Additional Physics

1. Additional Physics By: Peter Brookes

2. Contents • Representing Motion • Force, Mass and Acceleration • Weight and Friction • Kinetic Energy and Momentum • Static Electricity • Resistance and Resistors • Mains Electricity

3. Representing Motion

4. Representing Motion • The slope on a distance-time graph represents the speed of an object. • The velocity of an object is its speed in a particular direction. • The slope on a velocity-time graph represents the acceleration of an object. • The distance travelled is equal to the area under a velocity-time graph.

5. Speed, Distance and Time • When an object moves in a straight line at a steady speed, you can calculate its speed if you know how far it travels and how long it takes. • This equation shows the relationship between speed, distance travelled and time taken: • For example, a car travels 300 metres in 20 seconds. • Its speed is 300 ÷ 20 = 15m/s.

6. Distance-Time Graphs • The vertical axis of a distance-time graph is the distance travelled from the start. • The horizontal axis is the time from the start.

7. Features of the Graphs • When an object is stationary, the line on the graph is horizontal. • When an object is moving at a steady speed, the line on the graph is straight, but sloped. • The diagram shows some typical lines on a distance-time graph.

8. Velocity-Time Graphs • You should be able to explain velocity-time graphs for objects moving with a constant velocity or constant acceleration.

9. Background Information • The velocity of an object is its speed in a particular direction. • This means that two cars travelling at the same speed, but in opposite directions, have different velocities. • The vertical axis of a velocity-time graph is the velocity of the object. • The horizontal axis is the time from the start.

10. Features of the Graphs • When an object is moving with a constant velocity, the line on the graph is horizontal. • When an object is moving with a constant acceleration, the line on the graph is straight, but sloped. • The diagram shows some typical lines on a velocity-time graph.

11. Velocity-Time Graphs • The steeper the line, the greater the acceleration of the object. • The blue line is steeper than the red line because it represents an object with a greater acceleration. • Notice that a line sloping downwards - with a negative gradient - represents an object with a constant deceleration - slowing down.

12. Acceleration • You should be able to calculate the acceleration of an object from its change in velocity and the time taken.

13. The Equation • When an object moves in a straight line with a constant acceleration, you can calculate its acceleration if you know how much its velocity changes and how long this takes. • This equation shows the relationship between acceleration, change in velocity and time taken: • For example, a car accelerates in 5s from 25m/s to 35m/s. • Its velocity changes by 35 - 25 = 10m/s. • So its acceleration is 10 ÷ 5 = 2m/s2.

14. Distance-Time Graph Gradients • To calculate the gradient of the line on a graph, divide the change in the vertical axis by the change in the horizontal axis. • The gradient of a line on a distance-time graph represents the speed of the object. Study this distance-time graph.

15. Velocity-Time Graph Gradients • The gradient of a line on a velocity-time graph represents the acceleration of the object. • Study this velocity-time graph.

16. The Area • The area under the line in a velocity-time graph represents the distance travelled. To find the distance travelled in the graph above, we need to find the area of the light-blue triangle and the dark-blue rectangle. • 1- Area of light-blue triangle • The width of the triangle is 4 seconds and the height is 8 metres per second. To find the area, you use the equation: • area of triangle = 1⁄2 × base × height • so the area of the light-blue triangle is 1⁄2 × 8 × 4 = 16m. • 2- Area of dark-blue rectangle • The width of the rectangle is 6 seconds and the height is 8 metres per second. So the area is 8 × 6 = 48m. • 3- Area under the whole graph • The area of the light-blue triangle plus the area of the dark-blue rectangle is: • 16 + 48 = 64m. • This is the total area under the distance-time graph. This area represents the distance covered.

17. Summary • the gradient of a velocity-time graph represents the acceleration • the area under a velocity-time graph represents the distance covered

18. Force, Mass and Acceleration

19. Force, Mass and Acceleration • A stationary object remains stationary if the sum of the forces acting upon it - resultant force - is zero. • A moving object with a zero resultant force keeps moving at the same speed and in the same direction. • If the resultant force acting on an object is not zero, a stationary object begins to accelerate in the same direction as the force. • A moving object speeds up, slows down or changes direction. • Acceleration depends on the force applied to an object and the object's mass.

