20.1 Force, Motion, Simple Machines & Newton's Laws

Overview & Exam Relevance

Competency 007 of the TExES Core Subjects EC-6 Science exam (Subject Exam 904) assesses your pedagogical and content mastery of force, motion, kinematics, and simple machines. In the elementary classroom, physical science is rooted in everyday sensory experiences—pushing a swing, watching a ball roll down an incline, riding a bicycle, or lifting a heavy storage bin using a ramp. The Texas Essential Knowledge and Skills (TEKS) build these ideas gradually. In the primary grades, students describe how pushes and pulls change an object's position and motion. In the middle elementary grades they investigate forces that act in contact or at a distance, such as magnetism, gravity, and friction. By Grade 5 they explain how equal and unequal forces produce patterns of motion and design simple experimental investigations, such as a car on a ramp or a balloon rocket on a string. Simple machines, motion graphs, and Newton's laws extend these ideas to the teacher-level content the 391 expects.

On the TExES 391 exam, questions frequently test your capacity to identify and remediate pervasive student misconceptions. Chief among these are:

1. The Aristotelian Motion Misconception: Students frequently believe that an object requires a continuous, sustained force to remain in motion, assuming that an object naturally "runs out of force" and stops on its own. In reality, according to Newtonian mechanics, an object in motion maintains constant velocity indefinitely unless an unbalanced external force (such as friction or air resistance) acts to decelerate it.
2. The Heavy Fall Fallacy: Novice learners often believe that heavier objects fall faster than lighter objects due to greater gravitational pull. Candidates must understand that while gravitational force is greater on larger masses ($W = mg$), the greater mass also possesses proportionally greater inertia, causing all objects to accelerate at the exact same rate in a vacuum ($g \approx 9.8\text{ m/s}^2$).
3. Action-Reaction Cancellation: Students commonly assume that because Newton's third law action-reaction pairs are equal in magnitude and opposite in direction, they must cancel each other out to produce zero net force. Candidates must know that action and reaction forces act on two entirely separate bodies, meaning they never cancel each other out on a single object.
4. The "Free Energy" Machine Myth: Children often assume that simple machines reduce the total amount of "work" or physical effort required to lift a load. Candidates must emphasize that simple machines conserve work ($W = F \times d$); they reduce the required effort force only by proportionally increasing the displacement distance.

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Force Fundamentals: Contact vs. Non-Contact & Equilibrium

A force is defined in classical Newtonian physics as an interaction that, when unopposed, changes the motion of an object. It is a vector quantity, possessing both magnitude (measured in Newtons, $1\text{ N} = 1\text{ kg}\cdot\text{m/s}^2$) and a specific spatial direction. Forces in nature fall into two distinct physical classifications:

PHYSICAL FORCES IN ELEMENTARY SCIENCE
│
├── Contact Forces (Direct Physical Interface)
│   ├── Applied Force (F_app) ──► Direct physical push or pull exerted on an object
│   ├── Friction Force (F_f) ───► Opposes relative sliding motion between contacting surfaces
│   ├── Normal Force (F_N) ─────► Perpendicular support force exerted by a stable surface
│   ├── Tension Force (F_T) ────► Pulling force transmitted axially through a string, rope, or cable
│   └── Elastic/Spring Force ───► Restoring force exerted by deformed material (Hooke's Law: F = -kx)
│
└── Non-Contact / Field Forces (Action-at-a-Distance)
    ├── Gravitational Force ────► Universal mutual attraction between masses (W = mg)
    ├── Magnetic Force ─────────► Dipole attraction/repulsion between magnetic poles or moving charges
    └── Electrostatic Force ────► Coulombic attraction/repulsion between stationary electric charges

