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Any body will remain in it’s state of rest or uniform motion in a straight line unless caused by some external NET FORCE to act otherwise. It essentially means that a body will do one of two things: · accelerate if you apply a force to it · not accelerate if you don’t Explain the motion of the following, refer to all the forces acting on the object: •a car going “flat out” at 120 kmh-1 No acceleration as balanced forces of drag and weight reach equilibrium •a parachutist hitting the ground at 200 kmh-1 without a parachute if he jumps from 2000m or 5000m Has reached this equilibrium point - terminal velocity before he has fallen 2000m •the rate of acceleration of car decreasing as it gets faster. Engine produces a constant force - accelerates and so drag increases. This decreases the net accelerating force Using your knowledge of balanced forces draw on the size of forces and direction to simplified diagrams of these people travelling at constant velocity. Remember the size of the arrow indicates the size of the force. Objects in Equilibrium Decide for yourself what would happen to these objects! In all cases there is no resultant force so the balls stay in place! • In order to decide whether forces or velocity vectors do cause a resultant in any given direction we need to “add” them, taking into account their direction. • We have done this since Year 7 with Forces acting along the same line of action, even in 2 or 3D. • However the previous slide showed 3 forces at totally different angles. How, apart from the general feeling, can we prove they cancel each other out? • How can we calculate the resultant? • In all cases the Resultant is the “vector sum” of the components…………WHAT!!!!! For example, if you were swimming in a moving river, what direction would you end up moving in and how fast? Again you can get a feel for this from your everyday experience – USE THIS “FEEL” IN THE EXAM TO GAUGE IF YOU ARE RIGHT! There are two methods to solve this 1) Using Trigonometry and Pythagoras 2) Drawing a scale diagram and measuring the size and direction of the resultant. 1) Trigonometry and Pythagoras If a person can swim at 1.5 ms-1 in still water but the current of the stream flows at 2 ms-1 at 90o to the swimmer. What is their speed and direction? A person swims at 1.5 ms-1 in still water The RESULTANT is the vector that joins the start of one vector with the end of the last one after joining them as described! The vectors should always be drawn “nose to tail” as shown on the left. The current flows at 2 ms-1 1.5ms-1 Tan = 2 / 1.5 = 53.10 Using Pythagoras’ theorem 1.52 + 22 = 6.25 so R = 6.25 = 2.5ms-1 2 ms-1 So the RESULTANT is the person travelling at 2.5ms-1 in a direction 53o from the direction that the person was swimming in. How do you add vectors if they are not in the same line of action or at 90o ? This is best achieved at A level by drawing 2) A scale diagram and measure the angle between the vectors accurately. Make sure you specify the direction of the angle eg from the horizontal, vertical or one of the vectors This method is known as the parallelogram law as the two forces make up 2 sides of the parallelogram allowing us to measure the size of the resultant! RESULTANT R = A+B A B Example A body of mass 0.6kg falls vertically. A wind blows horizontally with a force of 8N. What is the magnitude and direction of the resultant force on the mass? (g=10 Nkg-1) 6N Tan() = 6/8 R2 = 62 + 82 = 37o R2 = 36 + 64 R2 = 100 8N R = 10N Which angle on the diagram is measured though?! Resolving Vectors If we want to know what the effect of a force is in a certain direction or if we are to add vectors, we need to know what they are doing in specific directions. The easiest to use are vertical and horizontal directions ie. Tension in the rope Vertical component Horizontal component Resolve them vertically and horizontally Sideways pull of rope on barge Forward pull of horse Actual Pull of horse Show your working and annotate the actions you are taking in these questions!! So how can we calculate the components of a force at 90o to each other? If the Horse pulls with a force of 750 N at an angle of 45o What would be the forwards force? Diagonal force upwards eg dragging a sledge If the force needed to pull this sled is 100 N and you pull at an angle of 25o what are the vertical and horizontal components of this force? If a husky pulls a sled at an angle of 10o to it’s line of travel, what is the vertical component of the force and the horizontal component if the dog pulls with a force of 700N. If the sled and load weighs 100Kg what acceleration will the dog cause the sled to have? The rate of change of momentum is directly proportional to the resultant force acting on an object and takes place in the direction of the resultant force. ..and we therefore get the maths bit!!! Force = Change in Momentum/Time Taken Force = (Final Momentum – Initial Momentum) Time Taken Force = (mv – mu)/t = m(v-u)/t F = ma F = kma is used to define the Newton and so k=1. Therefore a Force of 1N applied to a 1Kg mass, causes it to accelerate at 1ms-2. So … F = ma Note that this is not Newton’s second law. F dp/dt is! Impulse Generally we say that impulse is the product of the applied force and the time over which it is acting or the change in momentum Impulse = Ft = p Considering a car crash we all know how violent they are but how can we make them safer for the