Year 10 Physics Workbook The Polesworth School Forces ..., Lecture notes of Physics

Download Year 10 Physics Workbook The Polesworth School Forces ... and more Lecture notes Physics in PDF only on Docsity! Year 10 Physics Workbook The Polesworth School Forces and Motion 1 By the end of this booklet you should know the answers to all the common questions below Question Answer 1 What is a "scalar quantity"? A quantity with magnitude (size) only 2 What is a "vector quantity"? A quantity with both magnitude and direction 3 Define "speed" Rate of change of distance 4 Define "velocity" Rate of change of displacement 5 Define "displacement" Distance and direction 6 Give three examples of scalar quantities Distance, mass, energy 7 Give five examples of vector quantities Displacement, weight, force, velocity, acceleration 8 Define "acceleration" Rate of change of velocity 9 What is a typical speed for walking? 1.5m/s 10 What is a typical speed for running? 3m/s 11 What is a typical speed for cycling? 6m/s 12 What is a typical speed for a car? 15m/s 13 What is a typical speed for a train? 90m/s 14 What is a typical speed for a plane? 250 m/s 15 What is a typical speed for sound in air? 330m/s 16 What formula relates speed, distance and time? Speed = distance/ time 17 Describe speed and velocity in circular motion (HT) Constant speed, changing velocity 18 Give the formula for acceleration Acceleration = Change in velocity / time 19 What is acceleration due to gravity near Earth's surface? 9.8m/s2 4  A higher (steeper) gradient means a higher speed. In the graph above, the red line has a gradient of 120 ÷ 10 = 12m/s. The blue line has a gradient of 40 ÷ 10 = 4m/s. The green line has a gradient of 0, i.e. the object is stationary (stood still). 5 Questions 1. Copy the axes onto squared paper or use the one below: Draw lines to show the motion of an object that travels: a) 60m in 5s b) 100m in 5s c) 20m in 5s 2. Find the speed for each of the objects in (1) 6 3. Copy these axes onto squared paper or use the one below: Draw lines to show the motion of: a) An object that travels 10m in 10s b) An object that travels 100m in 10s c) An object that travels 40m in 10s. 4. Find the speeds of each of these objects. 9 Distance and displacement An object has a position relative to its surroundings at any instant in time. When an object moves, it changes its position. Distance is a scalar quantity that refers to “how much ground an object has covered” during its motion. Scalar quantities just have a number (magnitude). Displacement is a vector quantity that refers to “how far and in what direction the object’s position has changed”. Vector quantities have a magnitude and direction. Consider an object that starts at position A, and then moves to B, C and finally to D. The distance travelled by the object is (6 + 1.5 + 4) = 11.5m. The displacement of the object is 6.5m to the right. Questions 1. Define “distance” 2. Define “displacement”. 3. Draw a diagram to show the difference between distance and displacement. 4. Which quantity is a vector quantity: distance or displacement? 5. When people say “As the crow flies” are they referring to distance or displacement? 6. True or false: For a single object in motion, displacement can be equal to distance but it can never be bigger. 7. A car starts at A and travels to B, then to C, and then back to B. What is a) the distance travelled and b) the displacement of the car? 10 8. a) What is the displacement from B to A? b) What is the distance? 9. A walker travels from A to B, C, D, E and F. What is the distance travelled? What is the displacement? Calculating velocity and speed Speed is the rate of change of distance: Speed = distance ÷ time Distance = speed x time Speed is a scalar quantity: it only has magnitude, e.g. 14m/s Velocity is like speed, but it’s a vector quantity, so it always has direction as well as speed. This is because velocity is rate of change of displacement and displacement is a vector quantity. Velocity = displacement ÷ time 11 Displacement = velocity x time However, people often use the word “velocity” without stating a direction – this is sloppy but very common. Questions 1. Define speed 2. Define velocity 3. What is the difference between speed and velocity? 