Mechanic and Materials

• Scalars and vectors are physical quantities, scalars describe only a magnitude while vectors describe magnitude and direction.
• Examples of scalars include distance, speed, mass, and temperature.
• Examples of vectors include displacement, velocity, force/weight, and acceleration.
• There are two methods to add vectors: calculation and scale drawing.
• Young Modulus (E) can be calculated as Tensile Strain Tensile Stress, using the formulas from the previous section, as: E = F L Δ LA.
• The Young modulus of a material can be found from a stress-strain graph by finding the gradient of the straight part of the graph.
• The calculation method should be used when the two vectors are perpendicular.
• An example of using the calculation method is when two forces are acting perpendicular to each other and have magnitudes of 5 N and 12 N.
• To find the resultant vector (R) in the calculation method, use Pythagoras: 2 69 1 2 + 5 2 = 1 = R 2 3 N R = 1.
• The direction in the calculation method can be found using trigonometry: tan θ = 5 12 2.6° θ = 2.
• The scale drawing method should be used when vectors are at angles other than 90°.
• An example of using the scale drawing method is when a ship travels 30 m at a bearing of 060°, then 20 m east.
• To find the magnitude and direction of an object's displacement from its starting position, draw a scale diagram, use a ruler and a protractor, and measure the missing side and convert it to the magnitude.
• Change in gravitational potential energy is represented as E g Δ h Δ p, where Δ h is the change in height and Δ p is the change in potential.
• The maximum speed a pendulum can reach during its oscillation is calculated by equating the maximum gravitational potential energy to the kinetic energy formula, and rearranging to find v.
• Work is calculated as W = F s cos θ, where s is the distance travelled and θ is the angle between the direction of the force and the direction of motion.
• The area under a force-displacement graph is equal to the work done.
• The principle of conservation of energy states that energy cannot be created or destroyed, but can be transferred from one form to another, therefore the total energy in a closed system stays constant.
• Hooke’s law states that extension is directly proportional to the force applied, given that the environmental conditions (e.g temperature) are kept constant.
• The density of a material is its mass per unit volume, and it’s a measure of how compact a substance is.
• Kinetic energy is represented as E k = ½ mv², where m is the mass and v is the velocity.
• The limit of proportionality (P) is the point after which Hooke’s law is no longer obeyed.
• Efficiency is a measure of how efficiently a system transfers energy, calculated by dividing the useful power output by total energy input.
• The rate of doing work is the rate of energy transfer, represented by the symbol P.
• The opposite of adding two vectors is called resolving vectors, and is done using trigonometry.
• There are formulas to show how to resolve the vector V, into its components x and y.
• If you are moving from the original vector through the angle θ to get to your component, use cos.
• If you are moving away from the angle θ to get to your component, use sin.
• A free-body diagram is a diagram which shows all the forces that act on an object.
• Newton’s 2nd law and a free-body diagram are used to find the acceleration of an object.
• An explosion is another example of an inelastic collision as the kinetic energy after the collision is greater than before the collision.
• Momentum is the product of mass and velocity of an object.
• Impulse is the change in momentum as demonstrated in the Δ t F equation above.
• Work done (W) is defined as the force causing a motion multiplied by the distance travelled in the direction of the force.
• The change in momentum of the ball can be calculated using the equation Δ t (mv) F = Δ.
• Cars have crumple zones which crumple upon impact, seat belts which stretch upon an impact, and air bags all of which increases the impact time of the car or the passenger.
• Newton’s 2nd law states that a force is the rate of change of momentum.
• In a free-body diagram, if all the arrows look equal, it means the object is travelling at a constant velocity.
• Momentum is always conserved in any interaction where no external forces act, meaning the momentum before an event (e.g a collision) is equal to the momentum after.
• Newton’s 3rd law states that for each force experienced by an object, the object exerts an equal and opposite force.