mysolipsis

i agree with the resourceful one, you can't like of space like a finite shape, which student does. think of it as infinite layers, and sheets of rubber in all directions, where the mass effects the way it flexes therefore curving it.

to clarify: there is a tension being exherted down from the ceiling and equally there is a tension exerted up from the pully, and a weight which is pulling down from the mass, and a force pulling up from the force P as well as a tension in the rope moving up and moving down. now the tension up and down should be equal on both sides, assuming there is no slack in the rope, or kink in the pully. now. Tension up = Tension down = Weight - P, however, there is a mechanical advantage of the pully therefore 2(Tension up) = 2(Tension down) = Weight - P. therefore T = (Wg - P)/2 . yes or know?

equal and opposite forces, there is aprently no movement in the problem, therefore the sum of all the forces should be zero (vector sum). or am i incorrect with this statement?

you would have to assume that no energy is transferred into the house when the golf ball hits it

think of it like this, and i'm not giving you the answer, rather, the way to look at it. tension is a force. and the sum of the forces should equal zero. so you have a force due to gravity (weight) moving in the downward direction and a force P moving in the upward direction. now it should be easy for you to figure it out.

break down the equation piece by piece and you will see. Force is measured in Newtons, which are kg-m/s^2 now you have to masses over the the square of the distance which would give you kg^2/m^2 which is not a force, a constant is needed to ballance the equation, something which has an acceleration over a mass which would be m/(kg-s^2) which would then give you a proper measure of force. and as Atheist said, unless the gravitational constant G = 1 then the equation would not work.

the position of the fan may make a difference as well. for instance if you have a fan placed on the ceiling, then this will force the air from the upper part of the room down, hence pushing the air from the bottom of the room up (force air convection). now even though there isn't a drastic difference in temp, in theory the air at the top of the room should be warmer (heat rises) therefore the air at the feet (which should be cooler) pushes up and in a sense cools the ambient air around the upper part of our body, which most people seem to notice more. what do you think? ya? or na?

could possibly be that the difference in contact area is so small in comparison. when figuring out the contact area, things like the elasticity of the rubber which are steel belted radials (usually) and also how the air pressure get displaced. now it should make more contact area with the vehicle that weighs more, however, if the difference is so small it becomes almost negligible by comparison.

maybe move the source far away, say the radius between the objects was approaching infinity, then the limit of 1/ifinity^2 would be aproaching zero, which in a sense wouldn't make the object disapear (conservation laws) but would make it's effect zero

einstien defined space-time, and gravity is explained in the warping of space-time. think of it like standing on a huge trampoline. there is you and say a person who has twice your mass (you can say weight if you wish because you are both being effecting by the acceleration do to gravity, so the mass is proportional to the weight). now if you were to stand on the edge of the trampoline and the other person was to stand in the middle. as you get closer to the other person you can feel the effects of him on the trampoline, and in a sense with each step that you get closer, your ballance is thrown off more untill you get pulled into him. like this masses in space-time end up warping it, and the warp is so much that it pulls at it, hence gravity. now, there is even more deep explainations involving angular momentum, torque, and dark matter when deeling with planetary orbits, but this is the jist of it all

when ever you are lifing an object, you are doing work on the object. work by definition would be a force carried out in a certain distance. since the force to lift an object is the opposite of the weight, then the acceleration due to gravity is multiplied by the inertia. since the acceleration due to gravity on the moon is far less than that on earth, then the object would weight less, therefore less work would be needed to move the object.