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Work is force times the distance moved along it; it is the energy transferred, in joules, and no movement means no work.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
By the end of this lesson you will be able to find the work a force does, including when it does none, and link work to energy transferred.
You can find forces, including weights, and you know that energy comes in different forms and is measured in joules. This lesson connects forces to energy: when a force moves something, it transfers energy, and the amount is called work.
| Term | What it means |
|---|---|
| Work | Energy transferred by a force moving an object, $W = Fd$. |
| Joule | The unit of work and energy, one newton times one meter, J. |
| Kilojoule | A thousand joules, kJ. |
| Energy transferred | Energy moved from one object or form to another. |
| Potential energy | Energy stored by an object's position, such as its height. |
| Distance along the force | How far the object moves in the direction the force points. |
When a force moves an object in the direction of the force, it does work:
$$W = Fd.$$
Another way: picture
Picture carrying a backpack up a flight of stairs. Your legs push you and the backpack upward, and you rise several meters: that is work, and it leaves you breathing hard. Standing still holding the same backpack tires your arms, but the backpack does not move, so no work is done on it.
Another way: steps
A joule is a newton times a meter. A $50$ N push moving a cart $4$ m does $50 \times 4 = 200$ J of work. The unit, like the newton meter of torque, multiplies a force by a distance.
The joule is small. Lifting an apple one meter takes about one joule. Climbing a flight of stairs takes a few thousand, and a car's engine may do millions on a single trip.
When you do work on an object, you give it energy. Lifting a box onto a shelf transfers energy into the box's height; you could get it back by letting the box fall. Pushing a cart against friction transfers energy into heat in the wheels and floor.
Energy is never used up; it moves from one place or form to another. Work measures how much energy a force moves.
A weightlifter holding a heavy bar still above their head is working hard, but the bar does not move, so no work is done on it. The lifter's muscles use energy internally, which is why they tire, but none is transferred to the bar.
Pushing against a wall that does not budge is the same. You get tired, but in the physics sense you do no work on the wall.
Carrying a box across a level room, you hold it up with an upward force, but the box moves sideways. The upward force is at right angles to the motion, so it does no work on the box.
Only the part of a force pointing along the motion does work. That is why a suitcase on wheels is easier: you pull it along, in the direction it moves, instead of carrying its whole weight.
To lift an object at a steady speed, you must push up with a force equal to its weight, $mg$. Lifting it through a height $h$ does work $mgh$.
Only the height matters, not the path. Climbing a gentle ramp or a steep ladder to the same height takes the same work against gravity, though the ramp takes less force over a longer distance.
Checking an answer. Work is zero if nothing moves or if the force is at right angles to the motion. Doubling either the force or the distance must double the work.
Work is defined as force times the distance moved along the force, because that is exactly the amount of energy the force transfers. Experiments show that the energy gained by an object, as speed or height, matches the work done on it.
A force that does not move its object along its own direction cannot transfer energy to it, which is why such forces do no work, however large they are.
A ramp lets you lift a heavy object with less force, but over a longer distance. Pushing a wheelchair up a ramp takes a smaller force than lifting it straight up, but the ramp is longer than the height.
Ignoring friction, the work is the same either way: force times distance comes out equal. Ramps save force, not work. That is why the Americans with Disabilities Act requires long, gentle ramps: a small force is easier to supply.
Athletes do work on balls, bars and their own bodies. A pitcher does work on a baseball over the short distance the hand moves while throwing. A pole vaulter does work lifting their body over the bar.
Weightlifters measure their training partly by work: the weight lifted times the height, times the number of lifts. More reps or heavier weights mean more energy transferred and more training.
When you push a box across a rough floor at a steady speed, your push does work, but the box does not speed up or rise. The energy goes into heat: the box and floor warm up slightly where they rub.
Rubbing your hands together on a cold day is the same idea. The work you do against friction turns into warmth you can feel.
