Unit 11 · Forces, Motion and Energy

Push a shopping cart and it rolls. Pull a wagon and it follows you. A force is any push or pull on an object. Every force has a size, measured in a unit called the newton, and a direction. One newton is about the weight of a small apple in your hand. A gentle push might be 5 newtons. A car engine can push with thousands.

Most objects have several forces on them at the same time. A book on a desk has gravity pulling it down and the desk pushing it up. Two students can push the same box from opposite sides. To predict what happens, you add the forces up, keeping track of direction. The total is called the net force.

If two forces are the same size and point in opposite directions, they cancel. The net force is zero, and the motion does not change. If one is bigger, the net force points in the direction of the bigger force. In a tug of war, the rope moves toward the team with the greater pull, and the difference between the two pulls is what moves it.

Drawing forces as arrows helps. A longer arrow means a bigger force, and the arrow points in the force’s direction. Engineers draw these arrow diagrams for bridges, chairs and rockets before they build anything. The question is always the same: what is the net force, and which way does it point?

Slide a hockey puck across a rough rug and it stops fast. Slide it on ice and it glides far. On a perfectly smooth surface with no air, it would keep going forever. Nothing has to push it to keep it moving. This surprised people for a long time. Aristotle taught that objects needed a steady push to keep moving, and it took Galileo’s ramp experiments and Newton’s thinking to change that idea.

Newton’s first law says an object’s motion does not change unless a net force acts on it. A resting object stays put. A moving object keeps the same speed and the same direction. The tendency of objects to keep doing what they are doing is called inertia. The more mass an object has, the more inertia it has and the harder it is to change its motion.

You feel inertia every day. When a bus starts moving, your body wants to stay still, so you lurch backward. When the bus brakes, your body wants to keep moving, so you pitch forward. A seat belt gives the force that stops you with the car. Without it, you keep moving until the dashboard or the windshield stops you instead.

So why do things on Earth slow down? Because forces like friction and air resistance are always acting. Friction is a force between surfaces that rub, and it always pushes against motion. The puck on the rug did not stop by itself; friction stopped it. Remove the friction, and the first law shows itself clearly, as it does for a probe coasting through deep space.

Push an empty shopping cart and it speeds up quickly. Push a full one with the same effort and it speeds up slowly. Any change in speed or direction is called acceleration. Speeding up, slowing down and turning are all accelerations. A net force causes acceleration, and the amount depends on two things: how big the force is and how much mass the object has.

Newton’s second law puts it in one line: force equals mass times acceleration, or F = m × a. Double the net force on the same cart and it accelerates twice as fast. Double the mass and push with the same force, and the acceleration is cut in half. Mass is the amount of matter in an object, measured in kilograms. It does not change when you move to the Moon, even though weight does.

The units fit together. One newton is the force that gives one kilogram an acceleration of one meter per second every second. A 1,000-kilogram car that goes from 0 to 10 meters per second in 5 seconds accelerates at 2 meters per second per second. The net force on it must be about 2,000 newtons. If the engine pushes harder than that, friction and air are eating the difference.

The second law also explains slowing down. Brakes on a bike put a backward force on the wheels, so the bike accelerates backward, which we call decelerating. A heavier bike with the same brakes takes longer to stop. That is why loaded trucks need much longer stopping distances than cars, and why highway signs warn about it.

Stand on a skateboard and push a wall. You roll backward. You pushed the wall, but the wall pushed you too. Newton’s third law says forces always come in pairs. When object A pushes on object B, object B pushes back on object A with the same size force in the opposite direction. There is no such thing as a one-sided push.

This law confuses people, because it sounds like the two forces should cancel. They do not cancel, because they act on different objects. Your push acts on the wall. The wall’s push acts on you. The wall is attached to the building, so it barely moves. You are on wheels, so you roll. Each object responds to the net force on itself.

A rocket works this way. The engine pushes hot gas downward out of the nozzle. The gas pushes the rocket upward. A swimmer pushes the water backward with her hands, and the water pushes her forward. When you walk, your foot pushes the ground backward, and the ground pushes you forward. On ice, your foot slips instead of pushing, so the ground cannot push you.