4. Find the velocity of a car which travels 25m to the right over a period of 10 seconds. 5. What is the velocity of a hot air balloon which travels 125m up in a time of 50 seconds? 6. A diver travels 640m down during a 16-second dive. Find his velocity. 7. What is the displacement of a rocket travelling at a velocity of 150m/s up for 30 seconds? 8. Find the displacement of a beetle crawling for 180 seconds at a velocity of 0.25m/s to the left. 9. A car has a velocity of 24m/s to the right and travels for 58 seconds. Find its displacement. 10. A car travelling at a velocity of 2.75m/s travels for 185 meters. What time was taken? 11. Find the time taken by a rocket travelling at a velocity of 240m/s to reach a displacement of 15,000m. 12. A snail travels with a velocity of 0.08m/s. It reaches a displacement of 0.2m. Find the time taken. 14 5. What acceleration takes an object to 8m/s from 20m/s over a period of 3s? 6. An object starts at 100m/s and decelerates to 75m/s over a period of 5 seconds. Calculate the deceleration. 7. Find the deceleration of an object starting out at 45m/s and reducing its speed to 13m/s over a period of 12s. 8. An object with initial velocity of 48m/s decelerates to 3m/s over a period of 30s. What is the deceleration? 9. An object starts at rest and accelerates to 14m/s over a period of 3.5s. Find the acceleration. 10. An object accelerates to 105m/s from rest in 55s. Calculate the acceleration. 11. What acceleration takes an object from rest to 64m/s in 4s? 12. An object travelling at 35m/s slows to a stop over a period of 70s. What is the deceleration? 13. Find the deceleration when an object comes to rest from 12m/s over a period of 2.5s. 14. What deceleration occurs when an object travelling at 58m/s comes to rest over a period of 4s? 15. How long would it take an object with deceleration 2m/s2 to go from 10m/s to 4m/s? 16. What time would it take an object with acceleration 4.3m/s2 to accelerate from 9m/s to 85m/s? 17. For an object with acceleration 0.45m/s, find the time taken to accelerate from rest to 3m/s. 18. For an object with an acceleration of 6m/s2, what is the change in velocity over 15s? 19. For an object with an acceleration of -18m/s2, what is the change in velocity over 76s? 20. For an object with an acceleration of 0.9m/s2, what is the change in velocity over 200s? 15 Acceleration on a distance-time graph (HT) Acceleration is defined as rate of change of velocity. Since velocity is equivalent to the gradient on a distance-time graph, and accelerating object will have a changing gradient, i.e. a curved line:  This graph shows an object with increasing speed (positive acceleration) as the gradient is getting higher (steeper). 16  This graph also shows an object with positive acceleration (increasing speed). It looks different because this object is travelling backwards instead of forwards.  This graph shows an object moving forward with negative acceleration, i.e. slowing down. The gradient is decreasing. 19 12. Find the speed of the object in this graph: a. At 7 seconds b. At 11 seconds c. At 13 seconds d. Is the object moving forwards or backwards? e. Is the object accelerating or decelerating? 20 13. Find the speed of the object in this graph: a. At 7 seconds b. 10 seconds c. 12 seconds d. 14 seconds e. Is the object moving forwards or backwards? f. Is the object accelerating or decelerating? 21 14. Find the speed of the object in this graph: a. At 3 seconds b. At 6 seconds c. At 9 seconds d. Is the object moving forwards or backwards? e. Is the object accelerating or decelerating? 15. Find the speed of the object in this graph: a. At 3 seconds b. At 5 seconds c. At 8 seconds. d. Is the object moving forwards or backwards? e. Is the object accelerating or decelerating? 24 This graph shows an object moving at a constant velocity (steady speed). The gradient is 0 (horizontal line), so the acceleration is 0. Note this does not mean the object is stationary. In this example, the object is moving at a steady speed of 4m/s. 25  This graph shows an object which is stationary. The line shows the velocity stays at 0 for the time shown. Note that stationary is a form of constant velocity: the gradient is 0 (the line is horizontal). 