If a force is applied on a body in an isolated system, it gets accelerated, which means its velocity and hence its Kinetic Energy will go on increasing. How does law of conservation of  energy holds for this increase in Kinetic Energy?
121121
If it takes energy to slow an object down, and then the object also loses KE, then how is energy conserved? Don't you have a net loss of energy?
65843
I know that when riding close to another cyclist, I expend less energy to go the same speed. But does the Conservation of Energy "law" mean that the lead cyclist is going to expend more energy to allow me to expend less?  (i.e. Is there a physical reason to get angry at someone drafting behind you? Does riding in their slipstream cause drag for them?)
90395
We know that if an object has been lifted a distance $h$ from the ground then it has a potential energy change:  $$\Delta U = mgh $$  so $h$ is proportional to $\Delta U$.  However, we have also the gravitational potential energy law:  $$ U= -\frac{G M m}{r} $$  where the distance is inversely proportional to the potential energy.  What did I miss? Is the distance of the object proportional or inversely proportional to the potential energy?
7099
Does the force of kinetic friction increase with the relative speed of the objects involved?    I have heard and read that the answer is no.  This is counter intuitive, and is a big part of why the "Airplane on a Treadmill" question is so interesting.  What phenomena are at work with kinetic friction, and why does it not increase with relative speed?
8169
Yesterday, while studying a simple question, a rather strange doubt hit my mind:     Consider a ball of mass $m$ moving with velocity $v$ that collides with a wall in a perfectly elastic collision and rebounds back with the same velocity. Taking the direction of initial motion of the ball as positive, the change in momentum of the ball is $-2mv$ and the wall is clearly at rest.   So, in order to obey the law of conservation of momentum, the wall must gain a momentum of $2mv$.  Now, this itself confused me a lot. I then applied the law of conservation of kinetic energy to this situation, and clearly the magnitudes of the initial and final velocities of the ball are equal, so kinetic energy of the ball is conserved and hence the final kinetic energy of the wall must be zero in order to conserve energy.  Now, this contradicts with the law of conservation of momentum, which says that the wall must gain momentum of $2mv$.  One more point: If we are talking about a wall then it is an important fact, which must be considered, that the wall is fixed on earth and so the mass of the wall is equivalent to that of earth, say $M$. If the law of conservation of momentum is applied now then we get velocity of the wall, say $V=2mv/M$ which is no doubt an extremely small value. But, the law of conservation of energy strictly says that the velocity of the wall must be exactly zero, not even the smallest value is allowed (theoretically speaking).   Please clarify this and correct me anywhere if I'm wrong. I have tried my best to make it clear what I want to ask :).
47567
I don't understand the fact that let's say hypothetically I was pushing a block on a frictionless surface, and I kept applying the same force on the object how it would keep accelerating! Wouldn't there have to be a certain velocity where it would stop getting faster? If not then what is actually acting on the object to cause it to accelerate infinitely?
116246
So this is the question that's been bothering me:  Say you have a simple rigid body in space that is at rest or traveling with only translational motion at a constant speed. Say that the body is something like a rod and it's not rotating. So, at some point, an external force is acted on the rod, just for an instant and it is not acted along some axis that goes through the center of mass. What will happen??  My guess is that it will start rotating about the center of mass (because of torque) + it will get some translational motion towards the direction of the force. Is that correct? and if so, how much of the force becomes rotation and how much translational movement and why??  Please forgive my English and thnx in advance!!
38054
A body continues in its state of motion unless a force is applied to it. But how does an object stay in motion in the first place? A force must have caused it to move right?
28410
Why is force = mass $\times$ acceleration? I have searched in many sites but didn't actually get at it. Simply I want to know that if a mass in space moves (gains velocity thus further accelerates), how can I think, postulate and further believe that force = multiplication  of mass and its acceleration ?
54328
Newton's first law states that in an inertial frame, a body at rest continues to be at rest, and a body in constant rectilinear motion continues its motion, unless an external force is applied upon the bodies. My question is how far have these assertions been tested experimentally? More precisely, is there any need to test this statement, or is it taken as a "definition" of sorts?  I assume the body at rest is a trivial case. On the other hand the case of the body in constant motion would be considerably harder to test, since no external force on a body is an idealization. But I am still curious whether there have been any attempts to test the case of the moving body.