Even gravity comes in pairs. Earth pulls you down with your weight. You pull Earth up with exactly the same force. Earth has so much more mass that its acceleration toward you is far too small to notice, while your acceleration toward it is the familiar fall. Same force, very different masses, very different motions.

Catch a fast baseball with a stiff, straight arm and it stings. Catch it while letting your hand move back with the ball, and it does not. The ball loses the same motion either way. The difference is time. When the stop takes longer, the force can be smaller. When the stop is almost instant, the force must be huge.

The second law explains why. To stop an object, you must give it an acceleration backward. A quick stop is a big acceleration, and a big acceleration needs a big force. A slow stop is a small acceleration, so it needs only a small force. Engineers say the impact force depends on how long the collision lasts.

Think about the two eggs from the story. The taped egg hit hard tile and stopped in about a thousandth of a second. Maya’s egg stopped over a much longer time as the straws bent and the cup crumpled. Both eggs lost all their downward motion, but the force on Maya’s egg was far smaller, so its shell held.

The same thinking is everywhere. You bend your knees when you jump down from a step. Gymnasts land on thick mats. A car’s front end is built to fold. In every case the goal is the same. Make the stop take longer, so the force stays small enough to be safe.

A bike helmet looks like a hard shell, but the important part is the foam inside. In a crash, the foam crushes. Crushing takes time, and that time is the whole point. The head stops over a longer stretch instead of all at once, so the force on the skull and brain is much smaller. A helmet that has crushed once has done its job and should be replaced.

Cars use the same idea on a bigger scale. The front and back of a modern car are built with a crumple zone at each end: parts designed to fold up in a crash. That folding takes time and absorbs energy. The passenger area is built stiff so it keeps its shape. The car is wrecked on purpose so the people inside are not.

A seat belt supplies the stopping force from the first law. Without it, the car stops but you keep moving until you hit the dashboard, a very fast stop. A belt starts slowing you as soon as the car slows, and it spreads the force over your hips and chest. An airbag inflates in a fraction of a second and gives your head a soft, longer stop.

Engineers test these designs with crash test dummies full of sensors, then change the design and test again. The numbers guide each choice. The goal is never to make the crash disappear; that is impossible. The goal is to stretch it out and spread it around so the forces stay below what a body can take.

Suppose you want to know whether a bigger parachute makes an egg land more gently. You could just try it once and see. But a single drop can go wrong for many reasons: a gust of air, a crooked release, a soft spot in the box. Scientists and engineers plan a fair test so the answer comes from the thing they changed and not from luck.

A fair test starts with one variable, the thing you choose to change. Here it is parachute size. Everything else must stay the same: the egg, the cup, the drop height, the floor, the way you let go. Those are the controls. If you changed the parachute and the drop height at the same time, you could not tell which one mattered.

Next you decide what to measure. ’Landed gently’ is a feeling, not a measurement. Better choices are the time the fall takes, whether the egg cracks, or the dent left in a clay pad under the target. A phone’s slow-motion video can count frames. Numbers let two people compare results and agree.

Finally, repeat. Three drops per parachute size is better than one, and five is better than three. If the big parachute wins every time, the pattern is real. If it wins once and loses twice, the parachute size may not matter as much as you thought, and that is a useful discovery too.

Drop a pencil. It falls. Gravity is a pull between any two objects that have mass. Earth is enormous, so its pull on you is strong enough to feel every second of your life. Your weight is the force of Earth’s gravity pulling on your mass. Like every force, it is measured in newtons and has a direction: toward the center of Earth.

Mass and weight get mixed up, but they are different. Mass is how much matter you contain, and it does not change. Weight is a force, and it depends on where you are. Near Earth’s surface, gravity pulls on every kilogram with about 9.8 newtons. A 50-kilogram student weighs about 490 newtons here. On the Moon, the pull is only about one sixth as strong, so the same student weighs about 80 newtons but still has a mass of 50 kilograms.

Gravity also gives all falling objects the same acceleration when air is not in the way: about 9.8 meters per second every second near Earth’s surface. Drop a hammer and a feather in a room and the feather drifts down, because air pushes on it. In 1971, an Apollo astronaut dropped a hammer and a feather on the airless Moon. They hit the ground together.

