Physics Unit 1- Mechanics

1. PhysicsUnit 1- Mechanics

2. -Physical Quantities and Units Below are the SI Units used across the world:

3. -Physical Quantities and Units Below are the Unit prefixes:

4. -Scalar and Vector Quantities A scalar quantity is one that has magnitude (size) but not a direction. A vector quantity is one that has magnitude (size) and direction.

5. -Vector Component Forces Here is a triangle which trigonometry can be used to find unknowns: Fcos F Fsin

6. -Definitions in kinematics Speed is distance per unit time. Speed is the distance travelled per unit time- it is a scalar Velocity is the displacement per unit time- it is a vector Displacement is distance moved in a stated direction. Acceleration is the rate of change of velocity. Average speed = Average acceleration = Instantaneous speed is the speed at a given instant of time (it is the gradient of the graph of displacement against the against time at that instant)

7. -Graphs of Motion • Displacement/ Time graphs: • A straight line indicates constant velocity • The gradient of a straight line gives the velocity • The gradient at any point is the velocity, and this is called instantaneous velocity • Velocity/ Time graphs: • The gradient represents acceleration • The area beneath a velocity/ time graph represents the displacement

8. -Equations of Motion Summary of the equations of motion for constant acceleration: v = u + at Term not included: s v2= u2 + 2as Term not included: t s = ( ) t Term not included: a s = ut + ½ at2 Term not included: v s = vt- ½ at2 Term not included: u

9. -Free Fall An object undergoing free fall on the Earth has an acceleration of g = 9.81 m s-2. Acceleration is a vector quantity- and g acts vertically downward. Remember, when answering questions on free fall, make sure you deal with the horizontal and vertical components separately, and watch out for negative values.

10. -Measurement of g Below is a diagram on the ‘trap door and electromagnet method for determining g’. There will be a degree of uncertainty in this experiment because: If the electromagnet’s current is too strong there will be a delay in releasing the ball after the current is switched off and the clock is triggered. If the distance of fall is too large, or the ball is too small, air resistance might have a noticeable effect on its speed. You need you make sure you measure from the bottom of the ball when it is held by the electromagnet.

11. -Force and the Newton • -Types of Force • Generally, a force is push or pull, but can be others such as drag, tension, friction, weight and thrust. Thrust, for example, is the term used for the driving force provided by a jet engine. • Outside the nucleus of an atom, there is just three types of force, which are: • Gravitational force between two objects with mass. (Only one I will need is between the object and the Earth: The weight). • Magnetic force between two magnetic objects. At an atomic level this is a force between moving charges, and will only concern you in examples using magnetised forces. • Electrical force between charged objects, which is responsible for all interactions between objects. When two atoms collide, they exert an electrical force on one another, and may chemically bond as a result of the electrical attraction between them. • This list of the three basic forces outside a nucleus can be reduced to two by treating the electrical and magnetic forces as a single electromagnetic force. This is because the theory of electromagnetism establishes the connection between electrical and magnetic effects.

12. -Force and the Newton • The link between these three terms was first established by Newton, when he discovered that when an object has no resultant force on it, the object won’t accelerate; it will stay at a constant velocity. Once Newton established this, he found that: • Acceleration is proportional to force, if the mass is constant • Acceleration is inversely proportional to mass, if the force is constant. • Putting this algebraically: • a ∝ F and a ∝ , so F=ma A resultant force always causes acceleration. Zero resultant force implies a constant velocity, which may also be zero (it will be in equilibrium). Remember, forces cause acceleration, and not the other way round! One Newton is the force that causes a mass of one kilogram to have an acceleration of one metre per second every second.

13. -Motion with non-constant acceleration • Weight: • Weight is a force, so is measured in newton's. • The mass of an object is measured in kg. • To work out mass or weight, we can use the equation W=mg Weight is the gravitational force on a body Non-constant (non-linear) acceleration When an object travels through a fluid (liquid or gas), it experiences a resistive force, known as drag, which depends on several factors, such as velocity, roughness of surface, cross-sectional area and shape (how it is streamlined) Terminal Velocity: This is when the drag (upwards) becomes equal to the weight of the object (downwards) so the resultant force is zero, so it is travelling at a constant velocity. This is called terminal velocity.