Contact Forces

• Applied Force ($F_{\text{app}}$): A force applied directly to an object by a person, another object, or an external mechanism (e.g., a student pushing a wheeled cart across a tile floor).
• Friction ($F_f$): The contact resistance exerted by a surface when an object moves or attempts to move across it. Friction always acts in the direction opposite to relative motion. Elementary science examines three primary variants:
  • Static Friction: The resistive force that prevents stationary objects from starting to move when an external force is applied. It adjusts to balance the applied force up to a maximum threshold ($f_s \le \mu_s F_N$).
  • Kinetic (Sliding) Friction: The constant resistive force acting between surfaces in relative sliding contact ($f_k = \mu_k F_N$), which is usually lower than maximum static friction.
  • Rolling Friction and Fluid Drag: Rolling friction occurs when round objects roll over a surface (substantially lower than sliding friction, which is why wheels provide mechanical efficiency). Fluid friction (air resistance or hydrodynamic drag) opposes bodies moving through liquid or gas media, increasing dramatically with speed and surface cross-sectional area.
• Normal Force ($F_N$): The perpendicular contact force exerted by a surface upon an object resting on it. When a book rests on a horizontal table, gravity pulls downward with force $mg$, and the table's microscopic molecular bonds compress slightly, pushing vertically upward with equal magnitude $F_N$ to support the book.
• Tension Force ($F_T$): The pulling force transmitted through an elongated flexible connector, such as a rope, string, or cable, acting uniformly along its length away from the attached body.

Non-Contact (Field) Forces

• Gravitational Force ($F_g$): The attractive force exerted between any two masses in the universe. On Earth, gravity accelerates unsupported falling objects toward the planet's center at $g \approx 9.8\text{ m/s}^2$.
  • Mass vs. Weight: Mass is the fundamental, scalar measure of the amount of matter within an object, measured in kilograms ($\text{kg}$) or grams ($\text{g}$) using a balance. Mass remains completely unchanged regardless of location. Weight is the vector gravitational force acting upon that mass ($W = mg$), measured in Newtons ($\text{N}$) using a calibrated spring scale. An astronaut with a mass of $60\text{ kg}$ weighs $\approx 588\text{ N}$ on Earth, but weighs only $\approx 98\text{ N}$ on the Moon due to lunar gravity being one-sixth of Earth's, even though their mass remains exactly $60\text{ kg}$.
• Magnetic Force: The non-contact force produced by moving electrical charges and intrinsic magnetic moments. Magnetic fields have North and South poles: like poles repel (N-N, S-S), and opposite poles attract (N-S).
• Electrostatic Force: The attractive or repulsive force governed by Coulomb's Law between static electric charges: like charges repel (+ and +, or - and -), while opposite charges attract (+ and -).

Balanced vs. Unbalanced Forces, Net Force & Equilibrium

The vector sum of all individual forces acting simultaneously on a body is the net force ($\Sigma F$ or $F_{\text{net}}$).

• Balanced Forces ($F_{\text{net}} = 0$): When all opposing forces have equal magnitudes and opposite directions, they completely cancel each other out. The object is in a state of equilibrium and experiences zero acceleration ($a = 0$). The object either remains permanently at rest (static equilibrium) or moves along a perfectly straight path at an unchanging, constant velocity (dynamic equilibrium).
• Unbalanced Forces ($F_{\text{net}} \ne 0$): When opposing forces are unequal, a non-zero net force remains. An unbalanced force always produces an acceleration ($a \ne 0$), causing the object to speed up, slow down, or change its direction of travel.
• Free-Body Diagrams (FBD): In physics instruction, teachers construct free-body diagrams to visualize forces. An object is represented as a central box or point, with vector arrows pointing outwards in the direction of each applied force, where arrow length is strictly proportional to force magnitude.

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Kinematics in Elementary Science: Position, Velocity & Acceleration

Kinematics is the branch of classical mechanics describing the motion of points, bodies, and systems without considering the forces that cause them to move.

Reference Frames, Distance & Displacement

• Frame of Reference (Reference Point): Motion is entirely relative. An object is in motion only if its position changes relative to a designated stationary reference point. For example, a student seated on a moving school bus is stationary relative to their seatmate, but in rapid motion relative to a pedestrian standing on the sidewalk.
• Distance vs. Displacement:
  • Distance ($d$): A scalar quantity representing the total length of the physical path traversed by an object, regardless of heading (e.g., walking 400 meters around a circular track).
  • Displacement ($\Delta x$): A vector quantity representing the straight-line distance and compass direction from the initial starting position to the final terminal position ($\Delta x = x_f - x_i$). A runner who completes a full 400-meter lap on a track has traversed a distance of $400\text{ m}$, but their displacement is exactly $0\text{ m}$ because they returned to their starting point.

