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Level 1 Mechanics Notes Motion

Distance and Time Motion is a change in position of an object over time. The motion of an object (eg. car) is described using quantities like time, distance, speed and acceleration. Time (t) is measured in seconds (s) N  OTE: other units for time may be given eg. minute(min) or hour(h) converting into seconds could help sometimes depending on the question. Distance (d) is measured in meters  (m) NOTE: other units for distance are kilometer(km) and centimetre(cm) 1km= 1000m and 100 cm=1m Distance vs displacement Distance: How far. ("how much ground an object has covered" during its motion) Displacement: Shortest distance between the start and th end point ("how far out of place an object

is"; it is the object's overall change in position.) Speed Average speed is a measure of the distance travelled in a second, minute or hour. The average speed (v) for a journey is calculated from the total distance travelled divided by the total time taken to travel that distance (d/t), Average speed(velocity)=distance travelled/time taker OR v=Δd/Δt Instantaneous speed is the actual speed at any moment/ one instant in time. Eg. The speedometer in a car measures the instantaneous speed. The instantaneous speed of a car will usually change considerable during a journey. If the instantaneous speed does not change, then the speed is described as being constant, uniform or steady. If the speed in constant, the average speed is the same as the constant speed. NOTE: velocity and speed have the same unit (ms-1) Speed vs velocity Speed: How fast an object is traveling; rate of change of distance. Velocity:How fast an object is travelling in a certain direction (speed + direction) Distance-Time graphs Distance-time graphs show the time taken to travel a certain distance.The gradient gives information about speed. Gradient= change in y-axis/ change in x-axis = change in distance/ change in time. On distance-time graphs: ❏ The slope(gradient)of the graph represents the speed. ❏ A straight line has steady slope,and so represents constant speed. ❏ A horizontal line has slope, and so shows zero speed (not moving). The steeper the slope, the greater the distance travelled in the time taken, the greater the speed.

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When the distance-time graph is not a straight line, the slope is changing and so the speed is changing. ❏ The slope increasing shows acceleration (speeding up) ❏ The slope decreasing shows deceleration (slowing down)

Example of distance-time graph: ❏ A- speeding up (accelerating)because the slope of the graph line is increasing ❏ B- Constant speed because the graph line is straight. ❏ C- slowing down (decelerating) because the slope is decreasing ❏ D-stopped because the graph line is straight and horizontal.

Acceleration Acceleration is how quickly the motion is changing. When the speed of an object changes, either by slowing down or speeding up, the object is accelerating NOTE: Accelerating can apply to an object that is slowing down or speeding up. Deceleration is negative acceleration. If an object is accelerating, there is a net force acting on it. Average acceleration is a measure of how much the speed is changing every hour, minute or second. Average acceleration, symbol a is calculated from the change in speed divided by the time taken for the change in speed to occur. The unit for acceleration is a speed unit divided by a time unit. If the sped is in ms-1 and the time is in seconds (s) then the acceleration unit is ms-1/s=ms-2 and is read as “metres per second per second” or “meters per second squared”. E.g. an acceleration 5 ms-2 means that the speed is increasing by 5 ms-1 every second. a= Δv/Δt

Speed-time graphs A speed-time graph gives information about acceleration/ how an object’s speed changes over time. The slope (gradient) of a speed against time is found from: Slope= change in speed/time taken=acceleration On a speed-time graphs: ❏ The slope of the graph represents acceleration ❏ A straight line has a steady slope, and so represents constant acceleration

❏ A horizontal line has zero slope, and so shows zero acceleration, which is constant speed ❏ The steeper the slope, the greater the change in speed in the time taken,so the greater the acceleration. Distance travelled A speed-time graph also gives information about the distance an object has travelled.

The area of the shape under the plotted graph line down to the time axis, between any two time values, is the distance that has been travelled during the time interval.