26  This graph shows an object which is accelerating. The line has a gradient (it is sloping). The speed is changing. It starts off at 0m/s, and after 10 seconds it has increased to 2m/s. 29 Questions: State what each graph shows: acceleration, constant velocity, negative acceleration, or stationary: 30 Finding acceleration from the gradient of a velocity-time graph Because acceleration is change in velocity ÷ time, we can find acceleration of an object by finding the gradient of a velocity-time graph. The first thing we need to know is that: Change in velocity = final velocity – initial velocity = end speed - starting speed Change in velocity = 2 – 0 = 2m/s Acceleration = 2 ÷ 10 = 0.2m/s/s. We have to be careful to use change in velocity, not final velocity: 31 Change in velocity = 8 – 2 = 6m/s Acceleration = 6 ÷ 10 = 0.6m/s/s. ZL time ( fe 2) Ayooran N hu) Ajoot OjaA, time (s) (au fyoolan A} 2) Ayooren timé ( timé ( 34 35 Velocity-time graphs practice 1. A car on a journey: 2. A skier sking down a slope: 36 3. Velocity of the barge after the girder has been lifted: 39 6. An object is accelerated from 105m/s to 110m/s over a distance of 13m. What is the acceleration? 7. An object travels with an acceleration of 3.1m/s2. After it has travelled for 700m, it has reached a velocity of 207m/s. Find its initial velocity. 8. Find the initial velocity of an object travelling with an acceleration of 2.1m/s2, which after having travelled for 900m, has reached a velocity of 607m/s. 9. An object accelerates at a rate of 1.8m/s2. If it accelerates over a distance of 1600m, what must its initial velocity be in order to reach a final velocity of 560m/s? 10. An object has initial velocity 2m/s, final velocity 3m/s, and an acceleration of 0.25m/s2. Find the distance travelled. 11. What distance is travelled by an object travelling first at 6m/s, accelerating at 4m/s2 to a final velocity 30m/s? 12. An object has initial velocity 20m/s, final velocity 300m/s, and an acceleration of 18m/s2. Find the distance travelled. 13. An object has initial velocity 4m/s, final velocity 3m/s, and an acceleration of - 0.25m/s2. Find the distance travelled. 14. Find the final velocity of an object whose initial velocity is 400m/s, is travelling with an acceleration of -14.8m/s2, and travels for 240m. 15. An object travels with an acceleration of -3.1m/s2. After it has travelled for 700m, it has reached a velocity of 207m/s. Find its initial velocity. 16. What acceleration is needed to bring an object from a speed of 98m/s to a speed of 15.9m/s over a distance of 35m? 17. An object accelerates from rest to a velocity of 5m/s. If the acceleration is 0.9m/s2, calculate the distance travelled. 40 18. An object accelerates from rest to an unknown speed. If the object accelerates at 5m/s2 and travels for a distance of 15m, what is the final speed? 19. An object at rest begins to move and reaches a final speed of 165m/s after accelerating over a distance of 30m. What is the acceleration? 20. A moving object slows to a standstill at an acceleration of -20m/s2. If the distance travelled is 60m, find the initial velocity of the object. 21. A car travelling at 35m/s crashes into a wall and is stopped over a distance of 10.2m. Find the acceleration of the car. 22. A stone is dropped and is travelling at a speed of 1.3m/s just before it hits the ground. If the acceleration is -135m/s2, find the distance travelled into the ground by the stone. 41 Newton's Third Law Newton's Third Law states that: “For every action there is an equal and opposite reaction” What this means is that because forces are interactions between pairs of objects, forces always come in pairs. We call these “Newtonian pairs”. Consider an apple falling from a tree: The Earth pulls on the apple with a force of 1.5N. What’s surprising is that the apple is also pulling on the Earth with a force of 1.5N. The apple is the thing we see accelerating, because its mass is small enough for 1.5N to create a significant acceleration. Newton’s second law, F = ma is responsible for this. Let’s look at another example: two positively charged spheres, A and B: 44 Questions 1. State Newton’s third law. 2. What is a “Newtonian pair”? 3. Copy the diagram showing the gravitational forces between the Earth and an apple. 4. Why doesn’t the Earth appear to be affected by the force exerted on it by the apple? 