6.2 Work, Energy and Power

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6. Mechanical Comprehension

Work, Energy and Power

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Torque

Torque is the rotational force applied to an object. It is what makes something twist or turn around a pivot point. Torque is measured in newton-meters (N·m).

Torque = Force × Distance

$T = F \times d$

Two hands apply the same downward force to a wrench turning a bolt counterclockwise: on the short wrench the nut rotates slightly, while on the long wrench the same force produces much greater rotation, showing that a longer handle increases torque. — Torque

Torque increases as you increase the distance from the pivot point. If you want more torque without adding more force, increase the distance from the pivot. This is why a longer wrench makes a stuck bolt easier to turn. If you decrease the distance from the pivot point, you need more force to create the same amount of torque.

Example: Torque on a bolt

You apply $20$ N of force to a wrench at a distance of $0.5$ m from the bolt. How much torque do you create?

$T = F \times d$

$T = 20 \times 0.5$

$T = 10$ N·m

Answer: $10$ N·m

Work

Work is done when a force moves an object over a distance. Work is only done if there is movement. It is measured in joules (J).

Work = Force × Distance

$W = F \times d$

Sidenote

Same equation

You may notice that torque and work use the same equation. Both multiply a force by a distance, but the distances mean different things. In torque, the distance is from the pivot to where the force is applied, and torque is greatest when you push at $90°$ to the handle - nothing has to move. In work, the distance is how far the object actually moves in the direction of the force; if it doesn’t move, no work is done.

Kinetic and potential energy

Energy is the capacity to do work, measured in joules.

Kinetic energy is the energy of an object in motion.

Potential energy is stored energy an object has because of its position or condition (for example, height above the ground or a compressed spring). A moving object can have both kinetic and potential energy at the same time.

Gravitational potential energy equals weight times height: lifting a $20$ N box $3$ m off the ground stores $60$ J of potential energy, the same amount of work it took to lift it.

Kinetic energy equals $\frac{1}{2} \times mass \times speed^{2}$ , so doubling an object’s speed gives it four times the kinetic energy.

Kinetic and potential energy are forms of mechanical energy. Energy takes other forms too, and it changes from one form to another without being created or destroyed (the law of conservation of energy):

Thermal energy (heat) comes from the motion of a substance’s atoms and molecules.
Chemical energy is stored in the bonds of atoms and molecules, as in food, fuel and batteries.
Electrical energy is carried by moving electric charges, such as electrons flowing through a wire.
Radiant energy is electromagnetic energy such as light. Solar energy is the radiant energy the sun sends through the vacuum of space.
Sound energy is carried by vibrations moving through air, water or a solid.
Nuclear energy is stored in the nucleus of an atom.

A pendulum swinging between two raised positions, one on each side, through the bottom of its arc. Each raised position is labeled highest point, maximum potential energy and no kinetic energy. The bottom is labeled lowest point, maximum kinetic energy and minimum potential energy. — Pendulum: potential and kinetic energy

Power

Power is the rate at which work is done. It is measured in watts (W).

Energy is how much work can be done; power is how quickly it is done.

$P o w er = \frac{W or k}{T im e}$

$P = \frac{W}{t}$

Here $t$ is time, not torque.

Example: Work and power

How much work does it take to lift a $20$ N box $3$ m? If the lift takes $6$ seconds, how much power is used?

$W = F \times d = 20 \times 3 = 60$ J

$P = \frac{W}{t} = \frac{60}{6} = 10$ W

Answer: $60$ J of work; $10$ W of power

Pressure

Pressure is force distributed over an area. Pressure is measured in Pascals (Pa), but can also be measured in pounds per square inch (PSI).

$P r ess u r e = \frac{F or ce}{A r e a}$

$P = \frac{F}{A}$

Pressure and area

The same amount of force applied to a small area generates more pressure than when it’s applied to a large area. This is why a sharp knife cuts better than a dull one, since the force is concentrated on a smaller area.