That result matches Newton’s second law. Gravity pulls harder on the hammer, but the hammer also has more mass and more inertia. The bigger force and the bigger mass balance out exactly, so the acceleration is the same. Galileo argued this in the 1600s using ramps and careful timing, long before anyone could test it in a vacuum.

Every object with mass pulls on every other object. You pull on your desk and your desk pulls on you. You never notice, because the force is tiny. Gravity only becomes obvious when at least one of the objects is huge, like a planet. Two things set the strength of the pull: the masses involved and the distance between them.

More mass means more pull. Jupiter has far more mass than Earth, so its surface gravity is much stronger. More distance means less pull, and the drop-off is steep. Newton worked out that if you double the distance between two objects, the pull becomes only one fourth as strong. Triple the distance, and it is one ninth. That is why astronauts far from Earth feel almost nothing.

Gravity does not only pull things down. It also bends paths. The Moon is always falling toward Earth, but it is also moving sideways fast. The sideways motion and the downward pull combine into a curved path. That path never reaches the ground. It is an orbit. Newton imagined a cannonball fired from a mountaintop so fast that the ground curved away beneath it. That is exactly what a satellite does.

The same law reaches from a falling apple to the planets circling the Sun. Newton’s idea was bold. The force that drops an apple and the force that holds the Moon are one and the same. That single rule let astronomers predict eclipses. It helped them find new planets from the wobbles of known ones. It guides spacecraft to the Moon and Mars today.

Rub a balloon on your hair and hold it near the wall. It sticks. Hold it near a thin stream of water from a faucet, and the stream bends toward the balloon. Nothing is touching the water. A force is reaching across the gap. This is an electric force, and it comes from charge.

Everything is made of atoms, and atoms contain tiny particles with charge. Protons carry positive charge and electrons carry negative charge. Most objects have equal amounts and act neutral. Rubbing can move some electrons from one object to another. The balloon gains extra electrons and becomes negative. Your hair loses them and becomes positive.

Charges follow a simple rule: opposites attract, and likes repel. The negative balloon pulls on the positive hair, which is why hair stands up toward it. Two rubbed balloons push each other apart. The force is stronger when the charges are bigger and weaker when they are farther apart, much like gravity, but electric forces can push as well as pull.

Scientists describe the space around a charge as an electric field. It is the region where any other charge would feel a force. The field is strongest near the charge and fades with distance. You cannot see a field, but you can map it. Move a small test charge around and record the push or pull at each spot. Lightning, static shocks and the touch screen on a phone all work by electric force.

Hold two magnets near each other and you feel them pull or push before they touch. Every magnet has two ends called poles, north and south. Opposite poles attract and like poles repel. The space around a magnet where these forces act is its magnetic field. Sprinkle iron filings on paper over a magnet, and they line up in curves that show the field’s shape.

For a long time, people thought electricity and magnetism were separate. In 1820, a Danish scientist named Hans Christian Oersted noticed that a compass needle swung when he switched on an electric current in a nearby wire. Moving charge makes a magnetic field. That discovery joined two sciences into one and made the modern world possible.

Wrap a wire into a coil, run a current through it, and you have an electromagnet. Add an iron core, and it gets much stronger. Unlike a bar magnet, you can switch it off, and you can make it stronger with more coils or more current. Scrap yards use giant electromagnets to lift cars. Electric motors, speakers, doorbells and the drive of a Chicago ’L’ train all use them.

Fields explain how forces act without touching. Earth itself is a giant magnet, and a compass needle lines up with its field. That is why a hiker in a forest preserve outside Chicago can find north with a needle that has no idea where it is. Gravity, electricity and magnetism all reach across empty space in this way: through fields.

A moving bowling ball can knock down pins. A moving hammer can drive a nail. Anything that moves carries energy, the ability to make something happen: to push, to lift, to heat, to break. The energy of motion is called kinetic energy. The unit of energy is the joule. Lifting an apple about one meter takes roughly one joule.

Two things set how much kinetic energy an object has. The first is mass. A loaded truck at 30 miles per hour has far more kinetic energy than a bicycle at 30 miles per hour, and that is why it does far more damage in a crash. Double the mass at the same speed and you double the kinetic energy.