5. Copy the diagram showing the tension forces on the rope and the person pulling the rope. 6. Copy the diagram showing the normal forces between the book and the table. 7. What are the four characteristics of the forces in Newtonian pairs? 8. Copy and complete the following diagrams to show the second force in the Newtonian pair: a. b. normal force of the Jaron the desk: 5N tension force of bauble pulling ‘on string: 0.04N gravitational force of the Earth on the Sun:6 x 10°N 45  normal force of wall an arm: 4.7N Normal force of water on ship: 345,000N tension force of rape on swing: 860N 46 49 5. Acceleration = 2.4m/s2 Force = 75N Mass = ? 6. Acceleration = 0.6m/s2 Force = 5,000N Mass = ? 7. Force = 13kN Mass = 58kg Acceleration = ? 8. Force = 960N Mass = 21kg Acceleration = ? 9. Force = 0.4N Mass = 76kg Acceleration = ? 10. What force is needed to accelerate a mass of 10kg at a rate of 2m/s2? 11. An unknown force causes a mass of 180kg to accelerate at a rate of 90cm/s2. Calculate the magnitude of the force. 12. Nasa wish to accelerate a satellite of mass 460kg at a rate of 98m/s2. What force will they need? 13. An unknown mass is accelerated at 43m/s2 when a force of 700N is applied to it. Find the mass. 50 14. What is the mass of an object if a force of 57N is needed to accelerate it by 0.6m/s2? 15. A force of 0.5N causes an object to accelerate at 24cm/s2. Find the mass of the object. 16. A force of 430N is applied to a mass of 2.8kg. Find the acceleration. 17. What acceleration will an object of 5kg undergo if a force of 90N is applied? 18. Find the acceleration of a 360kg object when a 0.2N force is applied. Circular motion (HT) Uniform circular motion involves an object with a tangential motion and a force acting towards the centre of the circle. Consider a satellite orbiting the Earth: As the satellite travels on its circular path around the Earth, its velocity is constantly changing as it is changing direction. At any given moment, the satellite’s velocity is a tangent to the circle. There is a force constantly acting towards the centre of the circle: the force of the Earth’s gravity on the mass of the satellite. This force on the satellite causes it to accelerate: its direction constantly changes although its speed is constant. The acceleration is towards the centre of the circle: the satellite’s direction is constantly changing towards the centre of the circle. 51 In physics we do a demonstration with a bung on a string which we whirl around in a circle: As the bung travels on its circular path around the pupil’s hand, its velocity is constantly changing as it is changing direction. At any given moment, the bung’s velocity is a tangent to the circle. There is a force constantly acting towards the centre of the circle: the force of the string’s tension on the bung. This force on the bung causes it to accelerate: its direction constantly changes although its speed is constant. The acceleration is towards the centre of the circle: the bung’s direction is constantly changing towards the centre of the circle. 54 12. Christine observes an object moving with circular motion in an anti-clockwise direction. She knows that at any given moment this object has a force acting on it, a velocity and an acceleration. Copy the diagram and state the direction of each of these quantities. You may add arrows to the diagram if you wish. Newton’s First Law Newton’s first law states that: “When the resultant force on an object is zero: A stationary object will remain stationary; A moving object will continue to move at a constant velocity.” This means that a resultant force is needed to: • start a stationary object moving • slow down a moving object • speed up a moving object • stop a moving object • change the direction of a moving object This is counter-intuitive for a couple of reasons. 1. It is natural to think that if an object is moving it must have a resultant force acting on it – but this is false. Often in everyday life we need to apply a force to an object to keep it moving, such as sliding a book along a desk, but this is because we need to overcome the force of friction. 