Speed, Velocity & Acceleration

• Speed ($s$): The scalar rate at which an object covers distance over time:

$s = \frac{d}{t}$

• Velocity ($v$): The vector rate of change of position, requiring both speed magnitude and a directional heading (e.g., $15\text{ m/s}$ due East):

$v = \frac{\Delta x}{\Delta t}$

• Acceleration ($a$): The vector rate of change of velocity over time:

$a = \frac{v_f - v_i}{\Delta t} = \frac{\Delta v}{\Delta t}$

Critical Concept: In elementary science, students frequently equate acceleration solely with "speeding up." On the TExES exam, you must remember that acceleration occurs whenever velocity changes in any way:

1. Increasing speed (positive acceleration along the vector of motion).
2. Decreasing speed (deceleration or negative acceleration opposing the vector of motion).
3. Changing direction at a constant numerical speed (such as a car navigating a circular roundabout at an unvarying $20\text{ mph}$). Because velocity is a vector, turning a corner changes direction, which mathematically constitutes an acceleration (centripetal acceleration toward the curve center).

Interpreting Motion Graphs

Elementary teachers must guide upper-elementary students in reading, constructing, and interpreting graphical representations of linear motion.

DISTANCE-TIME GRAPH PATTERNS               SPEED-TIME GRAPH PATTERNS

Distance (m)                                Speed (m/s)
  │        / Constant Speed                   │
  │       /                                   │        ──────── Constant Speed (a = 0)
  │      /                                    │       /
  │  ───  Stopped / At Rest (v = 0)           │      / Uniform Acceleration
  │  /                                        │     /  (Increasing Speed)
  │ / Accelerating (Curving Up)               │    /
  └─────────────────────► Time (s)            └─────────────────────► Time (s)

• Distance-Time Graphs (Position vs. Time):
  • The slope of the line represents speed ($\text{slope} = \frac{\Delta y}{\Delta x} = \frac{\text{distance}}{\text{time}} = s$).
  • A horizontal flat line (slope = 0) indicates the object is stationary / at rest; position does not change as time elapses.
  • A straight diagonal line indicates constant, uniform speed.
  • A steep slope indicates rapid motion, whereas a gentle slope indicates slow motion.
  • A line curving upwards (parabolic increase) indicates positive acceleration (speeding up over time).
  • A downward-sloping straight line indicates the object is returning toward its origin at a constant speed.
• Speed-Time Graphs (Velocity vs. Time):
  • The slope of the line represents acceleration ($\text{slope} = \frac{\Delta y}{\Delta x} = \frac{\text{speed}}{\text{time}} = a$).
  • A horizontal flat line at zero indicates the object is at rest.
  • A horizontal flat line above zero indicates constant speed with zero acceleration ($a = 0$).
  • A straight upward diagonal line indicates constant, uniform acceleration.
  • A straight downward diagonal line indicates constant deceleration (slowing down).
  • The area beneath the curve corresponds to the total distance traveled.

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Newton's Three Laws of Motion

Sir Isaac Newton synthesized classical mechanics into three universal laws of motion that govern all macroscopic physical systems.

Newton's First Law: The Law of Inertia

An object at rest will remain at rest, and an object in uniform motion will remain in uniform motion along a straight line at constant velocity, unless acted upon by a net external, unbalanced force.

• Inertia is the intrinsic physical property of matter that resists any change in its existing state of motion. Mass is the direct quantitative measure of inertia; an object with greater mass has proportionally greater inertia, demanding a larger net force to alter its velocity.
• Elementary Misconception Remediation: When a hockey puck glides across ice and eventually stops, students assume it ran out of force. The teacher must clarify that the puck would glide forever at constant speed in a vacuum; it stops exclusively because external contact forces—ice friction and aerodynamic drag—exert an unbalanced backward force upon it.

Newton's Second Law: The Law of Force and Acceleration ($F = ma$)

The acceleration of an object is directly proportional to the net force acting upon it, occurs in the direction of the net force, and is inversely proportional to the mass of the object.

$\Sigma F = ma \quad \iff \quad a = \frac{\Sigma F}{m}$

• Direct and Inverse Proportionality:
  • Direct Proportionality: If you double the net force applied to a wagon of fixed mass, its acceleration doubles ($2F \implies 2a$).
  • Inverse Proportionality: If you double the mass of the wagon by loading it with rocks while keeping the pushing force constant, its acceleration is cut in half ($2m \implies \frac{1}{2}a$).
• Quantitative Applications on the TExES Exam:
  • Scenario: A toy car with a mass of $0.5\text{ kg}$ accelerates across a smooth track at $4.0\text{ m/s}^2$. What net force acted on the car?