passengers? If the impact is made to last longer by slowly crushing the car the impulse will be less. In other words the impact will be less violent and therefore less damaging to the frail humans inside the car. Unfortunately the car will be smashed! Look at the simulations on multimedia motion looking at the graphs of car crashes, tennis balls being hit and air track collisions. If we consider catching a cricket ball we all know there good ways and bad. You can really smack your hand or not. What is the difference – the impulse!! Which catch would hurt your hands the most is the balls were all traveling at the same speed?? If a ball hits a wall we can say the average force that the ball exerts on the wall is F1. According to Newton’s Third Law there should be an equal and opposite force exerted on the ball F2 Wall F2 F1 So Wall F1 = - F2 If the force acts for a short period of time t then F2 F1 t = - F2 t F1 Newton’s second law tells us that F= p/t And so p = F1t This implies that the units of IMPULSE are the same as MOMENTUM. Using your training in Base units and Quantities you should be able to prove that Ns = Kgms-1 Force The impulse can also be calculated from the area under a force time graph. Time Questions 1. A ball has a mass of 150g and is travelling at 20ms-1. It is caught and brought to rest in 75ms. What is the average force on the ball which brings it to rest? 1. F t = p F x 75X10-3 = 20x0.150 F = 20x0.150 / 75X10-3 F = 20x0.002x103 F = 40N 2.Over what distance did the force act? Work Done = Force * distance In this case the work done is in slowing the ball down to zero velocity so Work done = ½ mv2 ½ mv2 = F*d 0.5*0.150*202 = 40*d d = 0.075*400/40 d = 0.75m Remember the discussion about catching cricket balls and how to avoid hurting your hand! The following graph represent the force acting on a floor as a ball bounces on it. The ball changes direction because the force on the floor changes direction - Newton’s third law will show that this force acts on the ball too in the opposite direction. Force Time Explain what you can deduce about the motion of the ball and why. The change of momentum as it speeds up (second part of graph) is less that than the change in the first part. This means the ball leaves the floor travelling more slowly than it hit the floor. Force Time The area under the second part is less than the area in the first part. (area = impulse = p) For every action there is an equal and opposite reaction A moving object can have a number of forces acting on it and yet doesn’t change it’s motion – Newton’s first law – as long as the forces are balanced. Reaction Drag Thrust Weight In this case you can imagine that the cyclist carries on moving at the same speed as the forces are all equal and opposite. However what happens if you try to push an object? If the car handbrake is on the woman will be pushing as hard as she can and yet the car won’t move it must therefore be pushing her back with an equal force! Most people have tried to jump out of a dinghy or something on water. What happens and why? When the person tries to jump they have to exert a force on the boat which pushes the boat backwards, the boat exerts a force on them pushing them forwards. If this was not the case then the person couldn’t jump forwards!! The boat accelerates backwards and the person accelerates forwards. This animation should highlight the fact that … … … Forces always come in pairs and leads us to Newton’s first law https://www.youtube.com/watch?v=Xx9kiF0 0rts https://www.youtube.com/watch?v=cP0Bb3 WXJ_k Whenever a an object exerts a force on another object an equal but oppositely directed force of the same type acts on the first object. In other words… … … For every force there is an equal and opposite force. Whenever a force acts on a body an equal but oppositely directed force of the same type acts on a different body. Statement Meaning Example “Equal” They have the same magnitude or size 10 N and 10 N “opposite direction” They act in opposite directions Left and Right or Up and Down etc. They act through the same point so no turning effect (Moment) is experienced Same line of action NOT “Same type” The force on one body will be of the same type as the force on the other “acts on different bodies” The forces that act on each of the object come from a different object. As this would cause the block to spin! If one is magnetic the other one will be too! Eg. Magnetic forces on two magnets, forces come from each magnet. Pairs of forces obeying Newton’s first law don’t necessarily obey his third! Why not?? If a body is in equilibrium A person standing on the floor. Normal reaction • all forces acting on it will sum to zero and • act through the same point. Weight This, however, is NOT a Newton Pair The man pulls the Earth up with a gravitational force of 800 N In Newton pairs there are several key ideas: • Same line of action • Acting for the same period of time • Same type of force Weight Pull of man on Earth The Earth pulls the man down with a gravitational force of 800 N You should notice the two statements are identical except for the swapping of the objects causing and feeling the forces! In summary • They occur in pairs • Are the same in type • Equal in magnitude • Act in the opposite directions • But in the same line of action • They act on different bodies Factsheet 12 Laws of Motion Support Calculation sheet 7.2 Practical 7.2 – Investigating Collisions Practical 7.3 – Newton II