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Engineering
Grade 9-12
Mechanical Engineering Basics Cheat Sheet
A printable reference covering force, torque, stress, strain, work, power, mechanical advantage, and efficiency for grades 9-12.
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Mechanical engineering basics connect physics, math, materials, and design to explain how machines and structures work. This cheat sheet helps students organize the formulas used to analyze motion, forces, energy, and machine performance. It is useful for solving classroom problems and for thinking like an engineer during design challenges.
Key Facts
- Newton's second law is F = m × a, where F is net force, m is mass, and a is acceleration.
- Weight is W = m × g, where g is about 9.8 m/s² near Earth's surface.
- Torque is τ = F × r when the force is perpendicular to the lever arm, where r is the distance from the pivot.
- Work is W = F × d when the force acts in the same direction as the displacement.
- Power is P = W ÷ t, where W is work or energy transferred and t is time.
- Stress is σ = F ÷ A, where F is the applied force and A is the cross-sectional area.
- Strain is ε = ΔL ÷ L₀, where ΔL is the change in length and L₀ is the original length.
- Efficiency is efficiency = useful output energy ÷ input energy × 100%.
Vocabulary
- Force
- A push or pull that can change an object's motion, measured in newtons.
- Torque
- A twisting effect caused by a force acting at a distance from a pivot or axis.
- Stress
- The force applied per unit area inside a material.
- Strain
- The fractional change in length or shape of a material under load.
- Mechanical advantage
- The ratio of output force to input force for a machine.
- Efficiency
- The percentage of input energy that becomes useful output energy.
Common Mistakes to Avoid
- Confusing mass and weight is wrong because mass is measured in kilograms, while weight is a force measured in newtons using W = m × g.
- Forgetting the lever arm in torque problems is wrong because torque depends on both force and distance from the pivot using τ = F × r.
- Using work = force × distance for any force direction is wrong because that simple formula only applies when force and displacement are in the same direction.
- Ignoring units in stress calculations is wrong because stress equals force divided by area, so area must be converted consistently before using σ = F ÷ A.
- Assuming a machine can be 100% efficient in real life is wrong because friction, heat, sound, and deformation usually waste some input energy.
Practice Questions
- 1 A 12 kg object accelerates at 3 m/s². What net force acts on it?
- 2 A student pushes perpendicular to a wrench with 40 N of force at a distance of 0.25 m from the bolt. What torque is produced?
- 3 A machine uses 500 J of input energy and produces 375 J of useful output energy. What is its efficiency?
- 4 Why might an engineer choose a stronger material or a larger cross-sectional area when designing a bridge support?