The most common error is to count work when nothing moves. Holding, leaning and pushing on something fixed do no work on it. Another is to use mass in kilograms instead of weight in newtons when lifting.
A third is to use the wrong distance, such as the length of a staircase instead of its height, when finding the work against gravity.
A few benchmarks help. Lifting a textbook onto a desk takes about ten joules. Climbing one floor of a building takes a few thousand. Pushing a stalled car along a street for a block takes tens of thousands.
An answer far outside these ranges usually means a unit slip, such as a mass used as a weight or centimeters used as meters.
The energy your body uses to do work comes from food. Food labels in the United States list Calories, each about four thousand one hundred eighty-four joules.
Climbing ten flights of stairs does about thirty thousand joules of work against gravity, but your body burns several times that, because muscles turn only about a quarter of food energy into work and the rest into heat.
Machines do work for us. An elevator motor does work lifting passengers; a car engine does work pushing the car along; a crane does work raising steel beams.
Engineers measure machines by how much work they can do and how quickly. The next lesson looks at how fast work is done, which is called power.
Sometimes a force points against the motion. Friction on a sliding box pushes backward while the box moves forward, and a catcher's mitt pushes back on a ball while it moves forward into the glove. These forces take energy away from the moving object instead of giving it energy.
Physicists call this negative work. It is still force times distance, but it removes energy, which is why the box slows and the ball stops. In this course, most problems ask for the work done by a push or a lift, which is positive, but it helps to know that a force against the motion drains energy away.
When an object falls, gravity pulls it down and it moves down, so gravity does work on it. A ball dropped from a height gains energy of motion equal to the work gravity does, its weight times the height it falls.
That is why lifting and falling are partners. The work you do lifting a book onto a high shelf is stored, and if the book falls, gravity does the same amount of work returning that energy as motion. Hydroelectric dams use exactly this, letting falling water turn turbines.
A classroom spring scale measures the force needed to pull a block along a table. Multiplying that reading by the distance the block moves gives the work done. Repeating with different distances shows that the work grows in step with the distance.
Every spring, college football players hoping to join the NFL attend the Scouting Combine in Indianapolis. One test is the bench press: lifting a 225-pound bar, about one hundred two kilograms, as many times as possible.
Each rep lifts the bar's weight, about a thousand newtons, through roughly forty centimeters, about four hundred joules of work. A strong offensive lineman who completes thirty reps does about twelve kilojoules of work on the bar. Scouts use the rep count to compare players' strength and endurance, and the physics shows why reps add up: every lift transfers the same energy again. Lowering the bar does no work on it, since gravity pulls it down while the athlete only slows it.
Moving into a new apartment means carrying boxes, furniture and appliances, often up flights of stairs. The work done against gravity depends only on each item's weight and how high it goes, not on how long the staircase is.
Carrying a thirty-kilogram dresser up three floors, about ten meters, takes nearly three thousand joules of work. Moving companies use ramps, dollies and freight elevators to reduce the force their workers must supply, and many American cities require elevators in taller buildings so that no one has to do that work by hand.
In everyday speech, anything tiring is work. In physics, work needs a force and a movement along that force. Holding a heavy box still, or pushing a wall that does not move, may exhaust you, but it does no work on the box or the wall.
A related error is to count the work of carrying something level across a room. The upward force holding it is at right angles to the motion, so it transfers no energy to the object.
A shopper pushes a cart $15$ m with a steady $40$ N force. Write the formula.
$W = Fd$
Force times distance.
Substitute the values.
$W = 40 \times 15$
Newtons times meters.
Evaluate the work.
$W = 600\ \text{J}$
Energy transferred.
Find the work over $30$ m.
$W = 40 \times 30 = 1200\ \text{J}$
Twice the distance.
Say where the energy goes at steady speed.
$\text{heat from friction}$
The cart does not speed up.
A $6$ kg bag of groceries is lifted $1.5$ m onto a counter. Find its weight.
