is no negative sign in “mgh” because gravity is always pulling objects towards the ground.
Lets use W and I for to separate them, W= -MmG/R, U= mgh
U= mgh is an approximation for elevation close to the surface of the earth. for masses a lot smaller than then earth and describe the potential energy in a point relative to the surface
g =f/m = MG/r^2 with earth mass and earth radius and is the surface acceleration
So mgh =mhg =mhf/m =hf. That is force times distance and it works (energy)
The real potential energy would be integral to the force from the top to bottom location. Because elevation changes are usually very small compared to Earth’s radius
W is the energy that is required to go from an infinite distance from the earth to the surface. You gain energy so the required energy is negative. U is the energy release if the election change is h
You get it by integrating GMm/r^2 from infinity to R which is Earth’s radius.
So it is not exactly the same thing, one is an approximation close to the surface and one is from the surface to infinity. Because of the slight difference in definition, the sign is the opposite.
First, let’s talk about “mgh”. “m” stands for mass, “g” stands for the acceleration due to gravity, and “h” stands for the height above some reference point. This equation represents the potential energy an object has due to its position relative to a reference point. For example, if you lift an object of mass “m” to a height “h” above the ground, the potential energy it gains is given by “mgh”.
Now, let’s talk about “-MmG/R”. This equation represents the potential energy an object has due to its position relative to a central force, such as the force of gravity. “M” stands for the mass of the central object (e.g. the planet), “G” stands for the gravitational constant, “R” stands for the distance between the two objects, and the negative sign indicates that the force is attractive (i.e. it pulls objects together). This equation applies to situations where the object is in orbit around the central object, and it represents the potential energy an object has due to its position relative to the central object.
So, while both of these equations represent potential energy due to position, they are different because they apply to different situations. “mgh” applies to objects near the surface of the Earth, where the only significant force acting on them is gravity, whereas “-MmG/R” applies to objects in orbit around a central object, where there is a central force (like gravity) that is pulling the objects towards the center. The negative sign in “-MmG/R” indicates that the force is attractive, whereas there is no negative sign in “mgh” because gravity is always pulling objects towards the ground.
Lets use W and I for to separate them, W= -MmG/R, U= mgh
U= mgh is an approximation for elevation close to the surface of the earth. for masses a lot smaller than then earth and describe the potential energy in a point relative to the surface
g =f/m = MG/r^2 with earth mass and earth radius and is the surface acceleration
So mgh =mhg =mhf/m =hf. That is force times distance and it works (energy)
The real potential energy would be integral to the force from the top to bottom location. Because elevation changes are usually very small compared to Earth’s radius
W is the energy that is required to go from an infinite distance from the earth to the surface. You gain energy so the required energy is negative. U is the energy release if the election change is h
You get it by integrating GMm/r^2 from infinity to R which is Earth’s radius.
So it is not exactly the same thing, one is an approximation close to the surface and one is from the surface to infinity. Because of the slight difference in definition, the sign is the opposite.
Lets use W and I for to separate them, W= -MmG/R, U= mgh
U= mgh is an approximation for elevation close to the surface of the earth. for masses a lot smaller than then earth and describe the potential energy in a point relative to the surface
g =f/m = MG/r^2 with earth mass and earth radius and is the surface acceleration
So mgh =mhg =mhf/m =hf. That is force times distance and it works (energy)
The real potential energy would be integral to the force from the top to bottom location. Because elevation changes are usually very small compared to Earth’s radius
W is the energy that is required to go from an infinite distance from the earth to the surface. You gain energy so the required energy is negative. U is the energy release if the election change is h
You get it by integrating GMm/r^2 from infinity to R which is Earth’s radius.
So it is not exactly the same thing, one is an approximation close to the surface and one is from the surface to infinity. Because of the slight difference in definition, the sign is the opposite.
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