14. -Equilibrium Equilibrium: When there is zero resultant force acting on an object. The triangle of forces: Here are some examples of triangular forces: 3N 2.8N 4N 4N R=5N R= 5.7N 36.8o 5N 4N 5N 4N B R=1.4N A+B=C C+D=E A+B+D=E Resultant (almost) zero D C A E resultant A+B+D

15. -Centre of Gravity Whenever mass is used, the position of the weight of the object has to be considered. For all objects there is a point where the entire weight of the object can be considered to act as a single force, and this is called the centre of gravity of an object. Although the weight of an object does not act through just the centre of gravity, it does simply calculations. Finding the centre of gravity- Support the piece freely on a wire passed through a small hole. Hang a string with a small weight at the bottom. Repeat the procedure with a different hole, and the centre of gravity is where the lines meet.

16. -Turning Forces This is needed when doing things like designing building, to make sure it can support itself and will not collapse. Loading forces are usually vertically downwards, and need to be balanced by vertically upward support forces. We need to establish equilibrium when working with forces that are parallel.

17. -Turning Forces Terms associated with Turning Forces: Couple- A couple occurs when two forces are equal and opposite to each other, but are not in a straight line. No linear acceleration can be produced, as the upward and downward forces cancel. The resultant of theses forces is zero, however they can produce rotation. Torque- This can be applied to a couple and describes a turning effect of the couple. The formula for torque is: Y X Torque = one of the forces x perpendicular distance between the forces A couple is a pair of equal and parallel but opposite forces, which tends to produce rotation only. So torque is measured in newton metres, and produces rotation rather than linear motion, so the term is used in drills etc.

18. -Turning Forces Moment of force = Fx X Moment of a force: The moment of a force is the turning effect of a single force shown to the right. Moments are also measured in Newton metres. The principle of moments states that: For a body in rotational equilibrium, the sum of the clockwise moments equals the sum of the anticlockwise moments. (CW=ACW). P F F P X The moment of a force is the force multiplied by the perpendicular distance from the stated point. Equilibrium of an extended object A large object may have many forces acting on it. These forces may provide a resultant force, which will cause acceleration, and a resultant moment, which will cause rotation. For a large object to be in equilibrium, both the resultant force and the resultant moment must be zero.

19. -Density Density = , and density has the SI unit kg m-3. 1m3 = (100 cm)3 = 1 000 000 cm3. The volume of water has a mass of 1000kg, so the density is 1000 kg m-3. Density is defined as mass per unit volume.

20. -Pressure Pressure = , and the SI unit for pressure is the Pascal (Pa). 1 pascal represents the force of 1N spread uniformly over an area of 1 m2 and is a comparatively small unit of pressure. Pressure is defined as force per unit area. Pressure in a liquid is given by hpg, where h is height, p is density and g is 9.81m s-2. Eg) An oil tanker has a total mass of 400 000 tonnes (ship + oil). It has a width of 40m and a length of 500m. Force upward = Weight downward = mg = 400 000 000 kg x 9.81m s-2= 3.92 x 109N. Upward force due to water = pressure x area of base of ship, so 3.92 x 109 = hpg x 40 x 500 p = density of sea water = 1030 kg m-3. h= distance from the bottom of the ship to the surface, so h= = 19.4m

21. -Car stopping distances Force x distance gives the work done by a vehicle against its braking force. This quantity is called the kinetic energy of a vehicle. The table below shows a car (which including passengers and luggage is 1200kg) and its breaking distance. If you double the speed, the kinetic energy quadruples. So, for every given braking force, the braking distance is always four times larger when the car is travelling at twice the speed.

22. -Car stopping distances Thinking Distance + Braking Distance = Stopping Distance Thinking Distance = speed x reaction time Reaction time is increased by tiredness, alcohol/ other drug use, illness, and distractions such as children and phones. • Braking distance depends on the braking force, friction between the tyres and the road, the mass and the speed. • Braking force is reduced by reduced friction between the brakes and the wheels (worn or badly adjusted brakes) • Friction between the tyres and the road is reduced by wet or icy roads, leaves or dirt on the road, worn out tyre treads, etc • Mass is affected by the size of the car and what you put in it.