$F = ma = 0.5\text{ kg} \times 4.0\text{ m/s}^2 = 2.0\text{ N}$

• Scenario: A student applies an unbalanced force of $15\text{ N}$ to push a $3.0\text{ kg}$ box. What is the resulting acceleration?

$a = \frac{F}{m} = \frac{15\text{ N}}{3.0\text{ kg}} = 5.0\text{ m/s}^2$

Newton's Third Law: The Law of Action and Reaction

Whenever one object exerts a force on a second object, the second object simultaneously exerts an equal in magnitude and opposite in direction force on the first object.

$F_{A \text{ on } B} = -F_{B \text{ on } A}$

• Action-Reaction Pairs:
  • Forces in the universe always occur in matched pairs. You cannot touch something without it touching you back with equal intensity.
  • When a swimmer kicks water backward with their feet (Action: foot pushes water backward), the water pushes the swimmer forward with equal force (Reaction: water pushes foot forward).
  • When a model rocket launches, expanding combustion gases are expelled violently downward out of the nozzle (Action: rocket pushes exhaust downward), and the exhaust gas pushes the rocket upward (Reaction: exhaust pushes rocket upward).
• Crucial Pedagogical Distinction: Why do action and reaction forces not cancel out to prevent motion? Because action and reaction forces act on two completely different objects. Canceling requires two opposing forces to act simultaneously on the exact same body. In the rocket example, one force acts on the gas, while the opposing force acts on the rocket airframe.

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The Six Simple Machines & Mechanical Advantage

Work in Classical Physics

In physical science, work ($W$) has a strict, mathematical definition. Work is performed on an object only when an applied force causes a physical displacement of that object in the direction of the applied force:

$W = F \times d$

• Work is measured in Joules ($\text{J}$), where $1\text{ J} = 1\text{ Newton} \times 1\text{ meter}$.
• Zero Work Conditions: If a student pushes with immense effort against a solid concrete wall for an hour but the wall does not move ($d = 0$), mathematically zero work has been done on the wall. Similarly, if a student carries a heavy $50\text{-N}$ backpack while walking horizontally at constant speed, the vertical lifting force exerted by their shoulders is perpendicular ($90^\circ$) to the horizontal displacement, meaning the upward lifting force performs zero work on the backpack along the horizontal axis.

Mechanical Advantage & Conservation of Work

A simple machine is a mechanical device that changes the magnitude, direction, or distance of an applied force. Crucially, machines do not reduce the total work required to accomplish a task. According to the Law of Conservation of Energy, in an ideal frictionless system:

$W_{\text{input}} = W_{\text{output}} \implies F_{\text{effort}} \times d_{\text{effort}} = F_{\text{resistance}} \times d_{\text{resistance}}$

• Ideal Mechanical Advantage (IMA): The factor by which a machine multiplies input effort force:

$\text{MA} = \frac{F_{\text{resistance}}}{F_{\text{effort}}} = \frac{d_{\text{effort}}}{d_{\text{resistance}}}$

• Simple machines allow a human to exert a substantially smaller effort force over a proportionally greater distance. You do not "save work"; rather, you make the work physically manageable by trading distance for force.

THE WORK TRADE-OFF IN SIMPLE MACHINES

Without Machine:  [ Large Force (F) ] × [ Small Distance (d) ] = Total Work (W)
With Machine:     [ Small Force (f) ] × [ Large Distance (D) ] = Total Work (W)

The Six Classical Simple Machines

THE SIX SIMPLE MACHINES
│
├── Lever ──────────► Rigid beam pivoting on a fixed fulcrum (1st, 2nd, 3rd class)
├── Wheel & Axle ───► Two concentric cylinders of different radii rotating in unison
├── Pulley ─────────► Grooved wheel supporting a flexible cable (fixed, movable, compound)
├── Inclined Plane ─► Slanted flat ramp connecting lower elevation to higher elevation
├── Wedge ──────────► Portable double-inclined plane driven between objects to split or cut
└── Screw ──────────► Inclined plane wrapped helically around a central cylinder

1. The Lever

A rigid beam or bar that pivots around a fixed point of rotation called a fulcrum. Levers are categorized into three distinct classes based on the relative physical positions of the Fulcrum (F), Load/Resistance (L), and Effort Force (E). Memorize the universal mnemonic: FLE 1-2-3 (the letter in the middle identifies the class):

