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Download BGE – Dynamics and Space Summary Notes
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BGE β Dynamics and Space Summary Notes Speed The speed of an object is defined as the distance the object can travel in a given time. The greater the speed, the greater distance it will travel in a given time. It is represented in the following equation: π ππππ = πππ π‘ππππ π‘πππ The distance is measured in metres (m). The time is measured in seconds (s). The speed is measured in metres per second (ms-1). Using their symbols, the equation can also be written like this: π£= π π‘ Notice the symbol for speed is the letter v, not the letter s We usually split different speeds into two groups: Average and Instantaneous. The difference between the two is the time each one is measured over. Average speeds are measured over a large time interval and instantaneous speeds are measured over a small time interval. Example 1 Calculate the average speed of a cyclist who travels 500m in 90 seconds. π£= π π‘ π£= 500 90 π£ = 5.6ms-1 Example 2 A speed trap system is set up to measure the instantaneous speed of a car as it passes a point on the road. The car is deemed to have travelled 8m in 0.2 seconds. What is the instantaneous speed of the car at this time? π£= π π‘ π£= 8 0.2 π£ = 40ms-1 Experiment to measure Average Speed To measure the average speed of a car (or any object), you need to time how long it takes to travel a certain distance. The following diagram shows the apparatus required to measure average speed: Carry out the following steps to calculate average speed: ο· ο· ο· ο· ο· Measure a length of track, d, using a measuring tape/trundle wheel. Mark a start and finish line on the track. Start the timer/stopwatch when the car passes the start line. Stop the timer/stopwatch when the car passes the finish line. Use the following equation to calculate average speed: ππ£πππππ π ππππ ππ πππ = πππ π‘ππππ πππ‘π€πππ π π‘πππ‘ ππππ πππ πππππ β ππππ π‘πππ ππ π‘βπ π‘ππππ/π π‘πππ€ππ‘πβ NOTE: This must be written as a word equation! Speed / Time Graphs Sometimes when we describe the speed of an object over a journey, we display this information visually on a graph. A typical speed / time graph is shown in the diagram below: For this graph, there are 3 stages to the journey. Stage 1 = OA Stage 2 = AB Stage 3 = BC The first stage of the journey shows the speed of the car increasing at a constant rate. We know the speed is increasing constantly as the graph is a straight line. As the graph is a straight line going diagonally upwards, we know the speed is increasing. The second stage of the journey shows the speed of the car is staying the same for a time indicated between points X and Y on the time axis. The time will always be shown on the x-axis going horizontally. Similar to before, the straight line at this stage tells us that something is constant. The final stage of the journey shows the speed of the car decreasing at a constant rate. Again the graph is a straight line so something is staying constant but this time the graph is downwards which means the speed is decreasing. Any speed / time graph will show how the speed changes for the entire journey however you can use the graph to work out several things: 1. The total distance is equal to the area underneath the speed - time graph. 2. The average speed is equal to the total distance travelled divided by the total time. Acceleration If an object is not travelling at a constant speed, then it will have an acceleration. If an object is accelerating then its speed is changing either getting faster or slower. If an object is getting faster, we say it has a positive acceleration and if itβs getting slower, it has a negative acceleration. Negative accelerations are sometimes referred to as decelerations. The acceleration of an object can be calculated using the following equation: πππππππππ‘πππ = πππππ π ππππ β ππππ‘πππ π ππππ π‘πππ The acceleration is measured in metres per second squared (ms-2). The final and initial speeds are both measured in metres per second (ms-1). The time is measured in seconds (s). Using the symbols, the equation can also be written like this: π= π£βπ’ π‘ Experiement to measure Acceleration To measure acceleration, you must measure the speed of an object at 2 points, therefore we need to use 2 light gates as shown below: The experiment is the same as the average speed experiment in that by going through the first light gate, we can work out the speed of the car at this point. By passing through the second light gate, we can work out the speed of the car again. This gives us an initial speed and a final speed. These numbers can entered into the acceleration equation to give us the acceleration. In this case, the time, t, is the time taken for the trolley to travel from one light gate to the other. Example 3 A car takes 5 seconds to reach a speed of 20ms-1. If the car starts from rest, what is the acceleration of the car? π= π£βπ’ π‘ π= 20 β 0 5 π = 4ms-2 An acceleration