20. Resultant Force • An object may have several different forces acting on it, which can have different strengths and directions. • But they can be added together to give the resultant force. • This is a single force that has the same effect on the object as all the individual forces acting together.

21. When the Resultant Force is Zero • When all the forces are balanced, the resultant force is zero. In this case: • a stationary object remains stationary • a moving object keeps on moving at the same speed in the same direction • For example, in the diagram of the weightlifter, the resultant force on the bar is zero, so the bar does not move. Its weight acting downwards is balanced by the upward force provided by the weightlifter. • The longer the arrow, the bigger the force. In this diagram, the arrows are the same length, so we know they are the same size.

22. When the Resultant Force is Not Zero • When all the forces are not balanced, the resultant force is not zero. In this case: • A stationary object begins to move in the direction of the resultant force. • A moving object speeds up, slows down or changes direction depending on the direction of the resultant force. • In this diagram of the weightlifter, the resultant force on the bar is not zero. • The upwards force is bigger than the downwards force. The resultant force acts in the upwards direction, so the bar moves upwards. • In this next diagram of the weightlifter, the resultant force on the bar is also not zero. • This time, the upwards force is smaller than the downwards force. • The resultant force acts in the downwards direction, so the bar moves downwards.

23. Diagrams

24. Forces and Acceleration • You should know that objects accelerate when the resultant force is not zero, and understand the factors that affect the size of the acceleration.

25. Size of the Force • An object will accelerate in the direction of the resultant force. • The bigger the force, the greater the acceleration. • Doubling the size of the (resultant) force doubles the acceleration.

26. The Mass • An object will accelerate in the direction of the resultant force. • A force on a large mass will accelerate it less than the same force on a smaller mass. • Doubling the mass halves the acceleration.

27. Forces and Acceleration Calculations • You should know the equation that shows the relationship between resultant force, mass and acceleration, and be able to use it.

28. The Equation • Resultant force (newton, N) = mass (kg) × acceleration (m/s2) • You can see from this equation that 1N is the force needed to give 1kg an acceleration of 1m/s2. • For example, the force needed to accelerate a 10kg mass by 5m/s2 is: • 10 x 5 = 50N • The same force could accelerate a 1kg mass by 50m/s2 or a 100kg mass by 0.5m/s2. • Putting it simply, we can say that it takes more force to accelerate a larger mass.

29. Four Typical Forces That I Could Be Asked On • Air resistance - drag • When an object moves through the air, the force of air resistance acts in the opposite direction to the motion. Air resistance depends on the shape of the object and its speed. • Contact force • This happens when two objects are pushed together. They exert equal and opposite forces on each other. The contact force from the ground pushes up on your feet even as you stand still. This is the force you feel in your feet. You feel the ground pushing back against your weight pushing down. • Friction • This is the force that resists movement between two surfaces which are in contact. • Gravity • This is the force that pulls objects towards the Earth. We call the force of gravity on an object its weight. The Earth pulls with a force of about 10 newtons on every kilogram of mass.

30. Weight and Friction

31. Weight and Friction • Gravity is a force that attracts objects with mass towards each other. The weight of an object is the force acting on it due to gravity. The gravitational field strength of the Earth is 10 N/kg. • The stopping distance of a car depends on two things: the thinking distance and the braking distance.

32. Weight • Weight is not the same as mass. Mass is a measure of how much stuff is in an object. Weight is a force acting on that stuff. • You have to be careful. In physics, the term weight has a specific meaning, and is measured in newtons. Mass is measured in kilograms. The mass of a given object is the same everywhere, but its weight can change.

33. Gravitational Field Strength • Weight is the result of gravity. The gravitational field strength of the Earth is 10 N/kg (ten newtons per kilogram). This means an object with a mass of 1kg would be attracted towards the centre of the Earth by a force of 10N. We feel forces like this as weight. • You would weigh less on the Moon because the gravitational field strength of the Moon is one-sixth of that of the Earth. But note that your mass would stay the same.