$W_t = 6 \times 9.8 = 58.8\ \text{N}$
The lifting force.
Find the work.
$W = 58.8 \times 1.5 = 88.2\ \text{J}$
Weight times height.
The bag is carried $5$ m across the kitchen at the same height. Find the work by the upward force.
$W = 0$
At right angles to the motion.
It is lifted another $0.5$ m to a shelf. Find the extra work.
$W = 58.8 \times 0.5 = 29.4\ \text{J}$
Only height counts.
Find the total work against gravity.
$88.2 + 29.4 = 117.6\ \text{J}$
Total height $2$ m.
Check with the total height.
$58.8 \times 2 = 117.6\ \text{J}$
The same.
A $50$ kg crate must go onto a truck bed $1.2$ m high. Find the work lifting it straight up.
$W = 50 \times 9.8 \times 1.2 = 588\ \text{J}$
Weight times height.
A smooth ramp $4$ m long is used instead. Write the work rule.
$F \times 4 = 588$
Same work, no friction.
Find the push needed on the ramp.
$F = \dfrac{588}{4} = 147\ \text{N}$
Much less than the weight.
Compare with the weight.
$490\ \text{N}$
Lifting takes more force.
Find the push on a $6$ m ramp.
$F = \dfrac{588}{6} = 98\ \text{N}$
Longer, gentler.
Describe the trade-off.
$\text{less force, more distance}$
Same work.
Say what friction would change.
$\text{more work needed}$
Some energy becomes heat.
Write the formula.
$W = Fd$
Force times distance.
Substitute the values.
$W = 25 \times 6$
Newtons times meters.
Evaluate the work.
A student pushes a cart with a steady $200$ N force, moving it $1.5$ m in the direction of the push. How much work does the push do, in J?
Complete the worked solution: a $45$ kg student climbs $24$ stairs, each $0.2$ m high. With $g = 9.8$ N/kg, find the total height climbed in m, the student's weight in N, and the work done against gravity in J.
Find the total height.
$h = n \times s =$ h
Steps times step height.
Find the weight.
$W_t = mg =$ w
Earth's pull.
Find the work.
$W = W_t \times h =$ e
Weight times height.
Note where the energy goes.
$\text{stored as height, plus body heat}$
Muscles are not perfectly efficient.
Match each situation or term to what it means for work.
| force times distance moved along the force | a force of one newton acting over one meter | no work, because the box does not move | no work by the upward holding force, which is sideways to the motion | |
|---|---|---|---|---|
| work | ||||
| one joule | ||||
| holding a heavy box still | ||||
| carrying a box across a level room |
A stock clerk lifts $12$ kg boxes straight up onto a shelf $1.25$ m high. With $g = 9.8$ N/kg, fill in one box's weight in N, the work to lift one box in J, and the work to lift three boxes in J.
| value | |
|---|---|
| weight of one box (N) | |
| work for one box (J) | |
| work for three boxes (J) |
A $0.5$ kg object is lifted straight up at a steady speed. With $g = 9.8$ N/kg, write the work done lifting it, in J, as a function of the height $h$ in meters.
Answer:
A tractor does $5000$ J of work pulling a sled with a steady $250$ N force along its motion. How far does the sled move, in m?
Answer: m
At the NFL Scouting Combine, prospects bench-press a 225-pound bar, about $102$ kg, as many times as they can. Each rep lifts the bar about $0.4$ m. If a linebacker completes $22$ reps, how much work does he do lifting the bar, in kJ? Use $g = 9.8$ N/kg.
Answer: kJ
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A $10$ kg object is lifted straight up at a steady speed. With $g = 9.8$ N/kg, write the work done lifting it, in J, as a function of the height $h$ in meters.
Answer:
You can find work done. Explain to someone why holding a heavy box still does no work on it, even though it is tiring.
28. Your turn: a $25$ N force pushes a box $6$ m along the floor. How much work does it do?, step 3
$W = 150\ \text{J}$
Joules.