In the time interval t=0 to t=t1, under the graph line, we are measuring the area of the rectangle. Area=base x height => d=t1 x v1 In the time interval t=t1 to t=t2, the are under the graph line is the area of a rectangle plus the area of a triangle: area= (base x height)+ ½(base x height) => d= (t2-t1) x v1+½(v2-v1) Forces Introduction Forces are pushes or pulls. For example: ❏ Gravity pulls everything downwards towards the centre of the earth. ❏ If a box is resting on a table,because gravity is pulling it downwards, the box pushes down against the surface of the table. ❏ On a very windy day, the motion of the air, causing the wind, pushing against a tree and could push it over (force it downwards in the direction of the wind). Sometimes, forces make an object change its motion. A change in motion means that either the speed changes or the direction of the motion changes. A change in speed means acceleration or deceleration, i.e. An object is getting faster or slower. Sometimes forces change both speed and direction.E.g. when a ball is thrown up in the air , gravity pulls downwards on the ball, making it slow down on the way up, change direction and accelerate back down to the ground. A force F, has a size and a direction. The size of a force is measured in newtons (N). An arrow is used to show the direction of a force. Forces act on everything. Often, there is more than one force acting, and when this happens, it is a combined force called the net force. Force acting in the same direction add together, while forces acting in opposite directions are subtracted. The following diagrams have the same effects. - The forces in the second example are described as balance, because they combine to give zero net force. - The force in 1 and 3 are described as unbalanced, because their combined effect is not zero. - The force in the last diagram, to calculate the resultant force use pythagoras.

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Types of Forces: ➔ Contact forces act at the point of contact between 2 objects. Support is a force exerted by a surface that opposes the force of gravity. Push or Pull are forces exerted by people, animals or machines. ➔ Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. ➔ Tension is a pulling force exerted by a string or cable. ➔ Contact forces also act between an object and a liquid or gas Buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object.) Thrust when an object pushes gas or liquid it creates this force in the opposite direction. Drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers or a fluid and a solid surface.) Lift an upward force from a flow or air over an aerofoil or water over a hydrofoil. Non contact forces act between objects that are not touching. A gravitational force is the force of attraction between two objects due to their mass. A magnetic force is the force created by magnets. It can attract or repel. An electric force is the force created by electric charges. It can attract or repel.

Net force Net force is the single force which has the same effect as a combination of forces added head to tail. Forces, mass and acceleration When the forces acting on an object are unbalanced, the net force will make the object accelerate or decelerate. There is an important relationship between the net force, acceleration and mass: F=ma where: F is the combined force of N, m is mass in kg and, a is acceleration in ms-2. F is directly proportional to a, so if one increase so does the other. a is directly proportional to F, so if 1/m increases a decreases. M is inversely proportional to A.

The triangle allows you to rearrange the formula so you can find a, m or F.

Force and acceleration When different net forces are applied to the objects of the same mass, a greater net force produces a greater acceleration. Mass and acceleration When the same force is used to accelerate two different masses, the smaller the mass the greater the acceleration. Mass and weight

Mass is the amount of matter in an object, Since the amount of matter making up an object does not change, the mass also the same wherever the object is. Mass is measure in kg or g. In Science, the weight of an object is the force with which the object pushes down on whatever it is resting on. Weight is caused by gravity pulling an object downwards. The force of gravity on an object is often called weight force because they both have the same size. Like all forces weight is measured in Newtons. The weight in Newtons is always 10 times the mass in kg. This is because weight is calculated by multiplying the mass by gravity. The value of g (gravity) is 10 N per kg, 10 Nkg-1, on the surface of the earth. This means that every kilogram of mass pushes down with a weight of 10N. weight= mg m is mass and g in 10 Nkg-1. The value of g is often called the acceleration of gravity, because, if an object is dropped, it accelerates downwards with an acceleration that has the same value as g. E.g. at 10ms-2. Friction Friction is a force which is created as soon as something tries to slide past something else. Friction doesn’t exist until the sliding attempt starts, and so friction is called a reaction force. Friction always opposes the sliding motion. The more the two sliding surfaces press together, the more friction is generated. The rougher the sliding surfaces, the more friction is generated. Friction can happen between: - Two solid objects- e.g.dragging a bag of cement across the floor - Solid and liquid- e.g. a person wading through water. - Solid and air- e.g. air resistance when cycling into a head wind. - Liquid and air- e.g water falling over a waterfall is turned into spray by friction with the air. Friction can be useful, but sometimes it is a nuisance. Friction being useful

Friction being a problem

Car and bicycle tyres have tread to “grip” the road.