Because fluids can move in all directions, unlike solids, they behave differently when forces are applied to them. We will focus on air and water to keep things simple.

General fluid dynamics

An unbalanced pressure difference is what makes a fluid flow: the fluid moves from the high-pressure area toward the low-pressure area. Gravity can balance a difference, which is why water at the bottom of a still tank, under more pressure than the water above it, does not flow upward.

Because of this principle, we can use fluids to move very heavy objects through pneumatics, which use pressurized gases, or hydraulics, which use pressurized liquids.

These devices work because of Pascal’s principle: pressure applied to a fluid in a closed system pushes equally in every direction. Push down on a small piston, and that same pressure pushes up on a larger piston somewhere else in the system. Since pressure equals force divided by area, a small force on a small piston creates the same pressure as a large force on a large piston. That’s how a hydraulic jack can lift a car using just your hand.

The trade-off is distance: if the large piston has $10$ times the area of the small one, you get $10$ times the force, but you must push the small piston $10$ times farther than the large piston rises. Work in equals work out.

$\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}$

A closed container of fluid connects a narrow piston on the left, pushed down by a small force, to a wide piston on the right, which is pushed up with a larger force, illustrating how a small input force on a small piston creates a greater output force on a larger piston. — Hydraulics

Example: Hydraulic force

A hydraulic lift has a small piston with an area of $2$ in² and a large piston with an area of $20$ in². If you push down on the small piston with $10$ N of force, how much force does the large piston produce?

$\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}$

$\frac{10}{2} = \frac{F _{2}}{20}$

The ratio simplifies to $5$ , so $F_{2} = 5 \times 20 = 100$ N.

Answer: $100$ N

Air pressure

Air is a fluid too, so it follows the same rules as liquids. Fast-moving air has lower pressure than slow-moving air. Differences in air pressure help airplanes take flight. When air moves over the wing of an airplane, the shape and angle of the wing create lower air pressure at the top of the wing and higher pressure underneath. This pressure difference generates force upwards and creates lift.

Water pressure

Water pressure increases with depth. If you were to puncture a $5$ gallon water container near the top and near the bottom, the water at the bottom hole is under more pressure, so it shoots out faster and with more force. How far a jet travels before it lands also depends on how high its hole is: a jet from a hole near the bottom of a tank standing on the ground has only a short way to fall, so the lowest hole does not always land farthest.

A tank of water standing on the ground with three holes in its side. Water leaves the lowest hole fastest and the top hole slowest. The middle jet lands farthest from the tank, the top jet a little short of it, and the bottom jet closest. — Water jets at different depths

Torque

Rotational force: $T = F \times d$ , measured in N·m
Increasing distance from pivot increases torque without more force (longer wrench = easier turn)
Less distance requires more force for same torque

Work

Force moving an object over distance: $W = F \times d$ , measured in joules
Only counts if movement occurs
Shares formula with torque, but distance means different things:
- Torque: distance from pivot to applied force (no movement needed)
- Work: actual distance object moves in force’s direction

Kinetic & potential energy

Energy = capacity to do work (joules)
Kinetic energy (motion): $K E = \frac{1}{2} m v^{2}$ — doubling speed quadruples KE
Potential energy (stored, position-based): gravitational PE = weight × height
Object can have both simultaneously (e.g., swinging pendulum converts between the two)

Power

Rate of doing work: $P = \frac{W}{t}$ , measured in watts
Energy = how much work; power = how fast it’s done
Note: $t$ = time (not torque)

Pressure & fluid dynamics

$P = \frac{F}{A}$ , measured in Pascals or PSI
Same force over smaller area = greater pressure (why sharp knives cut better)
An unbalanced pressure difference drives flow from high-pressure toward low-pressure areas (in a still tank, gravity balances the higher pressure at the bottom)
Pascal’s principle: enclosed fluid transmits pressure equally in all directions
- Small piston force ÷ small area = large piston force ÷ large area: $\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}$
- Trade-off: smaller piston must travel farther than larger piston moves (work in = work out)
Applications: hydraulics (liquids), pneumatics (gases)