53761
I understand that energy conservation is not a rule in general relativity, but I'd like to know under what circumstances it can still be possible. In other words, when is it possible to associate a potential energy to the gravitational field, so that the energy is constant in the evolution of the system?  Here are some examples, is there a convenient way to define energy in these scenarios?   Just a system of gravitational waves. A point mass moving in a static (but otherwise arbitrary) space-time. Equivalent (if I'm not mistaken) to a test mass moving in the field of a second much larger mass, the larger mass wouldn't move. Two rotating bodies of similar mass.   Overall, I'm trying to understand what keeps us from associating a potential energy to the metric. When we break the time translation symmetry of a system by introducing an electromagnetic field, we can still conserve energy by defining an electromagnetic potential energy. Why can't we do the same when we break TT symmetry by making space-time curved?
88422
In all the places I've looked kinetic energy is derived from the definition of work, but I don't understand how the definition of work was developed with out the concept of kinetic energy. My question really is:  What is the logic behind the definition of  without referring to kinetic energy?  OR  What is the logic behind the definition of  without referring to work?
10066
Some physical quantities like position, velocity, momentum and force, have precise definition even on basic textbooks, however energy is a little confusing for me. My point here is: using our intuition we know what momentum should be and also we know that defining it as $p = mv$ is a good definition. Also, based on Newton's law we can intuit and define what forces are.  However, when it comes to  many textbooks become a little "circular". They first try to define work, and after some arguments they just give a formula $W = F\cdot r$ without motivating or giving intuition about this definition. Then they say that work is variation of energy and they never give a formal definition of energy. I've heard that "energy is a number that remains unchanged after any process that a system undergoes", however I think that this is not so good for three reasons: first because momentum is also conserved, so it fits this definition and it's not energy, second because recently I've heard that on general relativity there's a loss of some conservation laws and third because conservation of energy can be derived as consequence of other definitions.  So, how energy is defined formally in a way that fits both classical and modern physics without falling into circular arguments?
114011
Sorry for posting such a simple problem but I'm having trouble understanding this concept.  In the picture below, we have a force, $ \vec F_{app}$ acting on two objects, A and B.  Mass of block A: $ M_a = 4kg $  Mass of block B: $ M_b = 6kg$  The acceleration of the two blocks can be found using F=ma  $$ 20N = 10kg * a $$ $$ a = 2m/s^2 $$  If we find the force Fba on block B from block A we get:  $$ \vec F_{ba} = 6kg * 2m/s^2 $$ $$ \vec F_{ba} = 12N $$  What I am confused about here is why don't we say that the total force $ \vec F_{app} $ applied onto block A is also applied to block B (20N). Is the force somehow distributed into the blocks?
63036
I know work done is negative of change in potential energy, I.e., $W=-(∆U)$.  It means that Work done against a force (or work done on a system) increases its potential energy. And Work done by a force (or work done by the system) decreases its potential energy.  But why this is so that an internal force (by internal force I mean that a force created under a system) will always tend to decrease the potential energy of the system while the external force increase the potential energy of the system?
90646
I've never understood why the conservation of momentum law is taught in schools as "every force has an equal opposite reaction".   To me a gun's recoil is self explanatory; the explosion sits in-between the bullet and the back of the barrel and the gun and bullet fly in opposite directions (as would be expected). The bullet has a much higher velocity than the gun because of its lower comparative mass. Am I wrong here?  Same with stepping off a boat. You push against the boat and the mass differential between your body and the boat as well as the friction in the water enables you to jump off the boat onto the ground without falling on your face. The boat comparatively moves in the opposite direction minimally, but not because of some weird law, simply because you pushed it back!  To tell kids in school "every force has an equal and opposite force" is misleading I think. It makes it seem as if an equal mysterious force manifests out of thin air to keep the universe happy.   Just thinking - "direction of application" is only relevant to perspective, there really is no direction of application since the force and its counterpart occur simultaneously… so more accurately:   The total force can never be propagated along a single vector?
121441
Earth's orbit is a slight ellipse, so to conserve momentum its speed increases when it is closest to the Sun. If the speed changes there is an acceleration. If there is an acceleration there is a force. Even if the change is small and gradual, wouldn't we experience a force because the Earth is so massive?