• First-Class Lever (Fulcrum in the Middle: E - F - L):
  • Characteristics: The fulcrum sits between the applied effort force and the load. It always reverses the direction of the force (pushing downward lifts the load upward). If the fulcrum is positioned closer to the load, it multiplies force ($\text{MA} > 1$); if closer to the effort, it multiplies distance and speed ($\text{MA} < 1$).
  • Examples: Seesaw, crowbar, scissors (double first-class lever), claw hammer pulling a nail, pliers.
• Second-Class Lever (Load in the Middle: F - L - E):
  • Characteristics: The resistance/load is located between the fulcrum and the effort force. The effort and load move in the exact same direction. Because the effort arm is always longer than the load arm, the mechanical advantage is always greater than one ($\text{MA} > 1$). It always multiplies force at the expense of distance.
  • Examples: Wheelbarrow (wheel is fulcrum, basin load is middle, handles are effort), nutcracker, bottle opener, paper cutter.
• Third-Class Lever (Effort in the Middle: F - E - L):
  • Characteristics: The effort force is applied between the fulcrum and the load. Both effort and load move in the same direction. The effort arm is shorter than the load arm, meaning the mechanical advantage is always less than one ($\text{MA} < 1$).
  • Functional Advantage: Third-class levers do not multiply force; in fact, you must exert more effort force than the weight of the load. However, they provide an enormous advantage in increasing speed and range of motion (a small movement of the effort produces an expansive, high-velocity sweep at the load end).
  • Examples: Tweezers, sugar tongs, fishing rod, baseball bat, broom, the human forearm (elbow joint is fulcrum, bicep tendon attaches in the middle as effort, hand holds load).

2. The Wheel and Axle

Consists of two connected circular cylinders of different diameters that rotate together around a shared axis.

• When effort is applied to the outer wheel to turn the inner axle, the machine multiplies force ($\text{MA} = \frac{r_{\text{wheel}}}{r_{\text{axle}}} > 1$). Turning the large wheel a great distance rotates the small axle with immense torque. Examples: doorknob, steering wheel, screwdriver, water faucet handle.
• When effort is applied to the inner axle to turn the outer wheel, the machine multiplies distance and speed ($\text{MA} < 1$). Turning the axle slightly causes the outer rim to sweep through a large circumference at high speed. Examples: bicycle rear wheel driven by axle gear, Ferris wheel.

3. The Pulley

A grooved wheel that rotates on an axle, carrying a flexible rope, belt, or chain.

• Fixed Pulley: The axle is anchored to an immovable structure (e.g., ceiling or flagpole). A fixed pulley does not multiply force ($\text{MA} = 1$). Its sole mechanical function is to change the direction of the applied force (pulling downward on the rope allows a person to use their body weight to lift a load upward). Effort distance equals load distance ($d_e = d_r$).
• Movable Pulley: The pulley is attached directly to the load and moves along with it, while one end of the rope is anchored to an overhead support. A single movable pulley doubles the effort force ($\text{MA} = 2$); lifting a $100\text{-N}$ load requires only $50\text{ N}$ of effort force, but the user must pull $2\text{ meters}$ of rope for every $1\text{ meter}$ the load rises.
• Compound Pulley (Block and Tackle): A coordinated system combining multiple fixed and movable pulleys. The ideal mechanical advantage of a block and tackle equals the total number of rope segments that directly support the load (excluding the segment being pulled if pulling downward away from the load).

4. The Inclined Plane

A stationary, rigid, flat sloping surface that bridges a lower elevation to a higher elevation.

• By pushing an object up a gentle ramp rather than lifting it vertically, the worker exerts a substantially smaller effort force across a longer travel path:

$\text{IMA} = \frac{\text{Length of Incline (}\ell\text{)}}{\text{Vertical Height (}h\text{)}}$

• A ramp $6\text{ meters}$ long leading to a platform $2\text{ meters}$ high has an $\text{IMA} = 6/2 = 3$. An operator needs only one-third of the vertical lifting force to move the cargo up the ramp.

5. The Wedge

A portable, moving double-inclined plane that is driven into or between objects to split, cut, or secure them.

