machines scioly

Simple Machine

A device with few or no moving parts that makes work easier by changing the direction or magnitude of a force. The six types are: lever, pulley, wheel & axle, inclined plane, wedge, and screw.

Mechanical Advantage (MA)

The ratio of output force to input force for a machine. MA = F_out / F_in. A MA > 1 means the machine multiplies force; MA < 1 means it multiplies speed/distance instead.

Ideal Mechanical Advantage (IMA)

The mechanical advantage of a machine assuming no friction or energy loss. IMA = d_in / d_out (input distance divided by output distance). Always ≥ AMA.

Actual Mechanical Advantage (AMA)

The real mechanical advantage of a machine accounting for friction. AMA = F_out / F_in (measured). Always ≤ IMA due to energy losses.

Efficiency (η)

The ratio of useful output work to total input work, expressed as a percentage. η = (W_out / W_in) × 100% = (AMA / IMA) × 100%. Always less than 100% in real machines.

Work

W = F × d × cos(θ). Measured in joules (J). Work is positive when force aids displacement and negative when it opposes it. The conservation of energy means input work always equals or exceeds output work.

Power

The rate of doing work. P = W / t (watts). Also P = τ × ω for rotational systems. A machine with high power does the same work in less time.

Torque (τ)

The rotational equivalent of force. τ = F × r × sin(θ), where r is the lever arm length. Measured in N·m. A lever is in rotational equilibrium when the sum of all torques about the fulcrum equals zero.

Lever

A rigid bar that rotates about a fixed point called the fulcrum. IMA = effort arm length / load arm length = d_effort / d_load.

Fulcrum

The fixed pivot point of a lever about which it rotates.

Class 1 Lever

Fulcrum is between the effort and the load. MA can be > 1, = 1, or < 1 depending on arm lengths. Examples: seesaw, scissors, crowbar.

Class 2 Lever

Load is between the fulcrum and the effort. MA is always > 1 (force multiplier). Examples: wheelbarrow, nutcracker, bottle opener.

Class 3 Lever

Effort is between the fulcrum and the load. MA is always < 1 (distance/speed multiplier). Examples: tweezers, fishing rod, human forearm, broom.

Lever Equilibrium Condition

A lever is balanced when: F1 × d1 = F2 × d2 (sum of clockwise torques = sum of counterclockwise torques). For multiple masses: Σ(F × d) on each side must be equal.

Pulley

A wheel with a rope, chain, or cable wrapped around it used to change the direction or magnitude of a force.

Fixed Pulley

A pulley attached to a fixed point. IMA = 1. It only changes the direction of force, not its magnitude. Example: flagpole.

Movable Pulley

A pulley attached to the load that moves with it. IMA = 2. It reduces the required effort force. Example: crane block.

Compound Pulley System

A combination of fixed and movable pulleys. IMA = number of rope segments supporting the load. To find IMA, count the strands of rope directly supporting the movable block.

Block and Tackle

A system of multiple pulleys (blocks) used together to achieve a high mechanical advantage. IMA equals the total number of rope segments supporting the load.

Wheel and Axle

A large wheel fixed to a smaller axle that rotate together. IMA = radius of wheel / radius of axle = R_wheel / R_axle. Examples: steering wheel, doorknob, screwdriver.

Wheel and Axle (force applied to wheel)

When effort is applied to the wheel: IMA = R_wheel / R_axle > 1. The machine multiplies force (e.g., turning a large steering wheel to turn a small axle).

Wheel and Axle (force applied to axle)

When effort is applied to the axle: IMA = R_axle / R_wheel < 1. The machine multiplies speed/distance (e.g., bicycle wheel turning faster than the pedal axle).

Inclined Plane

A flat surface tilted at an angle to the horizontal (a ramp). IMA = length of slope / vertical rise = L / h. A longer, shallower ramp has a higher IMA.

Inclined Plane with Friction

When friction is present, the effort force needed is: F = mg(sin θ + μ cos θ). Friction reduces efficiency and increases required input force above the ideal.

Wedge

Two inclined planes joined back-to-back. IMA ≈ length of wedge / width (thickness) = L / w. Used to split or separate objects. Examples: axe, knife, doorstop.

Screw

An inclined plane wrapped helically around a cylinder. IMA = 2πr / p, where r is the radius of the applied force (handle) and p is the pitch (distance between threads). Examples: jar lid, bolt, screw jack.

Pitch (screw)

The distance between two adjacent threads on a screw, or the linear distance the screw advances per one full revolution. A smaller pitch means a higher IMA.

Compound Machine

A machine made of two or more simple machines working together. The total IMA of a compound machine is the product of the IMA values of its component simple machines. Example: scissors = lever + wedge.

Examples of Compound Machines

Bicycle (wheel & axle + pulley), scissors (lever + wedge), can opener (lever + wedge + wheel & axle), wheelbarrow (wheel & axle + lever), car jack (lever + screw).

Conservation of Energy in Machines

Machines do not create energy. Input work = output work + energy lost to friction. W_in = W_out + W_friction. This is why real efficiency is always less than 100%.