Air and water pressure

Air is a fluid; faster-moving air has lower pressure than slower-moving air
- Explains airplane lift: wing shape creates low pressure above, high pressure below
Water pressure increases with depth
- Deeper punctures in a container expel water faster and with more force, due to higher pressure

Next | 6.3 Simple Machines

Work, Energy and Power

Torque

Torque is the rotational force applied to an object. It is what makes something twist or turn around a pivot point. Torque is measured in newton-meters (N·m).

Torque = Force × Distance

$T = F \times d$

Example: Torque on a bolt

You apply $20$ N of force to a wrench at a distance of $0.5$ m from the bolt. How much torque do you create?

$T = F \times d$

$T = 20 \times 0.5$

$T = 10$ N·m

Answer: $10$ N·m

Work

Work is done when a force moves an object over a distance. Work is only done if there is movement. It is measured in joules (J).

Work = Force × Distance

$W = F \times d$

Sidenote

Same equation

Kinetic and potential energy

Energy is the capacity to do work, measured in joules.

Kinetic energy is the energy of an object in motion.

Gravitational potential energy equals weight times height: lifting a $20$ N box $3$ m off the ground stores $60$ J of potential energy, the same amount of work it took to lift it.

Kinetic energy equals $\frac{1}{2} \times mass \times speed^{2}$ , so doubling an object’s speed gives it four times the kinetic energy.

Thermal energy (heat) comes from the motion of a substance’s atoms and molecules.
Chemical energy is stored in the bonds of atoms and molecules, as in food, fuel and batteries.
Electrical energy is carried by moving electric charges, such as electrons flowing through a wire.
Radiant energy is electromagnetic energy such as light. Solar energy is the radiant energy the sun sends through the vacuum of space.
Sound energy is carried by vibrations moving through air, water or a solid.
Nuclear energy is stored in the nucleus of an atom.

Power

Power is the rate at which work is done. It is measured in watts (W).

Energy is how much work can be done; power is how quickly it is done.

$P o w er = \frac{W or k}{T im e}$

$P = \frac{W}{t}$

Here $t$ is time, not torque.

Example: Work and power

How much work does it take to lift a $20$ N box $3$ m? If the lift takes $6$ seconds, how much power is used?

$W = F \times d = 20 \times 3 = 60$ J

$P = \frac{W}{t} = \frac{60}{6} = 10$ W

Answer: $60$ J of work; $10$ W of power

Pressure

Pressure is force distributed over an area. Pressure is measured in Pascals (Pa), but can also be measured in pounds per square inch (PSI).

$P r ess u r e = \frac{F or ce}{A r e a}$

$P = \frac{F}{A}$

Pressure and area

Because fluids can move in all directions, unlike solids, they behave differently when forces are applied to them. We will focus on air and water to keep things simple.

General fluid dynamics

Because of this principle, we can use fluids to move very heavy objects through pneumatics, which use pressurized gases, or hydraulics, which use pressurized liquids.

$\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}$

Example: Hydraulic force

A hydraulic lift has a small piston with an area of $2$ in² and a large piston with an area of $20$ in². If you push down on the small piston with $10$ N of force, how much force does the large piston produce?

$\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}$

$\frac{10}{2} = \frac{F _{2}}{20}$

The ratio simplifies to $5$ , so $F_{2} = 5 \times 20 = 100$ N.

Answer: $100$ N

Air pressure

Water pressure

Achievable ASVAB

6. Mechanical Comprehension

Work, Energy and Power

9 min read

Font

Discuss

Feedback

Torque

Torque is the rotational force applied to an object. It is what makes something twist or turn around a pivot point. Torque is measured in newton-meters (N·m).

