Newton's third law only observes that the forces two objects exert on one another are equal in amount but opposite in direction. The law doesn't make any statement about the consequences of those forces on the objects involved. Moreover, it doesn't say that those forces are the only forces on the objects. When you push on an awake friend, your friend will obtain additional forces from the ground or a nearby wall, and will manage to avoid falling over. Even though you push your friend away from you, your friend will see to it that the ground pushes them toward you. As a result, they will probably stay in one place. But when your friend is asleep, they won't be able obtain the additional forces necessary to compensate for the force you exert on them and they may accelerate away from you or fall over.
First, let's suppose that the suitcase is resting directly on the escalator and you are not touching it (I had intend that you hold the suitcase in your hand). Because the suitcase is traveling at constant velocity, the net force on it must be zero. Since the suitcase has a downward weight, the escalator must be pushing upward on the suitcase with a force exactly equal in magnitude to the suitcase's weight. As you suggest, the force of the suitcase's weight and the support force of the escalator cancel one another to produce a net force of zero on the suitcase. Now, if you are holding the suitcase, it's your job to exert this upward force on the suitcase. Once again, that upward force is equal in magnitude to the weight of the suitcase.
If you push gently on the tip of one nail, it won't pierce your finger. When you push on the nail, it pushes back on you, but the force pushing the nail against your finger isn't strong enough to break your skin. If you push twice as hard on two nails at once, using two different fingers, then the force you exert on each nail will be the same as before and each nail will push back against one of your fingers with the same force as before. Once again, the nails won't break your skin. If you now push 100 times as hard against 100 nails, each nail won't push hard enough against you to break your skin. In fact, a few hundred nails will be able to push on you with an overall force equal to your weight without piercing you. That's the idea behind a bed of nails—by lying on many nails at once, you allow so many nails to push upward on you that, while the overall force they exert on you is enough to balance your weight, the force exerted by each individual nail isn't enough to draw blood. These nails have to be spread out around your body so that no individual nails bear more than their fair share of your weight. If one of the nails took too much of your weight, you'd be hurt by it.
Formally defined as "the capacity to do work", energy is a measure of an object's ability to make things happen. It is interesting to physicists for one important reason: it is a conserved physical quantity. By "conserved physical quantity", I don't mean that it's something that we try not to waste. I mean that the amount of energy in an isolated system can't change—energy can't be created or destroyed, it can only be transferred from one object to another or converted from one form to another. Because you can't make it or consume it, energy is an important characteristic of objects and systems. You can often watch it move from object to object and observe the consequences of this movement. For example, the energy that I'm using now to type at my keyboard arrived at the earth's surface as sunlight, was used by plants to build new molecules that eventually become part of my breakfast this morning and are now being combined with oxygen in my body to allow me to move my fingers. Nowhere along this chain was energy created or destroyed—it simply moved about and changed forms. It will still be here tomorrow, and then next day, and even the day after that.
Mechanical advantage is any process that allows you to exchange force for distance (or torque for angle) while performing a particular task. The amount of mechanical work you must do (i.e., the amount of energy you must supply) to perform that task won't change, but the relationship of force and distance (or torque and angle) will. For example, you can increase the altitude of a wooden block by 1 meter either by lifting it straight upward 1 meter or by pushing it several meters uphill along a ramp. In the first case, you'll have to exert a large upward force on the block but you won't have to move it very far to complete the task. In the second case, you'll have to exert a much smaller uphill force on the block but you'll have to move it a long way along the ramp. If you multiply the force you exert on the block times the distance that block travels while rising 1 meter, you'll find that it's exactly the same in either case. You've simply calculated the work required to raise the block 1 meter and that work won't change, regardless of how you perform the task! That's the crucial issue with mechanical advantage—it doesn't let you avoid doing the work, it just lets you do that work with a small (or larger) force exerted over a longer (or shorter) distance. In a situation involving rotation, mechanical advantage lets you do the same work with a smaller (or larger) torque exerted over a larger (or smaller) angle. In all of these cases, you're doing the same amount of work but you're making it more palatable by adjusting the balance between force and distance or between torque and angle.