23. -Car stopping distances Thinking, braking and stopping distances: Stopping distance = thinking distance + braking distance Thinking distance = Time taken to see the need to stop and apply the brakes Braking distance = The time taken from hitting the brakes to coming to a stop Eg) A car of mass 1000kg has brakes that are 75% efficient. It is travelling at 40ms-1 and it’s daylight and the road is dry. The driver takes 0.25 seconds to respond to an incident that requires an emergency stop. What’s the shortest possible distance for stopping? Thinking distance= 400.25s = 10m Acceleration while braking= Since, for braking: v2 = u2 + 2as 02 = 402 + 2 x (-7.35)s s = 109m + 10m = 119m

24. -Car Safety You can stop a moving vehicle with less braking force if you increase the braking distance, because kinetic energy = braking force x breaking distance. This becomes more relative when thinking of someone involved in a car crash. In a crash, you want to reduce the force, and you can do this by increasing the crash time, or the distance your body moves in a crash. A good car does this with crumple zones, seat belts and airbags. Crumple zones: These are meant to collapse during a collision (usually the front end). The crumple zones slightly decrease collision speed, which increases the collision time, so the average force you endure is less. Seat Belts: The distance in which a force can act is also increased by wearing a seatbelt, as it stretches during an incident. However, the main advantage of a seatbelt is to keep you kept in the car, as without one your body would be most likely stopped by the windscreen or another rigid part of the car.

25. -Car Safety • Airbags: These work well with seatbelts, as they should be fully inflated when you hit them, which they most likely won’t be without the aid of seatbelts. Airbags are designed to inflate in 0.05 s, and deflate in 0.3s, which is sufficient to slow you down. An airbag consists of three parts: • A flexible nylon bag that is folded into the steering wheel or dashboard • A sensor know as an accelerometer. When the front end of the spring is suddenly stopped, the mass on the end of the spring continues to move forward and makes contact with a switch, starting a chemical reaction. This occurs when the acceleration is around -10g, an acceleration that only occurs during an incident. • An inflation system in which a spark ignites a violent chemical reaction in which nitrogen gas is produced (it may sometimes be air, but usually Nitrogen gas)

26. -Car Safety Global Positioning System (GPS): A GPS in cars enable you to know where you are on the worlds surface within a distance of about 1m, using satellites orbiting Earth at the height of about 20 000km. At any one point, there will always be at least four satellites available for any GPS receiver. The system relies on accurately measuring time differences between the arrival of signals sent simultaneously from several satellites, and on the precise position of these satellites. The satellites clocks are synchronised with clocks on the ground and are accurate to one second in 100 million years.

27. -Car Safety Global Positioning System (GPS): The method used for determining the position of the GPS receiver in a car is called trilateration. If satellite A sends out a signal and it arrives after a known time ay the GPS receiver then, given the speed of travel of electromagnetic radiation, the distance of the receiver from the satellite can be found. We now repeat this for the other satellites, which gives your current location; where all the spheres meet! The in-car computer then plots this position on its map, and can guide the car along a suitable route to the requested destination. Although trilateration only needs 3 satellites, GPS systems actually use at least four satellites. You are here

28. -Work and the joule Work, is defined by the equation: work = force x distance moved in the direction of the force Since the definition has a direction for the force, you would think it is a vector but in fact it is a scalar. It defies the general rule of Vector x Scalar = Vector. The SI Unit for work is the joule, and 1 joule = 1 newton metre. Eg) Picking up a pen = 0.2N x 0.1m = 0.02Nm = 0.02J 1 joule is the work done when a force of 1 newton moves its point of application 1 metre in the direction of the force.

29. -Work and the joule Force at an angle to the direction of movement: Eg) A barrel of weight 200N is raised by a vertical distance of 1.8m by being moved along the ramp. The work done against gravity will be 200N x 1.8m = 360J If the ramp is at an angle of 25o to the horizontal, then the force required will be less but the total work done must, if the friction is negligible, be the same, so: Distance moved along the ramp = = 4.26 Force required = = 84.5N A simpler way is to use the vertical component of the distance moved along the slope: Work done = 200N x 4.26m x cos65o = 360J 65o is the angle between the force and the distance moved. In other words: Work done = force x distance moved in the direction of the force = F d cos Where d is the distance travelled and is the angle between the force and the direction of travel.

30. A barrel of weight 200N is raised by a vertical distance of 1.8m by being moved along the ramp. • A) what is the work done? • B) what force is required?

31. -Work and the joule The picture that was used in the example previously: 1.8m 4.26m 25o 200N

32. -Work and the joule Note that if the force and direction of travel are at right angles to one another, then no work is done as cos 90o is zero. This may seem rather irrelevant, as at first sight a force at right angles to the direction of travel seems impossible, however the force of gravity on the Moon as it orbits Earth is at right angles to the Moon’s direction of travel. So, despite the large gravitational force the Earth is exerting on the Moon, the Earth is not doing any work on the Moon, and so the Moon moves at a constant speed for a very long time.

