Physics questions on Gravitational Field?

Question

F=GMm/(r^2), g=GM/(r^2), Gravitational potential energy= -GMm/r , gravitation potential= -GM/r.
With all these similar equations, how do you memorise it and apply it correctly when facing a physics question??? I get a bit confused whenever i see all the equations. I would like to ask the physics experts on ways to understand all these equations in a simpler way???
(i must say that i have not been coping well with this gravitational field topic in school due to its complicated equations)

Answer 1

First, understand the physics. Equations are just a shorthand to explain physics; learn that and you'll be half way home to remembering the equation.

Second, learn the basic SI units for the answer (the dependent variable like F and g on the LHS of each equation for example). SI units, like kg-m-sec, (kg is a mass unit, meter m is a length unit, and sec is a time unit) are way more helpful than some arcane unit like Newton or Pound, which gives absolutely no hint as to what might be on the independent, RHS, of the equation.

Suppose the question you need to answer is "What's the force of gravity between you and the Earth while you stand at sea level on its surface?"

So, first, you recognize the physics...it's about force. We know force units are kg-m/sec^2 in metric SI units or slugs-ft/sec^2 in English units. Thus F ~ mass (kg) length (m)/time^2 (t^2) So our equation F ~ kg*m/t^2. What variables are there that would give us these units. Ah, what about F = Ma; where M is mass (kg) and a is acceleration (m/t^2 = meter/sec^2 = m/sec^2) and F = kg*m/sec^2 = Ma. And that's one equation, but where's the gravity?

Again the physics come into play. We know F = Ma and we know that the force of gravity (W) has the same units kg*m/sec^2 as any other force. And if you know your physics, you will know that the force of gravity is often called weight (W). Thus we have F = Ma = W when the force source is gravity. But then we also recall that W = Mg where g = 9.81 m/sec^2 and is the acceleration due to the force of gravity.

Again more physics...what does the force of gravity depend on. Clearly M and g; M is you, but what's g? It has m/sec^2 units, acceleration, to start with. So g ~ length/time^2. And we also recall the instructor kept harping on W ~ 1/R^2, which is to say the force of gravity (weight) varies inversely as the square of the distance between the centers of two masses (M and m).

Thus far, from the SI units and physics, we know W = Mg ~ Mm/R^2 = (kg)^2/m^2 in units, but that's hardly kg-m/sec^2; so are we wrong here? Nope, whenever we say something, like weight, is "proportional to" something else, there will be a constant of proportionality (e.g., G).

Thus we have W = Mg ~ Mm/R^2 = GMm/R^2 where the units for G are whatever we need to get kg-m/sec^2, the weight units, from (kg)^2/m^2, the units from Mm/R^2. We can set up an equation of units, like kg-m/sec^2 = G(kg^2/m^2); so that G = kg-m/sec^2//kg^2/m^2 = (kg-m/sec^2)(m^2/kg^2) and G = m^3/kg-sec^2 Thus, you have the equation derived from the physics and units; it is W = Mg = GMm/R^2 = F. Where M is your mass, m is the mass of Earth, R is the distance between you and the Earth's center (Earth's radius for the example question), and G is some contant of proportionality.

From these equations, we see g = Gm/R^2 = the acceleration due to gravity on Earth's surface, which is the answer to the illustrative question.

Bottom line, if you know the physics described by the equations and if you know the SI units of the dependent variable in each equation, you can often simply derive the equation you need...no memorization needed, except for the physics and SI units.

BTW...by knowing the dependent variable SI units, you can use that information to check your derivations of the RHS of the equation. That is, if the LHS units <> RHS units, you know you've made a mistake. Checking your own work that way will improve your grades.

Answer 2

You should not get confused when you see them. They are all related if you know the proper physics concepts.

Review Newtons 2nd Law and how force relates to a potential.

The reason I choose physics over the other sciences. Is that you don't need to alot memorize equations and exceptions. Many times you can derive needed equations from basic ones.

Also, just keep doing problems. After solving enough problems, some equations become second natures and don't require hours of flash cards.

Answer 3

(a) i think of they could be pondering the element from which the string hangs as being truly mounted relative to earth's floor; if so, a small centrifugal stress that acts on the stone will truly shrink the rigidity on the string. (b) you may calculate the centrifugal stress (mv^2/r) and locate out what number of mg is represented via mv^2/r. of course, the "m" cancels out and has no longer something to do with it. For "v" you ought to use 2 pi circumstances 6380 km divided via 24 hours, and convert each thing to meters and seconds so as that v^2/r comes out in m/s^2, this is the comparable as N/kg. 2. Use F = m1 m2 G / r^2, the place a typical guy or woman-mass must be 60 kg and a small separation between the centers of the two bodies must be 0.5 m or much less. look up vast G, the usually occurring gravitation consistent.

Answer 4

You have to review each equation and ask your self what is the physical meaning behind each. This is the difference between the A students and the c's

Answer 5

The way I always did it was to remember just one - the one for force. You can derive the rest in your head by integration or substitution.