Friction

A resistive force between surfaces in contact. F_friction = μ × N, where μ is the coefficient of friction and N is the normal force. Friction always reduces efficiency and increases required input force.

Coefficient of Friction (μ)

A dimensionless ratio that describes how much friction exists between two surfaces. F_friction = μN. Higher μ means more friction and lower machine efficiency.

Normal Force (N)

The contact force perpendicular to a surface. For an object on a horizontal surface, N = mg. On an inclined plane, N = mg cos θ.

Gear

A toothed wheel that meshes with another gear to transmit torque. Gear MA = N_out / N_in = r_out / r_in (ratio of teeth or radii). External gears in mesh reverse direction; internal gears do not.

Gear Train

A series of meshing gears used to transmit and transform rotational motion. The overall MA is the product of individual gear ratios.

Belt and Pulley System

Two pulleys connected by a belt. MA = r_driven / r_driver (ratio of radii). Unlike gears, belt pulleys do not reverse direction of rotation.

Differential Pulley

A pulley system with two wheels of different radii (R and r) on the same axle. IMA = 2R / (R − r). Used in chain hoists.

Torque Equilibrium (Lever)

For a lever in static equilibrium: Σ τ_clockwise = Σ τ_counterclockwise, i.e., Σ(F × d) = 0 about any point. Used to find unknown forces or distances on a balanced lever.

Kinetic Energy (KE)

KE = ½mv². The energy an object has due to its motion. Measured in joules (J).

Potential Energy (PE)

PE = mgh. The energy stored in an object due to its height above a reference point. Measured in joules (J).

Conservation of Mechanical Energy

In the absence of non-conservative forces (like friction), KE + PE = constant. In real machines, energy is lost to friction and heat.

Newton's Second Law

F = ma. The net force on an object equals its mass times acceleration. Force is measured in newtons (N = kg·m/s²).

Effort Force (F_in)

The force applied to a machine by the user. Also called input force. Machines are often used to reduce the required effort force.

Load / Resistance Force (F_out)

The force exerted by the machine on the load. Also called output force. This is the force doing the useful work.

Effort Arm

The perpendicular distance from the fulcrum to the line of action of the effort force on a lever.

Load Arm

The perpendicular distance from the fulcrum to the line of action of the load force on a lever.

Lever IMA Formula

IMA = d_effort / d_load = L_effort arm / L_load arm. The longer the effort arm relative to the load arm, the higher the mechanical advantage.

Inclined Plane IMA Formula

IMA = L / h = 1 / sin θ, where L is the slant length and h is the vertical rise (height). θ is the angle of inclination.

Pulley IMA Rule

IMA = number of rope segments supporting the movable block (load). Count only the strands attached to or supporting the moving pulley, not the free end being pulled.

Screw IMA Formula

IMA = 2πr / p, where r = radius of the turning handle/head and p = pitch (thread spacing). A smaller pitch or larger handle = higher IMA.

Wedge IMA Formula

IMA = L / w, where L is the length of the wedge and w is its width (thickness at the widest point). Longer, thinner wedges have higher IMA.

Wheel & Axle IMA Formula

IMA = R_wheel / R_axle. When force is applied to the larger wheel, force is amplified at the smaller axle. When force is applied to the axle, speed is amplified at the wheel.

Efficiency Formula

η = (W_out / W_in) × 100% = (AMA / IMA) × 100% = (F_out × d_out) / (F_in × d_in) × 100%.

Self-Locking Machine

A machine in which friction prevents the load from reversing the motion when input force is removed. Common in screws and steep inclined planes. A screw is self-locking when its efficiency is less than 50%.

Mechanical Energy

The sum of kinetic and potential energy in a system: ME = KE + PE. In an ideal (frictionless) machine, mechanical energy is conserved.

Rotational Speed and Gear Ratio

ω_out / ω_in = N_in / N_out = r_in / r_out. Increasing gear size reduces rotational speed but increases torque (and vice versa).

Static Equilibrium

A condition where an object is at rest and the net force and net torque acting on it are both zero. Levers in balance are in static equilibrium.

Lever Device (SciOly Build Component)

A lever-based measuring device constructed before competition to determine mass ratios of three test masses. Accuracy depends on minimizing friction at the fulcrum and careful calibration.

Mass Ratio Determination

Using a balanced lever: m1 × d1 = m2 × d2. By measuring the distances at which unknown masses balance a reference mass, mass ratios can be calculated without a scale.

Angular Velocity (ω)

The rate of rotation, measured in radians per second (rad/s). Related to linear speed by v = rω. Used in power calculations: P = τω.

Unit of Work and Energy

Joule (J) = N·m = kg·m²/s². Both work and energy are measured in joules.

Unit of Power

Watt (W) = J/s = N·m/s. Power measures how quickly work is done.

Unit of Torque

Newton-meter (N·m). Note: same units as joules, but torque is not energy—it is a vector quantity representing rotational force.

Unit of Force

Newton (N) = kg·m/s². Defined by F = ma.

Significant Figures in Machines

Measurements in the written test should use the correct number of significant figures based on given data. All calculations should maintain precision consistent with the least precise measurement.