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Drouin Secondary College VCE PHYSICS TOPIC: Motion VCE Physics Unit 3 Topic 1 Motion in 1 & 2 Dimensions Page 1 Drouin Secondary College VCE PHYSICS TOPIC: Motion INTRODUCTION. Unit Outline To achieve this outcome the student should demonstrate the knowledge and skills to: apply Newton’s laws of motion to situations involving two or more forces acting along a straight line and in two dimensions; analyse the uniform circular motion of an object moving in a horizontal plane (FNET = mv2/R) such as a vehicle moving around a circular road; a vehicle moving around a banked track; an object on the end of a string. Apply Newton’s 2nd Law to circular motion in a vertical plane; consider forces at the highest and lowest positions only; investigate and analyse the motion of projectiles near the Earth’s surface including a qualitative description of the effects of air resistance; apply laws of energy and momentum conservation in isolated systems; analyse impulse (momentum transfer) in an isolated system, for collisions between objects moving along a straight line (FΔt = mΔt); • apply the concept of work done by a constant force work done = constant force x distance moved in the direction of the force work done = area under force distance graph • analyse relative velocity of objects along a straight line and in two dimensions; • analyse transformations of energy between: kinetic energy; strain potential energy; gravitational potential energy; and energy dissipated to the environment considered as a combination of heat, sound and deformation of material; kinetic energy i.e. ½ mv2; elastic and inelastic collisions in terms of conservation of kinetic energy strain potential energy i.e. area under force-distance graph including ideal springs obeying Hooke’s Law ½ kx2 gravitational potential energy i.e. mgΔh or from area under force distance graph and area under field distance graph multiplied by mass • apply gravitational field and gravitational force concepts g = GM/r2 and F = GM1M2/r2 • apply the concepts of weight (W = mg), apparent weight (reaction force, N) , weightlessness (W = 0) and apparent weightlessness (N = 0) • model satellite motion (artificial, moon, planet) as uniform circular orbital motion (a = v 2/r = 4π2r/T2) • identify and apply safe and responsible practices when working with moving objects and equipment in investigations of motion. ___________________________________ Chapter 1. 1.0 Units. In Physics the Systeme Internationale d’Unites or SI (often incorrectly called the METRIC SYSTEM) of units is used. The system has two important characteristics; Different units for the same physical quantity are related by factors of 10.(eg. mm; cm; km) Most of the units are constructed out of a few basic units, in fact just _____, as listed below These are Length, Mass, Time, Electric Current, Temperature, Luminous Intensity and Amount of Substance. All other units are derived from combinations of these basic units. At this stage the important units are: Position (distance and/or displacement) is always measured in Metres (m). Time is measured in Seconds (s). Page 2 Drouin Secondary College VCE PHYSICS TOPIC: Motion Speed and/or Velocity is measured in metres per second (m/s) or more correctly (ms-1). Acceleration is measured in metres per second per second (m/s2) or more correctly (ms-2). 1.1 Position. In order to specify the position of any object we first need to define an _____________, or starting point, from which measurements can be taken. For example on a number line the point ____ is taken to be the origin and all measurements are related to that point. Thus a position +30 is 30 units to the __________ of point 0, while a position of -15 is 15 units to the ________ of point 0. -30 -25 -20 -15 The Number Line 0 -10 -5 5 10 -15 units 1.2 15 20 25 30 +30 units Vector and Scalar Quantities. In order to further investigate this section of the course two new quantities need to be introduced: A Scalar Quantity is completely defined by a ________ and a _________ eg. temperature (17o), Age (16 y), mass (1.5 kg). A Vector Quantity is completely defined by a _______________, a ___________ and a _________________ eg. Displacement 25 km West, Force 14 N downward. A direction may also be defined by using (+) to mean to the right and (-) to mean to the left. Vectors are usually represented by an arrow. The ___________ of the arrow is a measure of the magnitude or size of the vector quantity and the _________________ of the arrow represents the direction of the vector quantity. N A Vector of magnitude 15 units directed to the left Page 3 Drouin Secondary College 1.3 VCE PHYSICS TOPIC: Motion Vector Addition. When vectors need to be added, the process involves the drawing the first vector, adding the tail of the second vector to the head of the first and then drawing a line from the tail of the first to the head of the second. This line is the __________________ of the addition of the two vectors. Its magnitude and direction can be determined either by trigonometry or direct measurement from a scale diagram. Magnitude = N Direction: 1.4 Vector Subtraction. When vectors need to be subtracted, the negative vector has its _______________ reversed and then the two vectors are added as above. 8.0 ms-1 East 8.0 ms-1 South Magnitude = Direction: 1.5 Vector Components. A vector can be broken up into a number of components (usually, but not always, two components), this process is used to find two components which when added together produce the original vector. Page 4 Drouin Secondary College VCE PHYSICS TOPIC: Motion 40 ms-1 V VERTICAL 150 VHORIZONTAL VHORIZONTAL = V VERTICAL = _____________________________________________________________ Questions Adam is testing a trampoline. The diagrams show Adam at successive stages of his downward motion. Figure C shows Adam at a time when he is travelling DOWNWARDS and SLOWING DOWN. A B C D Q1: What is the direction of Adam’s acceleration at the time shown in Figure C ? Explain your answer. Page 5 Drouin Secondary College VCE PHYSICS TOPIC: Motion Chapter 2 2.0 Distance versus Displacement Distance is a ____________ Quantity having a unit and a magnitude. The S.I. unit for Distance is the ___________ (m) Distance is best thought of as: “How far you have travelled in your journey”. Displacement is a ____________quantity, having a unit, a magnitude and direction. Displacement is best defined as how far you are from your starting point. In a two dimensional system displacement must be defined using a coordinate system. Distance and Displacement may or may not be numerically __________, depending on the nature of the journey. 2.1 Speed versus Velocity Speed is defined as the ________Rate of Change of ____________.Speed is a ______________ Quantity. Mathematically: Speed = Distance/Time. The S.I. unit for Speed is metres/sec (ms-1) Velocity is defined as the Time Rate Of Change of _____________________. Velocity is a ___________ quantity. Thus: v = d/t v = Velocity (ms-1) d = Change in Displacement (m) t = Change in Time (s). INSTANTANEOUS vs AVERAGE VELOCITY The term velocity can be misleading unless a specific label is attached. The label indicates whether the velocity is an _______________ value calculated over a long period of time OR an Instantaneous value calculated at any _______________ of time. A simple example illustrates: A journey of 40 km across the suburbs takes 1 hour; VAV = = kmh-1 Page 6 Drouin Secondary College VCE PHYSICS TOPIC: Motion BUT VINST could be anything from _____ kmh-1 (stopped at traffic lights) to VINST = _______ kmh-1 (travelling along the freeway). IN ALL CALCULATIONS AND EQUATIONS USED IN THE COURSE, ASSUME _____________________ VALUES ARE REQUIRED UNLESS OTHERWISE STATED. 2.2 Some Common Speeds Event 1. Grass Growing 2. Walking Pace 3. Marathon Runner 4. 100 m Sprinter 5. Suburban Speed Limit 6. Freeway Speed Limit 7. Boeing 737 Cruising 8. Speed of Light 2.3 Speed (ms-1) 5.0 x 10-8 1-2 5 10 16.7 30.6 246 2.99 x 108 Speed (km/h) 1.8 x 10-7 4-8 18 36 60 110 886 1.1 x 109 Acceleration. Acceleration is defined as the time rate of change of ______________. Acceleration is a _______________ quantity. Thus: a = v/t -2 a = Acceleration (ms ) v = Change in Velocity (ms-1) t = Change in Time (s) Since acceleration is defined in terms of velocity, a body travelling at constant speed but with a constantly changing _____________ is defined as having an acceleration. So a cyclist travelling around a corner at constant speed is, in fact, _____________________ ! (More of this later). For an accelerating vehicle the velocity and acceleration are in the _________ direction. For a decelerating vehicle the velocity and acceleration are in ______________ directions. Page 7 Drouin Secondary College 2.4 VCE