The second is speed, and speed counts more than mass. Kinetic energy depends on speed multiplied by itself, the speed squared. Double the speed and the kinetic energy becomes four times bigger. Triple the speed and it becomes nine times bigger. That is why a car at 60 miles per hour needs about four times the stopping distance of the same car at 30, not twice.

You can test this with a ball and a cup on a table. Roll a ball slowly into a paper cup and the cup slides a little. Roll it twice as fast and the cup slides about four times as far. The distance the cup moves is a way to measure how much energy the ball delivered. More speed means much more energy to hand over.

A book on a high shelf is not moving, but it can still make something happen. Nudge it off and it falls, gaining speed and kinetic energy. The energy was there all along, stored by the book’s position. Stored energy that depends on position is called potential energy. Lifting the book gave it energy; falling releases it.

The most familiar kind is gravitational potential energy. It grows with mass and with height. Lifting a 1-kilogram book 1 meter stores about 10 joules. Lift it 2 meters and it stores about 20. A roller coaster at the top of a 60-meter hill has a huge amount, and every bit of it came from the chain motor doing work on the train during the climb.

Springs and rubber bands store elastic potential energy. Stretch a bow, and the bent limbs hold energy until the string is released and the arrow flies. A trampoline stores your energy as the mat stretches downward and then gives it back as it snaps up. A wind-up toy stores energy in a coiled spring and lets it out slowly through gears.

Fields store energy too. Pull a magnet away from the refrigerator and you store energy that is released when it snaps back. Push two like charges together and they store energy that is released when they fly apart. Even food and fuel store energy in the electric forces between atoms, which is why chemists call it chemical potential energy.

At the top of the first hill, the train has lots of gravitational potential energy and almost no kinetic energy. As it drops, height is traded for speed. At the bottom, it has little potential energy and lots of kinetic energy. Up the second hill, speed is traded back for height. The total, potential plus kinetic, stays nearly the same all the way through. This is the law of conservation of energy. Energy changes form, but it does not vanish.

That law explains why every hill after the first must be lower. The train can only rise as high as its energy allows, and the first hill set that budget. If a second hill were taller than the first, the train would roll backward. Coaster designers use this rule for every hill, loop and turn. They add a margin, so a heavy train on a cold day still makes it over.

But the hills shrink faster than a perfect trade would predict. Each hill is lower than the last because some energy leaks away as heat. Wheels rub the rails. Air pushes against the cars. Bearings warm up. None of the energy is destroyed; it spreads into the track, the air and the metal as thermal energy, where it can no longer lift the train. At the end, the brakes turn all the remaining motion into heat, which is why they are warm.

James Joule proved the connection between motion and heat in the 1840s with a paddle wheel spinning in water. A falling weight turned the paddle, and the water warmed by a tiny, measurable amount. Motion was becoming heat, and the amount matched. His careful measurements helped convince scientists that energy in all its forms is one thing, counted in one unit that now bears his name.

Everything is made of particles too small to see, and they never stop moving. In a solid they jiggle in place. In a liquid they slide past each other. In a gas they zip around and bounce off the walls. The energy of all this motion, added up, is the object’s thermal energy. Rub your hands together and they get warm because friction made their particles jiggle faster.

Temperature is different. It measures how fast the particles are moving on average, not how many there are. A thermometer reports the average, in degrees. Compare a cup of tea at 90 degrees Celsius with a bathtub of water at 40 degrees Celsius. The tea is hotter. But the tub holds far more water, so its total thermal energy is much larger.

A spark from a sparkler can be over 1,000 degrees Celsius, yet it does not burn you. It is tiny, so it carries very little total energy and cools in an instant. A pot of boiling water at 100 degrees Celsius is far more dangerous. It holds a huge amount of thermal energy and can pour it into your skin. Temperature tells you how hot. Thermal energy tells you how much.

Heat is the third word, and it is a verb as much as a noun. Heat is thermal energy on the move, flowing from a warmer object to a cooler one. When you hold a warm mug, heat flows into your hands. Hold an ice cube and heat flows out of your hand into the ice. The ice does not send cold into you; you send heat into it.