33. -The conservation of Energy Energy is the stored ability to do work. Total energy in = Total energy out • Energy cannot be created or destroyed. • Energy can be transferred from one form to another but the total amount of energy in a closed system will not change. • At a basic level, energy is either kinetic energy or potential energy. • Kinetic Energy: where movement is taking place • Potential Energy: Regions where electric, magnetic, gravitational and nuclear forces exist. Regions such as these are called fields. • Below are different forms of energy together with some details of how the energy is stored: • Chemical Energy: energy can be released when the arrangement of atoms is altered • Electrical potential energy: Eg) A positive charge is pushed close to another positive charge. This will often be called electrical energy. • Electromagnetic energy: includes all the waves that travel at the speed of light in a vacuum (gamma rays, X-rays, ultraviolet, light, infrared, microwaves, radio waves). These waves hold their energy in electric and magnetic fields.

34. -The conservation of Energy Gravitational potential energy: where an object is at a high level in the Earth’s gravitational field. Internal energy: the molecules in all objects have random movement and have some potential energy when they are close to one another. Kinetic energy: when an object has speed. Nuclear energy: energy can be released by reorganising the protons and neutrons in an atom’s nucleus. This form of energy is also known as atomic energy. Sound energy: in the movement of atoms Conservation of energy describes the situation in any closed system, where energy may ne converted from one from into another, but cannot be created or destroyed.

35. Potential and Kinetic energies Gravitational potential energy (GPE): this is the energy stored in an object (the work an object can do) by virtue of its position in a gravitational field. The formulae is: GPE = mgh Kinetic energy (KE): this is the work an object can do by virtue of its speed. The formulae is: kinetic energy (k.e.) = . Also, the kinetic energy of a moving body equals the work it can do as a result of its motion. Falling objects: An object of mass m, falling from rest, loses gravitational potential energy. From the principle of conservation of energy, it gains an exactly equivilant amount of kinetic energy as a result of the work being done on it by gravity, so: Mgh = , where v is its speed and h is the distance fell, m cancels to give: 2gh = v2 or v=

36. Power and the Watt Power is the rate of doing work. Power = One watt (W) is equal to one joule per second. 1kW = 1000 W 1MW = 1000kW = 1 000 000 W To power a 100 watt light bulb, an electric current must be flowing through the filament of the bulb. It supplies energy at the rate of 100 joules per second, so to power it for one hour it would be: 100J s-1 x 3600s = 360 000 J. Electrical energy is sold to domestic users in units called kilowatt- hours (kWh), which is equivalent to the use of 1000 W of power for an hour. Eg) 1kWh could be supplied to a 100W lamp over 10 hours. 1kWh = 1000J s-1 x 3600s = 3 600 000 J. Today one kWh of energy costs about 15p.

37. Power and the Watt You need to be careful when distinguishing between rates and totals. For example, you cannot buy a kW of power; you pay for energy. You can pay 1 kW used for 6 hours- 6kWh. Below is a table showing the relationship between rates and totals for several units. Human Power and Horse Power: 176W is a high rate of work that only a fit person could sustain for any length of time. Most people would find it difficult to work continuously at a rate of 70W. Horse power is still used to express some power ratings. 1 horse power is equal to 746W- though this isn’t really what horses achieve.

38. Efficiency Efficiency is expressed as: Efficiency = To convert electrical energy into heat, you just need resistance.

39. Sankey Diagrams Useful output energy Input energy The width of the arrows should relate to how much is wasted- don’t use fat arrows for things with small loss! (Do it to scale) Wasted output energy split into different types

40. Deformation of materials The word elastic can be applied to a collision. In an elastic collision no kinetic energy is lost. This can only happen when there is no permanent distortion of the objects colliding, because if there is permanent distortion some energy must have been used to create the distortion. Collisions which are not elastic collisions are not usually called plastic collisions but inelastic collisions. A stretch can be Elastic or Plastic… Elastic If a deformation is elastic, the material returns to its original shapeonce the forces are removed. When the material is put under tension, the atoms of the materials are pulled apart from one another. Atoms can move small distances relative to their equilibrium positions, without actually changing position in the material. Once the load is removed, the atoms return to their equilibrium distance apart. For a metal, elastic deformation happens as long as Hooke’s law is obeyed. Plastic If a deformation is plastic, the material is permanently stretched. Some atoms in the material move position relative to one another. When the load it removed, the atoms don’t return to their original position. A metal stretched past its elastic limit shows plastic deformation.