Friction causes surfaces in machinery to heat and wear out.

Parachutes work because of friction with air.

Friction with the air slows moving vehicles down.

Brakes on cars and bicycles use friction to slow down and stop them.

Friction can cause abrasions if a person falls over.

Friction can be reduced by: ❏ Lubricating oil and grease between surfaces. ❏ Wheels or ball-bearings to roll the surfaces past each other. ❏ Streamlined shapes to keep air resistance to a minimum. ❏ Cushions of air, as in a hovercraft. Static friction is the friction which stops sliding motion from starting. If a block of wood, resting on the floor, is pulled gently, friction starts up and matches the pulling force, but in the opposite direction, so the block doesn’t move.The harder the pull, the greater the friction force that is generated. It is called the static friction force and is different for different surfaces. If the pull gets larger than the static friction between a block and the floor, the block will accelerate across the floor.

Air resistance If an object is dropped and allowed to fall downwards through the air, its slow speed causes little drag. The resulting net force causes the object to accelerate downwards. (the pull of gravity makes it accelerate at 10 ms-2). However, air resistance (upwards friction) increases as the object moves faster and so the net downwards force (gravity force, less friction force) gets smaller. Eventually, the downwards pull of gravity is balanced by the upwards air resistance. When this happens, there is zero net force and so no more acceleration. The object continues to fall at whatever speed it had reached when the forces became balanced. This speed is called terminal speed. However, if a parachute is released, the drag suddenly increases. The resulting force causes the object to accelerate. Drag decreases as the object slows down and force become balanced. E.g. Terminal speed is important when a skydiver jumps from a plane. ❏ The downwards pull of gravity stays constant because the mass of the skydiver stays constant. ❏ As the skydiver falls faster, the upwards friction force (air resistance) increases. ❏ Eventually the upwards air resistance force and downwards gravity force become equal and the speed stops increasing. The skydiver in free fall, terminal velocity is about 200 km h-1. When the skydiver opens their parachute, their air resistance increase markedly; their terminal velocity is now small enough to land safely. Balanced Forces When the forces acting on an object are balanced, it means all the forces combine to cancel each other out and so the net force is zero.If there is no net force, there can be no acceleration. If there is no acceleration there is no change in speed, which means the object could either be stationary or travelling at a constant speed. If the forces on an object are unbalanced, then the object will accelerate. E.g. when a book rests on a table, the downwards push of the book’s weight is balanced by any upwards push force from the table. The upwards push from the table is called a reaction force because it happens only if the book pushes downwards. Pressure Pressure is the force per unit area acting on a surface. As well as being able to change motion, a force is sometimes able to change the shape of whatever it is acting on. ❏ If someone stands on soft, wet sand, their feet may sink into the sand a bit. The weight force of the person has changed the shape of the surface of the sand. ❏ When making bread, a baker kneads the dough. The push force of the baker’s hands on the bread dough is constantly changing its shape. The amount of change a force can make in the shape of whatever it is acting on depends on the pressure the force is able to create. Pressure depends on the area over which a force is acting. Pressure= force/area => P=F/A. Units: ● Newtons per square metre Nm-2 ● Pascal - Pa Air Pressure

Air is the collective term for the mixture of gases that makes up the Earth’s atmosphere. The molecules of these gases are constantly on the move, in random directions, and they are constantly hitting against anything that is in the air. This continual bombardment of air gas molecules is called air pressure. The pressure of the air at sea level is about 101 kNm-2. This is the same as 10N force on every square centimetre. Living creatures on Earth have adapted to this pressure, and it isn’t noticed.