• While an inclined plane remains stationary as a load moves up it, a wedge moves through the object. A downward driving effort force at the blunt end is converted into massive lateral, outward splitting forces perpendicular to the sloping faces. A longer, thinner wedge yields a higher mechanical advantage. Examples: axe blade, chisel, knife, wedge doorstop, front incisor teeth.

6. The Screw

An inclined plane wrapped helically in a spiral around a central rigid cylinder.

• The spiraling ridges are known as threads. The linear distance between two consecutive threads is called the pitch. Rotating the screw head with a screwdriver translates rotational effort over a large circular distance into a powerful, slow linear thrust along the screw's axis. The closer the threads (smaller pitch), the higher the mechanical advantage and gripping power. Examples: wood screws, threaded bolts, jar lids, mechanical car jacks, drill bits.

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Comparison Table: The Six Simple Machines

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Classroom Instructional Strategies & Scenario Application

5E Inquiry Framework for Force and Motion

Effective science pedagogy replaces passive lecturing with active, inquiry-based investigations:

1. Engage: Present an intriguing physical discrepant event. For example, place an index card over a plastic cup with a coin resting on top. Flick the index card rapidly with a finger. The card flies horizontally across the room, but the coin drops straight into the cup. Challenge students to explain why the coin did not fly away with the card, introducing Newton's First Law and Inertia.
2. Explore: Provide student collaborative teams with dynamic track sets, low-friction toy carts, washers (weights), and photogates or digital stopwatches. Students systematically investigate Newton's Second Law:
   • Investigation A (Varying Force): Keep cart mass constant; increase pulling force using a hanging string attached to 1, 2, 3, and 4 hanging washers over a pulley. Record cart acceleration.
   • Investigation B (Varying Mass): Keep pulling force constant (2 hanging washers); add incremental mass blocks into the cart ($100\text{ g}, 200\text{ g}, 300\text{ g}$). Record cart acceleration.
3. Explain: Students plot their collected data on two separate graphs:
   • Acceleration vs. Force yields a straight line with positive slope (direct proportionality).
   • Acceleration vs. Mass yields a decaying downward curve (inverse proportionality).
   • The teacher formally introduces the mathematical synthesis: $F = ma$.
4. Elaborate: Students apply their kinematic understanding to design a protective "lunar lander" capsule using simple materials (straws, cotton balls, index cards) that drops an egg safely from a height of $2\text{ meters}$. Students must explain how increasing collision impact time (crumple zone) reduces the decelerating force acting on the egg (Impulse-momentum connection: $F = \frac{\Delta p}{\Delta t}$).
5. Evaluate: Formative assessment through authentic graph interpretation, scenario explanations, and laboratory practical challenges.

Classroom Scenario Application

Classroom Context: Mr. Harrison's 5th-grade science class is participating in a STEM playground design challenge. The students must design a functional mechanical system to lift a heavy $120\text{-N}$ bucket of damp mulch from the ground up to an elevated treehouse platform $3\text{ meters}$ high.

Student Dilemma: The students attempt to pull the bucket straight up using a single rope looped over a fixed tree branch (a fixed pulley). The students struggle and complain that the bucket feels just as heavy as lifting it by hand.

Teacher's Guided Questioning & Pedagogical Intervention:

1. Address the Fixed Pulley Limitation: Mr. Harrison asks: "What did our fixed tree branch pulley change about your pull? Did it change the number of Newtons of force you needed to pull?" Students review their force-meter data and realize a fixed pulley has a mechanical advantage of 1 ($\text{MA} = 1$); it changes only the direction of the pull, not the required force.
2. Implement a Compound Pulley Rig: Mr. Harrison provides a second pulley and challenges the team to attach one pulley directly to the bucket handle (creating a movable pulley) and route the rope through both. The students test the new block-and-tackle system with a spring scale. They observe that the effort force required to hoist the bucket drops from $120\text{ N}$ to approximately $60\text{ N}$.
3. Reinforce Conservation of Work: Mr. Harrison prompts: "Did we magically destroy half the work needed to lift the mulch?" A student measures the length of rope pulled: to lift the bucket $3\text{ meters}$, they had to pull $6\text{ meters}$ of rope. The class calculates work: $W = 120\text{ N} \times 3\text{ m} = 360\text{ J}$, and $W = 60\text{ N} \times 6\text{ m} = 360\text{ J}$. The work remained perfectly identical; the simple machine reduced the force by doubling the distance.