Torque = Force × Distance

$T = F \times d$

Example: Torque on a bolt

You apply $20$ N of force to a wrench at a distance of $0.5$ m from the bolt. How much torque do you create?

$T = F \times d$

$T = 20 \times 0.5$

$T = 10$ N·m

Answer: $10$ N·m

Work

Work is done when a force moves an object over a distance. Work is only done if there is movement. It is measured in joules (J).

Work = Force × Distance

$W = F \times d$

Sidenote

Same equation

Kinetic and potential energy

Energy is the capacity to do work, measured in joules.

Kinetic energy is the energy of an object in motion.

Gravitational potential energy equals weight times height: lifting a $20$ N box $3$ m off the ground stores $60$ J of potential energy, the same amount of work it took to lift it.

Kinetic energy equals $\frac{1}{2} \times mass \times speed^{2}$ , so doubling an object’s speed gives it four times the kinetic energy.

Thermal energy (heat) comes from the motion of a substance’s atoms and molecules.
Chemical energy is stored in the bonds of atoms and molecules, as in food, fuel and batteries.
Electrical energy is carried by moving electric charges, such as electrons flowing through a wire.
Radiant energy is electromagnetic energy such as light. Solar energy is the radiant energy the sun sends through the vacuum of space.
Sound energy is carried by vibrations moving through air, water or a solid.
Nuclear energy is stored in the nucleus of an atom.

Power

Power is the rate at which work is done. It is measured in watts (W).

Energy is how much work can be done; power is how quickly it is done.

$P o w er = \frac{W or k}{T im e}$

$P = \frac{W}{t}$

Here $t$ is time, not torque.

Example: Work and power

How much work does it take to lift a $20$ N box $3$ m? If the lift takes $6$ seconds, how much power is used?

$W = F \times d = 20 \times 3 = 60$ J

$P = \frac{W}{t} = \frac{60}{6} = 10$ W

Answer: $60$ J of work; $10$ W of power

Pressure

Pressure is force distributed over an area. Pressure is measured in Pascals (Pa), but can also be measured in pounds per square inch (PSI).

$P r ess u r e = \frac{F or ce}{A r e a}$

$P = \frac{F}{A}$

Pressure and area

Because fluids can move in all directions, unlike solids, they behave differently when forces are applied to them. We will focus on air and water to keep things simple.

General fluid dynamics

Because of this principle, we can use fluids to move very heavy objects through pneumatics, which use pressurized gases, or hydraulics, which use pressurized liquids.

$\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}$

Example: Hydraulic force

A hydraulic lift has a small piston with an area of $2$ in² and a large piston with an area of $20$ in². If you push down on the small piston with $10$ N of force, how much force does the large piston produce?

$\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}$

$\frac{10}{2} = \frac{F _{2}}{20}$

The ratio simplifies to $5$ , so $F_{2} = 5 \times 20 = 100$ N.

Answer: $100$ N

Air pressure

Water pressure

Torque

Rotational force: $T = F \times d$ , measured in N·m
Increasing distance from pivot increases torque without more force (longer wrench = easier turn)
Less distance requires more force for same torque

Work

Force moving an object over distance: $W = F \times d$ , measured in joules
Only counts if movement occurs
Shares formula with torque, but distance means different things:
- Torque: distance from pivot to applied force (no movement needed)
- Work: actual distance object moves in force’s direction

Kinetic & potential energy

Energy = capacity to do work (joules)
Kinetic energy (motion): $K E = \frac{1}{2} m v^{2}$ — doubling speed quadruples KE
Potential energy (stored, position-based): gravitational PE = weight × height
Object can have both simultaneously (e.g., swinging pendulum converts between the two)

Power

Rate of doing work: $P = \frac{W}{t}$ , measured in watts
Energy = how much work; power = how fast it’s done
Note: $t$ = time (not torque)

