At the center of the earth, the man would be truly weightless and the space around him would be exactly flat (no curvature due to gravity). This special situation occurs because the gravitational effects of the earth around the man are perfectly balanced. With equal amounts of the earth's mass on each side, there is no special direction in which the man would accelerate.
When you accelerate forward from a stop, the car's kinetic energy is increasing. The time it takes you to reach cruising speed is largely determined by how fast the car's engine can increase the car's kinetic energy. Stopping speed is similarly determined by how quickly the brakes can remove the car's kinetic energy. While your car still has the same mass that it had before you changed wheels, and thus would seem to require the same transfers of energy to start and stop, that's not the case. Transferring mass from the car's body to its wheels has substantially increased the amount of kinetic energy the car has when it's moving at cruising speed. That's because each spinning wheel has two forms of kinetic energy. First, its center of mass is heading forward at cruising speed, so it has a translational (motion along a line) kinetic energy proportional to its mass. Second, it is spinning about its center of mass, so it has a rotational kinetic energy proportional to its moment of inertia (the rotational equivalent of mass). If most of each wheel's mass is located near its periphery, its rotational kinetic energy will be roughly equal to its translational kinetic energy. The 40 pounds you transferred to the wheels is counting twice as much as before! You've effectively added 40 pounds to the mass of your car. Your new wheels and tires are demanding far more energy from your car's engine and delivering far more energy to your car's brakes than the old wheels did and you'll have to remove an additional 40 pounds from the car's body to compensate.
While people are always trying to build perpetual motion machines, they will never succeed. All of these devices are intended to obtain useful energy—what physicists call "work"—from either nowhere or from less useful energy—what physicists often call "heat" or "thermal energy". Obtaining work from nowhere is really impossible; energy is a conserved quantity, meaning that it simply cannot be created or destroyed. For a machine to do work, it must obtain energy from somewhere or something else. So if anyone tries to sell you a car engine that doesn't take any fuel at all—thus creating work out of nowhere—don't buy it! It's a fraud.
As for machines that try to convert thermal energy completely into work, they are also impossible, but for a different reason. While they don't violate the conservation of energy, they do violate the laws of thermodynamics. Thermal energy is disordered energy—it is energy that has been distributed randomly among the individual atoms and molecules in an object so that it cannot be easily reassembled to do useful work. When you burn a candle, all of the energy the candle once had is still in the room, but it's much harder to use. Just as a coffee cup is much more useful before you drop it than after you drop it, so energy is much more useful before you disorder it than after you disorder it. The difficulty with reassembling thermal energy to do useful work is a statistical one: it's unlikely that this energy will spontaneously reassemble itself in a useful manner, just as its unlikely that a dropped coffee cup will spontaneously reassemble itself in a useful manner. The laws of mechanics don't prevent either of those reassemblies from occurring, but both reassemblies are statistically very unlikely to occur. How often have you dropped a broken cup and had it fall together rather than apart? So if someone tries to sell you a car engine that uses the thermal energy in the surrounding air as "fuel"—thus turning thermal energy completely into work—don't buy it! It's also a fraud.
It takes no additional energy to keep those objects orbiting—the earth's inertia keeps it moving around the sun. If the sun weren't there, the earth would continue forward in a straight line at a steady pace forever because that is how free objects behave. It takes no energy or force to keep them moving. But the earth is drawn continuously inward by the sun's gravity and so it travels in an elliptical arc instead of a straight line. Assuming that nothing adds or subtracts energy from the earth and sun, the earth will continue to orbit the sun forever. The same applies for the other planets and for electrons orbiting nuclei in an atom. In the latter case, it is electromagnetic forces that draw the electrons inward, rather than gravity.
When two surfaces slide across one another, some of the mechanical energy in those surfaces is converted to thermal energy (or heat). That's because the surfaces are microscopically rough and their atoms collide as the surfaces slide pass one another. Each time a collision occurs, the atoms that collide begin to vibrate more vigorously than before. In this process, the surfaces lose some of their overall mechanical energy but the atoms gain some randomly distributed local vibrational energy—more thermal energy. Those surface atoms become hotter. As the sliding continues, large regions of the surfaces become hotter and the surfaces lose much of their energy. If you don't push them to keep them sliding across one another, they'll come to a stop as all their mechanical energy is converted into thermal energy.
The pendulum experiences friction and air resistance, both of which extract energy from the pendulum. Friction turns that energy into thermal energy and air resistance transfers the energy to the air.
Yes. If the pendulum had no way to convert its energy into thermal energy (e.g., via friction) and no way to transfer that energy elsewhere (e.g., via air resistance), it would continue to swing forever. While its energy would transform from gravitational potential energy (at the ends of each swing) to kinetic energy (at the middle of each swing) and back again, over and over, the total amount of energy it has won't change.
In both cases, I was referring to the total momentum of the ball and me. The total momentum of the ball and me was zero before I threw the ball and it was still zero after I threw the ball. However, before I threw the ball nothing was moving and after I threw the ball the two of us were moving in opposite directions. It was our total momentum that was zero after the throw, not our individual momenta. While the ball and I each had a nonzero momentum after the throw, our momenta were equal in amount but opposite in direction—the ball's momentum was exactly opposite mine. If you were to add our momenta together, they would sum to zero. Since momentum is conserved and we couldn't exchange momentum with anything around us, the ball and I began and ended with the same total amount of momentum: zero.
Adding sandbags to the back of a pickup truck increases the truck's traction and adds to the truck's mass. Fortunately, the truck's traction increases more dramatically than its mass and it becomes easier to start and stop the truck, rather than the reverse. That's because even a modest amount of sand can double the force pressing the rear wheels against the road and thus double the frictional forces the wheels can experience. That same amount of sand won't double the total mass of the truck.
Friction is caused by contact and collisions between the tiny projections that exist on all surfaces. When you put one block on top of another, the tiny projections on the bottom of the upper block touch the tiny projections on the top of the lower block. If you then try to slide one block across the other, these projections begin to collide with one another and they oppose the sliding motion.
If the two blocks have rough surfaces, then the projections that are colliding are obvious to your eyes. But if the two blocks have very smooth surfaces, you can't see their surface projections. However, the invisibility of these projections doesn't make them insignificant. Even the smoothest surfaces are rough at the atomic scale. When you press two smooth surfaces against one another, their microscopic projections still touch one another and those projections still collide when you try to slide the surfaces across one another. In short, smooth surfaces still experience friction.
But it's also possible for attachments to form between portions of the two smooth surfaces when they touch. This molecular adhesion makes it even harder to slide the two surfaces across one another. You can feel this adhesion when you press two pieces of very clean glass against one another—they form bonds that partially stick them together. Actually, this sort of sticking would be quite common if it weren't for water. Almost all surfaces are coated with a layer or two of water molecules. These water molecules lubricate the interface between any two surfaces and make it hard for those surfaces to stick to one another. But if you get rid of the water molecules, the sticking becomes quite severe. This effect causes trouble in my laboratory, where sliding mechanisms that move easily in air stop working properly when we put them in a vacuum chamber and remove the water on their surfaces.
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