of 4ms-2 means that the speed of the car is increasing by 4ms-1 every second. Space Physics The Solar System All the planets in our solar system exist in an orbit around the sun. The sun is a star which is located at the centre and accounts for over 99% of our solar system! A star is defined as: a large ball of burning gas in space which produces light. All stars are examples of chemical reactions where the gas they are made of is used as a fuel source. Depending on the colour of the star, we can tell how much fuel the star is burning every second. If a star is blue, it is referred to as short β lived because it is burning lots of fuel in a very short time. This also means the temperature of the star is quite high. Stars which are red are referred to as long β lived because they use their fuel up over a longer time. Due to this, they donβt release as much heat energy as blue stars. There are 8 planets which currently make up the rest of the solar system and they are: 1. 2. 3. 4. 5. 6. 7. 8. Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune The solar system is defined as: the sun and all the planets which are in orbit around it. A planet is an object which orbits a star and is held by its gravitational field. The Sun is the closest star to Earth and it takes light roughly 8 minutes to travel from the Sun to the Earth. The Sun is one of billions of stars which make the Milky Way, the galaxy we belong too. A galaxy is defined as: a collection of billions of stars. Each of the planets in the solar system have their own moon(s). Some have more than one and are given different names, some are named after Greek and Roman Gods. The moons of the planet Uranus are even named after Shakespeare characters! A moon is defined as: a natural satellite of a planet. All these individual stars, moons, planets and galaxies make up the universe. We only usually talk in terms of our universe and as a result, the universe is defined simply as space and everything it contains. Light Years As distances between objects in space are typically very large, we talk about units of light years as opposed to metres. To calculate the distance of one light year, you use the same equation relating speed, distance and time: π£= π π‘ A light year is the distance travelled by light in one year. d=vxt d = 3x108 x (365x24x60x60) d = 9.46x1015m Example 4 Proxima Centauri is the nearest star to us at 4.2 light years away. How far is this in metres? d = 9.46x1015 x 4.2 d = 3.97x1016m Re-entry During any space shuttle mission, the Orbiter is travelling 25 times faster than the speed of sound. This speed must be reached to escape from the gravitational pull of Earth. When in space, this is not a problem. The speed of the orbiter is only a problem when trying to return to Earth. When the orbiter reaches the Earthβs atmosphere it hits against billions of gas particles which generate lots of friction. This friction causes the temperature of the orbiter to rise and can destroy it. Several techniques are used to protect the orbiter and the occupants: ο· ο· ο· Silica tiles are fitted to the underside of the orbiter. This acts as insulation which stops the temperature getting too high. The nose of the orbiter is designed to be very blunt to smash into the atmosphere and remove as many particles out of the way as possible. The orbiter hits the atmosphere at a large angle to ensure that it passes through the atmosphere rather than bounce off it. Forces Forces can change three things about an object. They can change an objects: ο· ο· ο· Shape Speed Direction Forces are measured using a Newton balance and are measured in units of Newtons (N). Newton balances contain a spring which will change its length when an object is placed on it. From here, the corresponding weight can be read off the scale. The weight of an object is related to the mass of an object. The mass is a measure of how many particles there are inside any object and is measured in kilograms (kg). The equation linking the mass and weight of an object is: Weight = mass x gravitational field strength The gravitational field strength is a value associated with each of the planets in the solar system. It is different for each planet because the mass and the radius of each of the planets are different. For planet Earth, g = 9.8 Nkg-1. If the gravitational field strength of a planet increases, the weight of anything on that planet will also increase. The same expression can be written in equation form as: W=mxg Example 5 Calculate the weight of a bag of sugar which has a mass of 0.5 kg. W=? Weight = mass x g m = 0.5 kg Weight = 0.5 x 9.8 Weight = 4.9N The weight of anything on Earth is equal to 9.8 times the mass. The factor of 9.8 comes from the Gravitational Field Strength on planet Earth. Each planet has a different gravitational field strength so a 1kg mass will have a different weight on each planet. There is gravity everywhere and it depends on how close you are to a planet. There is even gravity in space however because you are very far away the planet(s), the gravitational field strength will be very small. Due to this, the weight of any object will changed depending on where you are however the mass of the object will stay the same. Newtonβs Laws If any object is stationary or moving with a constant speed, we know that the forces acting on the object must be equal and opposite. 