Pressure & fluid dynamics

$P = \frac{F}{A}$ , measured in Pascals or PSI
Same force over smaller area = greater pressure (why sharp knives cut better)
An unbalanced pressure difference drives flow from high-pressure toward low-pressure areas (in a still tank, gravity balances the higher pressure at the bottom)
Pascal’s principle: enclosed fluid transmits pressure equally in all directions
- Small piston force ÷ small area = large piston force ÷ large area: $\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}$
- Trade-off: smaller piston must travel farther than larger piston moves (work in = work out)
Applications: hydraulics (liquids), pneumatics (gases)

Air and water pressure

Air is a fluid; faster-moving air has lower pressure than slower-moving air
- Explains airplane lift: wing shape creates low pressure above, high pressure below
Water pressure increases with depth
- Deeper punctures in a container expel water faster and with more force, due to higher pressure

Next | 6.3 Simple Machines

Work, Energy and Power

Torque

Torque is the rotational force applied to an object. It is what makes something twist or turn around a pivot point. Torque is measured in newton-meters (N·m).

Torque = Force × Distance

$T = F \times d$

Example: Torque on a bolt

You apply $20$ N of force to a wrench at a distance of $0.5$ m from the bolt. How much torque do you create?

$T = F \times d$

$T = 20 \times 0.5$

$T = 10$ N·m

Answer: $10$ N·m

Work

Work is done when a force moves an object over a distance. Work is only done if there is movement. It is measured in joules (J).

Work = Force × Distance

$W = F \times d$

Sidenote

Same equation

Kinetic and potential energy

Energy is the capacity to do work, measured in joules.

Kinetic energy is the energy of an object in motion.

Gravitational potential energy equals weight times height: lifting a $20$ N box $3$ m off the ground stores $60$ J of potential energy, the same amount of work it took to lift it.

Kinetic energy equals $\frac{1}{2} \times mass \times speed^{2}$ , so doubling an object’s speed gives it four times the kinetic energy.

Thermal energy (heat) comes from the motion of a substance’s atoms and molecules.
Chemical energy is stored in the bonds of atoms and molecules, as in food, fuel and batteries.
Electrical energy is carried by moving electric charges, such as electrons flowing through a wire.
Radiant energy is electromagnetic energy such as light. Solar energy is the radiant energy the sun sends through the vacuum of space.
Sound energy is carried by vibrations moving through air, water or a solid.
Nuclear energy is stored in the nucleus of an atom.

Power

Power is the rate at which work is done. It is measured in watts (W).

Energy is how much work can be done; power is how quickly it is done.

$P o w er = \frac{W or k}{T im e}$

$P = \frac{W}{t}$

Here $t$ is time, not torque.

Example: Work and power

How much work does it take to lift a $20$ N box $3$ m? If the lift takes $6$ seconds, how much power is used?

$W = F \times d = 20 \times 3 = 60$ J

$P = \frac{W}{t} = \frac{60}{6} = 10$ W

Answer: $60$ J of work; $10$ W of power

Pressure

Pressure is force distributed over an area. Pressure is measured in Pascals (Pa), but can also be measured in pounds per square inch (PSI).

$P r ess u r e = \frac{F or ce}{A r e a}$

$P = \frac{F}{A}$

Pressure and area

Because fluids can move in all directions, unlike solids, they behave differently when forces are applied to them. We will focus on air and water to keep things simple.

General fluid dynamics

Because of this principle, we can use fluids to move very heavy objects through pneumatics, which use pressurized gases, or hydraulics, which use pressurized liquids.

$\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}$

Example: Hydraulic force

A hydraulic lift has a small piston with an area of $2$ in² and a large piston with an area of $20$ in². If you push down on the small piston with $10$ N of force, how much force does the large piston produce?

$\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}$

$\frac{10}{2} = \frac{F _{2}}{20}$

The ratio simplifies to $5$ , so $F_{2} = 5 \times 20 = 100$ N.

Answer: $100$ N