55 2. When objects keep moving, such as a kicked ball, it is natural to think they have a force propelling them forward – but this is false. If we look at a free-body diagram of an object, showing the forces on it, it is impossible to tell whether the object is moving or stationary. What we can tell is whether it has a constant velocity or is accelerating. In everyday life we tend to distinguish between “moving” and “not-moving”. In physics, we distinguish between “constant velocity” and “accelerating”. Questions 1. State Newton’s First Law. 2. This object is accelerating. Why? 3. This object is either at rest or travelling at a constant velocity. Why? 56 Inertia (HT) Objects with mass have a tendency to resist changes to their motion. This tendency is called inertia. Consider a 10kg block at rest: It will be fairly difficult to get it moving at 5m/s. Once it is moving at 5m/s, it will be fairly difficult to get it to slow down or stop. A 20kg block will be twice as difficult to get moving at the same speed. it will also be twice as difficult to stop from the same speed. The 20kg block has twice as much inertia as the 10kg block. Closely related is the concept of inertial mass. Inertial mass is a measure of how difficult it is to change the velocity of an object. inertial mass = force ÷acceleration Questions 1. Define “inertia” 2. Which has more inertia, a moving 2kg block or a stationary 6kg block? 3. What does “inertial mass” measure? 4. Give the formula for inertial mass. 5. An object requires 200N to accelerate it by 5m/s. Calculate its inertial mass in kg. 59 9. The manufacturer of a family car gave the following information. Mass of car 950 kg The car will accelerate from 0 to 33 m/s in 11 seconds. (a) Calculate the acceleration of the car during the 11 seconds. (b) Calculate the force needed to produce this acceleration. (2) (c) The manufacturer of the car claims a top speed of 110 miles per hour. Explain why there must be a top speed for any car. 10. The graph shows how the vertical velocity of a parachutist changes from the moment the parachutist jumps from the aircraft until landing on the ground. Using the idea of forces, explain why the parachutist reaches a terminal velocity and why opening the parachute reduces the terminal velocity. 60 Stopping distance When a driver sees something that means they need to break, nerve signals must travel around the body in order for the foot to press the brake pedal. The foot does not press the brake immediately but a short time after the hazard is seen. This time is called the thinking time. When a car brakes, the breaking force acts on it to reduce its velocity to zero. The car does not stop immediately but takes an amount of time to come to a stop. This time is called the braking time. The car travels during these times. The distance travelled during “thinking” is called the thinking distance. Thus we can define thinking distance as “the distance travelled while the need to brake is processed by the nervous system”. The distance travelled during braking is called braking distance. Thus we can define braking distance as “The distance travelled while the braking force decelerates the car to 0 velocity”. The total of these two distances is called the stopping distance. Thinking distance + braking distance = stopping distance 61 For a given braking force, the greater the speed of the vehicle, the greater the stopping distance. Questions 1. What is “thinking distance”? 2. What is “braking distance”? 3. What is “stopping distance”? 4. For a given braking force, what is the relationship between speed and stopping distance? 64 Momentum can be described as the amount of movement an object has. If an object is moving faster it has more movement, and a more massive object has more movement than a less massive one at the same speed. Because momentum depends on both mass and velocity, it is possible for a lorry and a bullet to have equal momentum: Questions 1. Write the formula for momentum 2. What are the units of momentum? 3. What two things is momentum a product of? 4. mass = 4kg velocity = 12m/s momentum = ? 5. mass = 118kg velocity = 0.2m/s momentum = ? 65 6. mass = 45kg velocity = ? momentum = 90kgm/s 7. mass = 200kg velocity = ? momentum = 67kgm/s 8. mass = ? velocity = 16m/s momentum = 64kgm/s 9. mass = ? velocity = 58m/s momentum = 232kgm/s 10. Find the momentum of an object of mass 23kg travelling at a velocity of 4m/s 11. A trolley of mass 1.2kg has a velocity of 5.1m/s. Find its momentum. 