Energy Energy ‘makes things happen’. Energy takes many different forms and changes readily from one form to another. Energy is defined as the capacity to do work which is the capacity to exert a force that will cause motion. It is measured in Joules. Active Energy Some forms of energy are active; their effects are easily seen or detected. Active forms of energy are: - Kinetic energy, Ek- the energy of an object when it is moving. - Light energy - Heat energy - Sound energy Potential energy Forms of energy which are stored and only have an effect when they are changed to active energy are called potential energy, Ep. Some forms of potential energy follow. ❏ Chemical potential energy- changed to active energy by chemical reactions. Food, fuels and explosives contain chemical potential energy. ❏ Elastic potential energy- energy stored when a material is stretched or compressed. It is changed from active energy when the tension is released. ❏ Gravitational potential energy- The energy an object gains when it is lifted up. This energy is changed to active energy when the object falls down. ❏ Electrical energy- Energy that is stored in a power source (e.g battery). This energy is changed to active energy when the circuit is switched on. ❏ Nuclear energy- energy that is stored in a nucleus. This energy is changed to active energy in nuclear reactors or atomic bomb explosions. Solar energy (light, heat and other of energy) is produced from nuclear reactions within the sun. All forms of energy are measured in Joules (J). 1 kJ= 1000 J. Gravitational potential energy Gravitational potential energy (GPE) is the potential energy an object has because of its height. The unit for GPE is Joules. When the height of an object changes, its GPE changes. The higher the object is lifted the greater the GPE. The following equation is used to find the increase in GPE when an object is lifted:

ΔEp= mg x Δ h Where: Δ Ep is the increase in gravitational potential energy in joules, J. M is the mass, in kilograms of the object being lifted. g is the strength of gravity 10 Nkg-1 Δh is the change in height, in metres. Since g is always 10, the formula ΔEp= mgΔh becomes: ΔEp= mx 10 Δh

When an object’s height decreases, the object loses gravitational potential energy. The same formula (ΔEp= mg x Δh) is used to calculate the loss in GPE. When calculating the change in GPE, it is the vertical change in height which must be used in the calculation. An important use made of GPE is in hydroelectric power stations. Water stored behind the dam has GPE. The water goes through an exit at the top of the dam and drops to the bottom of the dam. As the water falls, GPE is changed into kinetic energy. At the bottom of the dam, the kinetic energy of the water is changed into electrical energy by the turbines in the power station.

Kinetic energy Kinetic energy, Ek, is the energy an object has because it is moving. The unit for kinetic energy is the joule, J. Ek= ½ mv² Where: M is the mass is kg. V is the speed in ms -1. Kinetic energy and mass The greater the mass of a moving object, the greater the kinetic energy of the object. If the mass of the object doubles and the speed remains the same, the kinetic energy will double. Kinetic energy and speed The faster an object moves, the greater the kinetic energy. When the speed of an object doubles and the mass remains the same, the kinetic energy is four times what it was. This is because the amount of kinetic energy is related to the square of the speed. This means that: - If the speed doubles, the kinetic energy increases to 4 times its original value (2²=4)  - If the speed increases by 3 times, the kinetic energy increases to 9 times its original value (3²=9). The relationship between speed and kinetic energy has important consequences for road safety. If a car doubles its speed, there is four times the amount of kinetic energy to lose before the car becomes stationary. With the same brakes used in the same way, it will take a car travelling twice as fast about four times the distance to stop.

If a moving car has an accident, such as hitting a power pole, large amounts of Kinetic energy must be ‘converted’ very suddenly. Doubling the speed of a car increases the risk of injury and damage by a factor of four. Energy transformation Energy can be readily changed from one type to another. Eg.- A rock on top of a cliff (GPE), that becomes dislodged will fall to the ground below (kinetic energy) - A garage door often has a spring (elastic potential energy) to make it easier for the door to raise (gravitational potential energy) the door. Conservation of energy The principle of conservation of energy states that ‘energy cannot be created or destroyed, but can only change from one form to another’. It is impossible to make energy from nothing. E.g. motor vehicles can gain kinetic energy (speed up) when rolling down a hill. The energy has come from gravitational potential energy (drop in height) Work Work, W, is is the energy transferred when a force makes an object move from ...