Put a cold spoon into hot soup. The spoon warms and the soup cools a tiny bit. Leave them long enough and they reach the same temperature. Heat flows on its own in only one direction: from hot to cold. It never flows from a cold spoon into hotter soup by itself. When two objects reach the same temperature, the flow stops, and we say they are in thermal equilibrium.

Why one direction? Picture the fast-jiggling particles of the soup bumping the slow ones in the spoon. On average, the fast ones lose a little speed in each bump and the slow ones gain a little. Energy spreads out from where it is concentrated to where it is not. It would take an outside push, like a refrigerator’s motor, to move heat the other way.

In 1798, an American-born scientist working in Germany, Benjamin Thompson, known as Count Rumford, watched cannon barrels being drilled. The metal got hot enough to boil water, and it kept getting hot as long as the drill kept turning. Most scientists then thought heat was an invisible fluid stored in matter. Rumford argued that a fluid would run out; the drilling did not. He concluded that heat was being made by motion.

Rumford’s cannon and Joule’s paddle wheel point at the same idea from two directions. Rub, drill, stir or brake, and you turn motion into thermal energy. That energy then flows from the warm spot outward into cooler surroundings. This is why a drill bit gets too hot to touch, why brakes glow on a mountain road, and why a meteor streaking through the air burns bright.

Leave a metal spoon in a pot of hot soup and the handle soon burns your fingers. Leave a wooden spoon and the handle stays cool. Heat moved along the metal spoon by conduction. Fast-moving particles at the hot end bump their neighbors. Those bump theirs. The energy passes along the spoon, but the particles themselves barely move.

Some materials pass this energy along quickly. Metals like copper and aluminum are excellent. Each is a conductor, a material that passes heat quickly. Their loose electrons help carry energy through the metal. Other materials pass it along slowly. Wood, plastic, foam, wool and glass are poor conductors. We call a poor conductor an insulator. Still air is one of the best insulators of all. That is why fluffy materials full of air pockets keep you warm.

Conduction explains why a metal railing feels colder than a wooden one on a winter morning, even though both are the same temperature. The metal pulls heat out of your hand fast, so your skin cools and reports cold. The wood pulls heat slowly, so your skin stays warm. Your hand is measuring how fast heat leaves, not how cold the object is.

Engineers choose materials for conduction on purpose. Pot bottoms are copper or aluminum to move heat into food quickly. Pot handles are plastic or wood to keep it away from your hand. A winter coat traps air. A foam cooler is mostly trapped gas bubbles. In every case, the question is the same: do you want heat to move fast or slow?

Watch a pot of water on the stove just before it boils. Water at the bottom warms first, expands, and becomes a little less dense than the cooler water above it. So it rises. Cooler water sinks to take its place, warms, and rises in turn. This rolling loop is a convection current. Heat is carried by the moving water itself, not passed particle to particle.

Convection works in any fluid, which means any liquid or gas. Warm air from a heater rises to the ceiling while cool air slides along the floor, which is why your feet are the coldest part of a room. Smoke rises above a candle. A hawk circles without flapping inside a column of warm air rising from a sun-baked parking lot.

Chicago feels convection on a large scale. On a hot summer afternoon, the land warms faster than Lake Michigan, so air over the land rises. Cooler air from over the lake slides in to replace it, and the neighborhoods near the shore get a lake breeze that can be many degrees cooler than the suburbs. Weather forecasters for the city mention it all summer long.

Convection shapes the planet. Air warmed near the equator rises and moves toward the poles, driving winds. Ocean currents carry warm water from the tropics to cooler seas. Even Earth’s interior churns by convection over millions of years, slowly moving the plates that carry the continents. The same loop in a soup pot is at work under your feet.

Stand near a campfire and your face feels warm. The air between you and the fire is cool, and the wind may blow the other way. So the heat is not conducted through the air. It is not carried by rising air either, because you are beside the fire, not above it. It arrives as radiation: waves of light. Most of it is a kind your eyes cannot see, called infrared.

Every object warmer than absolute zero gives off infrared radiation. Warmer objects give off more of it. Your body glows in infrared all the time, which is how a thermal camera can find a person in the dark. Hold your hand near a hot stove burner without touching it and you feel that glow directly. Very hot objects like the burner’s coil also glow in visible red.

