Newton's third law pairs forces. You may have heard that the two forces in a pair cancel each other out. In fact they do not. The two forces in a third-law pair are equal and opposite, but they act on different objects, so they do not cancel. Take a swimmer and a pool wall. The swimmer pushes the wall, and the wall pushes the swimmer. Only the push on the swimmer changes her motion.
Rockets use the same pairing. A rocket moves forward by expelling gas backward at high speed, and the gas pushes the rocket forward. A rocket does not push off the ground or the air. Rockets actually work better in a vacuum, so rockets do speed up in space. Jets follow the same rule. The engine sends hot exhaust gas backward, and in reaction the engine is pushed forward. A wing bends the airflow downward, and the wing is pushed upward in return.
Air and water are fluids, and a solid object moving through one feels drag. It is a contact force, so without a fluid, or without relative motion between object and fluid, there is no drag. For most large objects moving through air at reasonable speeds, such as bicyclists, cars and baseballs, drag varies as the square of the speed. Doubling your speed roughly quadruples the air pushing back on you.
A falling skydiver keeps speeding up until the air's push matches gravity's pull, and after that the speed holds steady. That steady speed is the terminal velocity. Falling head first, a 75-kilogram skydiver tops out near 350 km/h, which is about 220 mph. Spread out flat, the same person tops out near 200 km/h, and a parachute, once open, cuts the speed much further.
Where does friction come from? It comes partly from the roughness of surfaces, but much of it comes from attractive forces between the molecules of the two objects. That is why even perfectly smooth surfaces are not friction-free. Friction also changes once something starts to slide. Say a 100-kilogram crate rests on a floor where the static coefficient is 0.45. Starting it takes more than roughly 440 newtons of push. After it slides, a kinetic coefficient of 0.30 lowers the push needed to roughly 290 newtons for a steady speed.
A lever trades force for distance. A small push through a long distance can balance a large force acting through a short distance. A lever is a rigid bar that pivots at a fixed point called the fulcrum, and a nail puller is one example, giving a large mechanical advantage. Mechanical advantage compares the force that comes out with the force that goes in. A ramp makes a similar trade. A load can be raised with a push smaller than its weight if the push is applied along a slope, at the cost of a longer path. In every case, no machine gives out more energy than it takes in.
Momentum is mass in motion: it is mass times velocity. A car of 1,400 kilograms moving 15 meters per second has a momentum of 21,000 kg·m/s. Momentum is larger for an object that is both heavy and fast. Momentum is also different from kinetic energy: momentum depends equally on an object's mass and velocity.
Galileo had to answer an objection to the idea that Earth moves. If Earth moved, the objection went, a dropped ball would be left behind. Galileo replied that a cannonball dropped from a tower lands at the tower's foot, because the ball keeps moving along with the tower after release. That, he said, is inertia at work.
Weight and mass are often mixed up. Mass measures the amount of stuff in an object, and it stays the same everywhere. Weight is a force, the pull of gravity, and it depends on where you are. Multiply an object's mass by g, whose value on Earth is 9.8 newtons for each kilogram, and you get its weight. On the Moon, gravity has about one-sixth of its strength on Earth, so the same person would weigh far less.
The Apollo 15 test put the idea of equal falling to a check on the Moon. A 1.32-kilogram hammer and a 0.03-kilogram feather were released from about 1.6 meters. They reached the Moon's surface together, as theory predicted. NASA called the result reassuring, not a surprise. It matched well-established theory, and NASA notes that the trip home depended on that theory being right.
In September 2022, NASA's DART spacecraft crashed into the asteroid Dimorphos. Dimorphos circles a larger partner called Didymos. NASA reports that the hit shortened the time Dimorphos takes to circle Didymos by 32 minutes, from 11 hours 55 minutes to 11 hours 23 minutes. One spacecraft changed the motion of an asteroid.
Words to know
- vacuum: empty space
- relative: compared with
- molecules: tiny particles
- fulcrum: pivot point
- momentum: mass times velocity