As for actual mechanical advantage, it's simply a recognition that any mechanical system involves imperfections. The work that you do with the help of a machine doesn't all go toward your goal. Instead, you end up doing some work against sliding friction or air resistance and that work is lost to thermal energy. For example, when you slide a block up a ramp, friction with the ramp wastes some of your energy. If you multiply the uphill force you exert on the block while pushing it up the hill times the distance it travels along the ramp, you'll find that you must do somewhat more work while raising the block 1 meter than you would have done by simply lifting the block directly upward that 1 meter. So ideal mechanical advantage assumes no change in the work you do while actual mechanical advantage recognizes that you're going to end up doing extra work whenever you employ a machine to obtain mechanical advantage.
There are two forces present when the cars collide: each car pushes on the other car so each car experiences a separate force. As for the strength of these two forces, all I can say is that they are exactly equal in amount but opposite in direction. That relationship between the forces is Newton's third law of motion, the law dealing with action and reaction. In accordance with this law of motion, no matter how big or small the cars are, they will always exert equal but oppositely directed forces on one another.
The amount of each force is determined by how fast the cars approach one another before they hit and by how stiff their surfaces and frames are. If the cars are approaching rapidly and are extremely stiff and rigid, they will exert enormous forces on one another when they collide and will do so for a very short period of time. During that time, the cars will accelerate violently and their velocities will change radically. If you happened to be in one of the cars, you would also accelerate violently in response to severe forces and would find the experience highly unpleasant.
If, on the other hand, the cars are soft and squishy, they will exert much weaker forces on another and they will accelerate much more gently for a long period of time. That will be true even if they were approaching one another rapidly before impact. When the collision period is over, the cars will again have changed velocities significantly but the weaker forces will have made those changes much more gradual. If you have to be in a collision, chose the soft squishy cars over the stiff ones—the accelerations and forces are much weaker and less injurious. That's why cars have crumple zones and airbags: they are trying to act squishy so that you don't get hurt as much.
When an egg is sitting on a table, each object is exerting a support force on the other object. Those two support forces are equal in magnitude (amount) but opposite in direction. To be specific, the table is pushing upward on the egg with a support force and the egg is pushing downward on the table with a support force. Both forces have the same magnitude—both are equal in magnitude to the egg's weight. The fact that the egg is pushing downward on the table with a "support" force shows that not all support forces actually "support" the object they are exert on. The egg isn't supporting the table at all. But a name is a name and on many occasions, support forces do support the objects they're exerted on.
The enormous upward force on the egg when it hits the table does cause the egg to accelerate upward briefly. The egg loses all of its downward velocity during this upward acceleration. But the egg breaks before it has a chance to acquire any upward velocity and, having broken, it wastes all of its energy ripping itself apart into a mess. If the egg had survived the impact and stored its energy, it probably would have bounced, at least a little. But the upward force from the table diminished abruptly when the egg broke and the egg never began to head upward for a real bounce.
Different forces acting on a single object are not official pairs; not the pairs associated with Newton's third law of action-reaction. While it is possible for an object to experience two different forces that happen to be exactly equal in magnitude (amount) but opposite in direction, that doesn't have to be the case. When an egg falls and hits a table, the egg's downward weight and the table's upward support force on the egg are equal in magnitude only for a fleeting instant during the collision. That's because the table's support force starts at zero while the egg is falling and then increases rapidly as the egg begins to push against the table's surface. For just an instant the table pushes upward on the egg with a force equal in magnitude to the egg's weight. But the upward support force continues to increase in strength and eventually pushes a hole in the egg's bottom.
You are merging two equations out of context. The force you exert on an object can be non-zero without causing that object to accelerate. For example, if someone else is pushing back on the object, the object may not accelerate. If the object moves away from you as you push on it, then you'll be doing work on the object even though it's not accelerating. The only context in which you can merge those two equations (Force=mass x acceleration and Work=Force x distance) is when you are exerting the only force on the object. In that case, your force is the one that determines the object's acceleration and your force is the one involved in doing work. In that special case, if the object doesn't accelerate, then you do no work because you exert no force on the object! If someone else is pushing the object, then the force causing it to accelerate is the net force and not just your force on the object. As you can see, there are many forces around and you have to be careful tacking formulae together without thinking carefully about the context in which they exist.
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