41. Deformation of materials Tensile and compressive forces Forcesthat stretch objects like wires, springs and rubber bands are called tensile forces, because they cause tension in the object. Therefore, for there to be tension in a fixed stretched wire, there must be equal and opposite forces on it at either end. With a spring, it is possible to reduce its length by squeezing it, and in this instance the forces applied are called compressive forces. Unless the spring is accelerating, equal and opposite forces must be applied. Once the elastic limit has been passed, the stretch becomes permanent. Plastic deformation- the object will not return to its original shape when the deforming force is removed, it becomes permanently distorted.

42. Hooke’s Law Hooke’s Law- the extension of an elastic body is proportional to the force that causes it. The equation is F= kx, where F is the force causing extension x, and k is known as the force constant (stiffness constant). The force constant is expressed in newton's per metre. k tells us how much force is required per unit of extension. Eg) A k of 6N mm-1 means it takes 6N to cause an extension of 1mm. Note that the force constant can only be used when the material is undergoing elastic deformation. When deformation become plastic, the force per unit extension is no longer constant. Graphs- When extension is plotted on the x-axis, the area beneath the line is equal to the work required to stretch the wire. Work done = area of triangle = ½ Fx And since F=kx… Work done = In the case of elastic deformations, the elastic potential energy E equals the work done, giving: E = .

43. Hooke’s Law Energy stored in plastic deformation: The graph shown below could be produced by stretching a copper wire beyond its elastic limit. The work done stretching the wire is given by the area A + B. If the tension is then reduced to zero, the wire behaves elastically, contracting to a permanent extension x. As the tension is reduced, energy equivalent to area B is released from the wire. The net result of the wire having work A + B done on it, but only releasing energy B, is that the wire becomes hot to the touch.

44. Young’s modulus • Stress and Strain: • Stress is force per unit cross-section area, therefore is expressed in the SI Unit newton per square metre. N m-2. This unit is called pascal (Pa), which is also used to quantify pressure. • Strain is extension per unit length. As a result, strain does not have a unit, since it is length divided by length; sometimes it is quoted as a percentage. A strain of 2% is the same as a strain of 0.02 and implies that a material has extended 2cm for each metre of its original length. Stress is force per unit cross-sectional area. Strain is extension per unit length.

45. Young’s modulus Stress on a material causes strain. How much strain is caused depends on how stiff it is. A stiff material, such as cast iron, will not alter its shape much when a stress is applied to it, but a relatively small stress will cause a substantial strain in a soft material, such as clay. Young's Modulus is the ratio between stress and strain, measured in pascals (Pa). The formulae is as follows: Young Modulus (E) = Where, F = force in N, A = cross-sectional area, l = initial length in metres and e = extension in m

46. Categories of materials Material variety: There are many materials now, all with different strengths and weaknesses. Some of the properties materials may have are: Ductility, brittleness, stiffness, density, elasticity, plasticity, toughness, fatigue resistance, conductivity, and fire resistance. The properties of individual material types can be illustrated clearly by sketching graphs of stress against strain. Ductile- materials that have a large plastic region (therefore they can be drawn into a wire); for example, copper. The strain on a ductile material may be around 50% Brittle- A material that distorts very little even when subject to a large stress and does not exhibit any plastic deformation; for example, concrete. Polymeric material- A material made of many smaller molecules bonded together, often making tangled long chains. These materials often exhibit very large strains (e.g. 300%) for example rubber.

47. Interpreting Stress-Strain Graphs Stress-Strain graphs for Ductile materials curve Yield point The material suddenly starts to stretch without any extra load. The yield point is the stress at which a large amount of plastic deformation takes place with a constant or reduced load. Stress (Nm-2) Strain Limit of Proportionality Stops obeying Hooke’s Law but would still return to original shape Elastic Limit Starts behaving plastically, and would no longer return to original shape once the stress was removed.

48. Interpreting Stress-Strain Graphs Stress-Strain graphs for Brittle materials don’t curve • Brittle materials obey Hooke’s Law. • When the stress reaches a certain point, the material snaps (it does not deform plastically). • When stress is applied to a brittle material any tiny cracks get bigger and bugger until the material breaks completely. This is called brittle fracture. Material fractures Stress (Nm-2) Strain

49. Interpreting Stress-Strain Graphs Rubber and Polythene are Polymeric Materials Polythene Rubber Loading Loading Stress (Nm-2) Stress (Nm-2) Unloading Unloading Strain Strain Rubber returns to its original length when the load is removed- it behaves elastically. Polythene behaves plastically- it has been stretched to a new shape. It is a ductile material.

50. Acceleration (a)- the rate of change of velocity, measured in metres per second squared (m s-2); a vector quantity Sample- definition Definitions