Mechanics and materials

• Forces can be represented with vectors, which show both direction and magnitude
• If two forces act on an object, there is a resultant force
• Resultant force is found by adding the vectors, considering one force as negative if they are in opposite directions
• If vectors are at right angles, Pythagoras can be used to find the resultant
• If a quantity has magnitude but no direction, it's called a scalar, not a vector
• Displacement is distance traveled with a direction, while velocity is the vector form of speed
• Weight is the force due to gravity acting on an object, calculated by mass * gravitational field strength (9.8 N/kg on Earth)
• If you hold an object up, you must push up with a force equal to its weight for balanced forces
• Energy used to lift an object can be calculated using the equation for work done: force * distance moved
• Gravitational potential energy is calculated using the equation: mass * gravitational field strength * height
• Newton's first law states that when there's no resultant force, an object's motion is constant
• Newton's second law involves unbalanced forces, where force = mass * acceleration
• Newton's third law states that for every action force, there is an equal and opposite reaction force
• On a slope, weight tries to pull an object down, while the reaction force of the slope pushes perpendicular to the slope
• The combination of weight and reaction force on a slope results in a force pulling down parallel to the slope
• To find the resultant force in any situation, sum all forces in one direction and subtract the sum of forces in the opposite direction
• Momentum is equal to mass times velocity, and total momentum is always conserved in a collision
• In collisions, kinetic energy isn't always conserved, but total momentum always is
• Impulse is the change in momentum, and it has the same unit as momentum (kg m/s)
• Total kinetic energy is rarely conserved in collisions, with inelastic and elastic collisions being examples
• Force and momentum are closely linked, with force also being equal to the rate of change of momentum
• Upthrust is the force a fluid exerts upwards on an object, equal to the weight of the fluid displaced
• Hooke's Law states that force equals spring constant times extension for elastic objects
• Stress is force per unit area, and strain is the ratio of extension to original length in deforming objects
• The Young Modulus is the ratio of stress to strain, unique to each material
• Materials can undergo elastic deformation up to a limit, beyond which they experience plastic deformation
• The ultimate tensile stress is the maximum stress a material can withstand before breaking
• Ductile materials have a large plastic region, while brittle materials snap suddenly