34. Weight • On Earth, if you drop an object it accelerates towards the centre of the planet. You can calculate the weight of an object using this equation: • weight (N) = mass (kg) × gravitational field strength (N/kg)

35. Falling Objects • You should be able to describe the forces affecting a falling object at different stages of its fall. Usually, you need to think about two forces: • 1- The weight of the object. This is a force acting downwards, caused by the object’s mass the Earth’s gravitational field. • 2- Air resistance. This is a frictional force acting in the opposite direction to the movement of the object.

36. Three Stages of Falling • When an object is dropped, we can identify three stages before it hits the ground: • 1- At the start, the object accelerates downwards because of its weight. There is no air resistance. There is a resultant force acting downwards. • 2- As it gains speed, the object’s weight stays the same, but the air resistance on it increases. There is a resultant force acting downwards. • 3- Eventually, the object’s weight is balanced by the air resistance. There is no resultant force and the object reaches a steady speed, called the terminal velocity.

37. Terminal Velocity • What happens if you drop a feather and a coin together? The feather and the coin have roughly the same surface area, so when they begin to fall they have about the same air resistance. • As the feather falls, its air resistance increases until it soon balances the weight of the feather. The feather now falls at its terminal velocity. But the coin is much heavier, so it has to travel quite fast before air resistance is large enough to balance its weight. In fact, it probably hits the ground before it reaches its terminal velocity.

38. On the Moon • An astronaut on the Moon carried out a famous experiment. He dropped a hammer and a feather at the same time and found that they landed together. The Moon's gravity is too weak for it to hold onto an atmosphere, so there is no air resistance. When the hammer and feather were dropped, they fell together with the same acceleration.

39. Stopping Distances • The following are factors that affect stopping distance of cars.

40. Thinking Distance • It takes a certain amount of time for a driver to react to a hazard and start applying the brakes. During this time, the car is still moving. The faster the car is travelling, the greater this thinking distance will be. • The thinking distance will also increase if the driver's reactions are slower because they are: • under the influence of alcohol • under the influence of drugs • tired

41. Braking Distance • The braking distance is the distance the car travels from where the brakes are first applied to where the car stops. If the braking force is too great, the tyres may not grip the road sufficiently and the car may skid. The faster the car is travelling, the greater the braking distance will be. • The braking distance will also increase if: • The brakes or tyres are worn. • The weather conditions are poor, such as an icy or wet road. • The car is more heavily laden, for example, with passengers and luggage.

42. Stopping Distance • The stopping distance is the thinking distance added to the braking distance. The graph shows some typical stopping distances.

43. Kinetic Energy and Momentum

44. Kinetic Energy and Momentum • Work done and energy transferred are measured in joules (J). • The work done on an object can be calculated if the force and distance moved are known. • A change in momentum happens when a force is applied to an object that is moving or is able to move. • The total momentum in an explosion or collision stays the same.

45. Work, Force and Distance • You should know, and be able to use, the relationship between work done, force applied and distance moved.

46. Background • Work and energy are measured in the same unit, the joule (J). • When an object is moved by a force, energy is transferred and work is done. • But work is not a form of energy - it is one of the ways in which energy can be transferred.

47. The Equation • This equation shows the relationship between work done, force applied and distance moved: • work done (joule, J) = force (newton, N) × distance (metre, m) • The distance involved is the distance moved in the direction of the applied force.

48. Gravitational Potential Energy • Any object that is raised against the force of gravity stores gravitational potential energy. • For example, if you lift a book up onto a shelf, you have to do work against the force of gravity. • The book has gained gravitational potential energy.

49. Elastic Potential Energy • Elastic objects such as elastic bands and squash balls can change their shape. • They can be stretched or squashed, but energy is needed to change their shape. • This energy is stored in the stretched or squashed object as elastic potential energy.

50. Kinetic Energy • Every moving object has kinetic energy (sometimes called movement energy). • The more mass an object has, and the faster it is moving, the more kinetic energy it has. • You should be able to discuss the transformation of kinetic energy to other forms of energy.