Mechanics

• 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, which can be rewritten 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.
• The resultant vector (R) can be found using Pythagoras: 2 69 1 2 + 5 2 = 1 = R.
• The direction of the resultant vector can be found using trigonometry: an θ t = 5 12 2.6° θ = 2.
• The opposite of adding two vectors is called resolving vectors, and is done using trigonometry.
• Formulas can be used to show how to resolve the vector V, into its components x and y: x = V cos θ y= V sin θ.
• A ball has been fired at a velocity of 10 m/s, at an angle of 30° from the horizontal, find the vertical and horizontal components of velocity: x= 10 cos 30° y= 10 sin 30° = 8.7 m/s = 5 m/s.
• 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.
• Work is calculated as W = Fs cos θ, where s is the distance travelled and θ is the angle between the direction of the force and the direction of motion.
• Change in gravitational potential energy is represented as E g Δh Δp, where Δh is the change in height and Δp is the change in potential.
• The density of a material is its mass per unit volume, and it’s a measure of how compact a substance is.
• 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.
• Kinetic energy is represented as E k = ½ mv², where m is the mass and v is the velocity.
• 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.
• The limit of proportionality (P) is the point after which Hooke’s law is no longer obeyed.
• Hooke’s law states that extension is directly proportional to the force applied, given that the environmental conditions (e.g temperature) are kept constant.
• For an object in equilibrium, the sum of anticlockwise moments about a pivot is equal to the sum of clockwise moments.
• Velocity-time graphs represent the change in velocity over time, with the gradient of a velocity time graph being acceleration, and the area under the graph being displacement.
• Acceleration (a) is the rate of change of velocity.
• Uniform acceleration is where the acceleration of an object is constant.
• Acceleration-time graphs represent the change in acceleration over time, and the area under the graph is change in velocity.
• When an object is moving at uniform acceleration, the following formulas can be used: t v = u + a, t s = (2 u + v), and t s = u + 2 at 2.
• Displacement-time graphs show change in displacement over time, and so their gradient represents velocity.
• Instantaneous velocity is the velocity of an object at a specific point in time, which can be found from a displacement-time graph by drawing a tangent to the graph at the specific time and calculating the gradient.
• Average velocity is the velocity of an object over a specified time frame, which can be found by dividing the final displacement by the time taken.
• Speed is a scalar quantity which describes how quickly an object is travelling.
• Velocity (v) is the rate of change of displacement.
• The centre of mass of an object is the point at which an object’s mass acts.
• Displacement (s) is the overall distance travelled from the starting position, including a direction as it is a vector quantity.
• Newton’s 2nd law and a free-body diagram are used to find the acceleration of an object.
• Newton’s 2nd law states that a force is the rate of change of momentum.
• If the objects in a collision stick together after the collision, it is an inelastic collision.