In 1800, the astronomer William Herschel spread sunlight into a rainbow with a prism and placed thermometers in each color. Red warmed the thermometer more than violet. Then he tried the dark space just beyond the red, where no color was visible. That thermometer warmed the most of all. He had found invisible light that carried heat: infrared.

Radiation is the only way heat can cross empty space. Conduction and convection both need matter. The Sun’s energy reaches Earth this way, across about 150 million kilometers of nearly empty space. Dark, rough surfaces absorb radiation well. Shiny surfaces reflect it. That is why a black car seat gets hotter in the sun than a white one. It is also why a foil blanket keeps a runner warm.

A hot chocolate on a January morning in Chicago cools fast. Heat leaves the cup in all three ways. It conducts through the cup walls into the air and your hand. Rising warm air and steam carry it away by convection. And the cup’s warm surface radiates infrared into the room. A good container fights all three at once, and the same design keeps a cold drink cold.

To slow conduction, surround the drink with an insulator: foam, cork, layers of paper, or a wall with a gap of still air. To stop convection, put on a lid. Then warm air cannot rise away and carry heat with it. To reduce radiation, use a shiny inner surface that reflects infrared back toward the drink. A vacuum flask does all three. It has two shiny walls with almost no air between them, plus a tight stopper.

Testing is where the science happens. Fill several containers with water at the same starting temperature. Put a thermometer in each. Record the temperature every five minutes for an hour. Keep everything else the same: the same amount of water, the same room, the same starting temperature. Then compare. The container whose water changed the least is the best insulator.

Real designs involve trade-offs. Thick foam insulates well but is bulky. A metal vacuum flask works best but costs more and can dent. A lid slows convection but makes drinking awkward. Engineers weigh cost, weight, size and how well it works. The data from a fair test tells them which trade is worth making.

You are a machine that runs on stored energy. Every step, heartbeat and thought is powered by energy released from food. The energy is stored in the chemical bonds that hold food molecules together. When your body breaks those bonds and combines the pieces with oxygen, energy is released, and your body uses it or gives it off as heat.

Food labels measure this energy in Calories. One food Calorie is about 4,200 joules, enough to lift a small apple about four kilometers straight up. Different foods store different amounts. Fats hold about 9 Calories per gram. Carbohydrates and proteins hold about 4 Calories per gram. Water and fiber hold almost none, which is why a big salad has fewer Calories than a small handful of nuts.

Scientists first measured food energy by burning it. A calorimeter is an insulated container where a sample burns and the heat released warms a known amount of water. Measure the temperature rise, and you know the energy. Your body does something like slow, controlled burning, without the flame, and ends up with the same energy total.

Where does the energy go? Some becomes the kinetic energy of your muscles. Some builds new tissue. A lot becomes heat, which is why a room full of people warms up and why you sweat on a run. Your body runs at about 37 degrees Celsius, and food is the fuel that keeps it there on a cold day.

Gasoline, natural gas, coal, wood and the batteries in a phone all store energy. Gasoline is the fuel in most cars. When it burns with oxygen in an engine, chemical energy becomes hot gas that pushes pistons and turns the wheels. A large share of that energy becomes waste heat out the tailpipe and radiator, which is why engines need cooling.

In Illinois, electricity comes from several sources. The state has more nuclear reactors than any other. It also burns natural gas and some coal. Wind farms across the prairie and solar panels add a growing share. Each source turns stored or moving energy into electric energy that reaches a wall outlet. There, a charger turns it into chemical energy stored in a battery.

No fuel is free of trade-offs. Coal and gasoline store a lot of energy in a small space and are easy to move. But burning them releases carbon dioxide, which traps heat in the atmosphere, along with other pollution. Wind and sunlight release no carbon dioxide while making power. But they depend on the weather and need batteries or other backup. Nuclear plants make steady power without carbon dioxide. But they leave waste that must be stored safely for a very long time.

Scientists measure what each source costs, how much energy it delivers, and what it leaves behind. Citizens and lawmakers decide how to weigh those numbers. Understanding energy transfer lets you read those debates with clear eyes. Every bit of energy at the outlet came from somewhere. It changed form several times, and it left a trail of heat behind.