10N 10N In the above diagram, there is a force of 10N acting to the left and to the right. Both of these forces when added together, cancel the effect of the other and as a result, this block will either be moving with a constant speed or not moving at all. If the forces acting on an object are not balanced then the object will begin to accelerate in the direction of the unbalanced force. The same also applies to objects travelling vertically. If any object falls through the air, there is a downwards force provided by the weight. As the object travels downwards, there is an upwards force provided as the object rubs against millions of air particles. This is known as the friction force and it always acts in the opposite direction to the movement of the object. When anything falling through the air travels fast enough, it reaches a point where the friction force is equal and opposite to the weight of the object and at this point the object will travel downwards with a constant speed. At this point, we say the object has reached terminal velocity and will not get any faster. Newtonβs 2nd law Newtonβs first law deals with situations where the forces acting on an object are balanced. The second law deals with situations where the forces acting on an object are unbalanced. This can be both horizontal forces and vertical forces. If the forces acting on an object are unbalanced, it will experience a constant acceleration. This acceleration is proportional to the unbalanced force, shown by the following equation: Fu = m x a In the diagram shown above, the weight of the rocket is exerting a downwards force and the thrust is exerting an upwards force. Overall when both are taken into consideration, we can work out the unbalanced force which represents the combined effect of both of them. The acceleration acts in the same direction as this unbalanced force. Example 6 Calculate the acceleration of a car with a mass of 1000 kg if the unbalanced force acting on the car is 100 N. Fu = 100 N m = 1000 kg Fu = m x a 100 = 1000 x a 100 a = 1000 a = 0.1 ms-2 Example 7 A rocket of mass 500 kg produces has an engine which produces a thrust force of 10,000 N at lift off. a) What is the acceleration of the rocket at take off? b) Explain what happens to the acceleration of the rocket in the minutes after launch. a) Fu = Thrust β weight Fu = 10,000 β (m x g) Fu = 10,000 β (500 x 9.8) Fu = 10,000 β 4,900 Fu = 5,100N Fu = m x a 5,100 = 500 x a a= 5,100 500 a = 10.2ms-2 b) As the fuel is used up during the first few minutes, the weight of the rocket decreases. Since the thrust force from the engine remains constant, this means that the unbalanced force increases. Therefore the acceleration of the rocket increases. Satellites A satellite is the name given to any object which travels in orbit around a planet. There are many satellites in orbit around Earth, most of which are man-made. The Moon is an example of a natural satellite since we didnβt make it and it does travel around Earth. The Moon takes one month to orbit once completely around the Earth. For any satellite both man-made and natural, the period of the satellite depends only on the height of the orbit, i.e. the distance between the satellite and the centre of the Earth. If the height of the orbit increases, the period of the orbit will increase. Most satellites in orbit around Earth are man-made and are used every day. They are used to communicate with people on the other side of the world and are also commonly used for satellite navigation (SAT NAV) in cars: Satellite dishes used for communication e.g. Sky TV, rely on sending and receiving signals from all around the world using communication satellites in orbit as shown above. Any customer will have a satellite dish, known as a parabolic reflector on the side of their house: The parabolic reflector is designed to receive as many signals as it can from satellites in orbit where they reflect to one point called the focus / focal point. This is where the signal is the strongest to increase the quality of the signal. In winter, sometimes ice and snow can land on the dish and ruin the quality of the signal as the radio waves donβt focus at the one location. Any communication satellite must always stay in the one location relative to Earth at all times to be used accurately. These satellites are called Geostationary satellites. Geostationary satellites are defined as: a satellite which always stays above the same point above the Earthβs surface. Geostationary satellites have the same period as the Earth, 24 hours. To receive 24/7 world-wide communication between any two points on Earth you need a minimum of three geostationary satellites. GEO SAT 1 GEO SAT 2 GEO SAT 3