12. An object has a momentum of 58kgm/s and a mass of 12kg. Find its velocity. 13. Find the velocity of a cart with a momentum of 90kgm/s if its mass is 63kg. 14. What is the mass of a truck if it has a momentum of 18,000kgm/s at a velocity of 3.4m/s? 15. Find the mass of an object with mass 37kg and momentum 780kgm/s. 16. Find the momentum of each trolley: Conservation of momentum The principle of conservation of momentum: “In a closed system, the total momentum before an event is equal to the total momentum after the event.” A closed system is an object or group of objects to which no energy is added and from which no energy is removed. 66 We consider two types of events: explosions and collisions. Explosions In an explosion, two (or more) objects start off touching each other and at rest. The explosion occurs, sending each object off in opposite directions. Because they are travelling in opposite directions, their momentums can add up to 0. This means that momentum will be conserved as momentum before the explosion was 0. The object with a lower mass moves with a higher velocity, while the object with a higher mass moves with a lower velocity. (This is because of inertia and F=ma.) The momentum of the two objects is equal but opposite. Because momentum is a vector quantity, the momentums of the two objects add up to give 0. Therefore momentum is conserved – it is the same before and after the explosion. We say “in a closed system”, because if energy was added to or taken away from the two objects, the velocity would be increased or decreased and momentum would not be conserved. 69 (b) The space shuttle takes 9 minutes to reach its orbital velocity of 8100 m/s. (i) Write down the equation that links acceleration, change in velocity and time taken. (ii) Calculate, in m/s2, the average acceleration of the space shuttle during the first 9 minutes of its flight. (iii) How is the velocity of an object different from the speed of an object? 3 The diagram shows an orbiter, the reusable part of a space shuttle. The data refers to a typical flight. (a) (i) What name is given to the force which keeps the orbiter in orbit around the Earth? (ii) calculate the kinetic energy, in joules, of the orbiter while it is in orbit. (iii) What happens to most of this kinetic energy as the orbiter re- enters the Earth’s atmosphere? (b) After touchdown the orbiter decelerates uniformly coming to a halt in 50 s. (i) Calculate the deceleration of the orbiter. Show clearly how you work out your answer and give the unit. 70 (c) Calculate, in newtons, the force needed to bring the orbiter to a halt. Show clearly how you work out your answer. 4. The figure below shows the horizontal forces acting on a car. (1) a) Will the car be accelerating, decelerating, or travelling forward at a constant speed? b) During part of the journey the car is driven at a constant speed for five minutes. In this time it covers a distance of 5km. What is the speed of the car? (1) (c) During a different part of the journey the car accelerates from 9 m/s to 18 m/s in 6 s. Calculate the acceleration of the car. (d) The mass of the car is 1120 kg. The mass of the driver is 80 kg. Calculate the resultant force acting on the car and driver while accelerating. (e) Calculate the distance travelled while the car is accelerating. (h) A car driver sees a fallen tree lying across the road ahead and makes an emergency stop. The braking distance of the car depends on the speed of the car. For the same braking force, explain what happens to the braking distance if the speed doubles. You should refer to kinetic energy in your answer. 71 5. The diagram below shows a person using a device called a jetpack. Water is forced downwards from the jetpack and produces an upward force on the person. (a) State the condition necessary for the person to be able to remain stationary in mid-air. (b) The person weighs 700 N and the jetpack weighs 140 N. (i) Calculate the combined mass of the person and the jetpack. Gravitational field strength = 10 N/kg (ii) Increasing the upward force to 1850 N causes the person to accelerate upwards. Calculate the acceleration of the person and the jetpack.