PHYSICS TOPIC: Motion Graphical Relationships. Much of the information delivered in this Physics course is presented graphically. Generally, graphs “____________________” and you need to develop the ability to “read” the story the graph is telling. There are two basic families of graphs you should be familiar with: (a) _____________ Graphs, paint a broad brush, general picture of the relationship between the quantities graphed. (b) _______________ Graphs from which exact relationships may be deduced and/or exact values may be calculated. Sketch graphs of this and other types are very useful and powerful tools and pop up in all areas of this subject. You need to develop the skills to interpret them correctly. Don’t forget to label the axes Story: Story: Story: Story: Page 8 Drouin Secondary College VCE PHYSICS TOPIC: Motion ________________________________________________________________ Questions In a road test, a car was uniformally accelerated from rest over a distance of 400 m in 19 sec. The driver then applied the brakes, stopping in 5.1 sec with constant deceleration. The graphs A to F below should be used to answer the questions below. The horizontal axis represents time and the vertical axis could be velocity or distance. A B C D E F Q2: Which of the graphs, A to F, represents the velocity time graph for the entire journey ? Q3: Which of the graphs, A to F, best represents the distance time graph of the car for the entire journey ? 2.5 Exact Graphical Relationships. In the interpretation of relationships and the determination of exact values obtainable from graphs the following table contains all the theoretical knowledge you need to obtain any piece of data. Graph Type Distance or Displacement versus Time Speed or Velocity versus Time Acceleration versus Time Read Directly from Graph ______________ _____________ Speed or Velocity Acceleration Obtain from Slope of Graph Speed or _____________ _____________ No Useful Information Obtain from Area under Graph No Useful Information ______________ or Displacement ______________ Page 9 Drouin Secondary College 2.6 VCE PHYSICS TOPIC: Motion Equations of Motion. The equations of motion are a series of equations linking velocity, acceleration, displacement and time which allow calculations of these quantities without the need for a graphical representation. The equations can only be used if the ___________________ is constant. They are summarised below. v = u + at v² = u² + 2ax x = ut + ½at² u = Initial Velocity (ms-1) v = Final Velocity (ms-1) a = Acceleration (ms-2) x = Displacement (m) t = Time (s) Whenever using these equations always list out the information given and what is required, then choose an appropriate equation. Some problems may require a two step calculation. It is sometimes necessary to define a positive direction, right or left in horizontal motion problems, up or down, in vertical motion problems. Questions In a road test, a car was uniformally accelerated from rest over a distance of 400 m in 19 sec. The driver then applied the brakes, stopping in 5.1 sec with constant deceleration. Q4: Calculate the acceleration of the car for the first 400 m. Page 10 Drouin Secondary College VCE PHYSICS TOPIC: Motion Q5: Calculate the average speed for the entire journey, covering both the accelerating and braking sections. CHAPTER 3. 3.0 Newtonian Motion. Sir Isaac Newton (1642 - 1727) was unique for a number of reasons, but mostly because he developed a set of laws describing the ________ of objects in the universe. Prior to Newton, scientists believed that a set of laws existed which explained motion on Earth and these laws had to be ______________ to describe motions in all other parts of the universe. Page 11 Drouin Secondary College VCE PHYSICS TOPIC: Motion Newton was the first scientist to realise that all motion anywhere in the universe could be described by a single set of laws which then had to be modified for use in the ______________ riddled confines of the Earth. 3.1 Newton’s Laws FIRST LAW A body will remain at _________or in a state of uniform motion unless acted upon by a net external ________. Often called the Law Of Inertia, (Inertia is the reluctance of a body to change its state of motion). SECOND LAW The __________________ of a body is directly proportional to the net force applied and inversely proportional to its __________ ie. a = F/m or as more often written F = ma. THIRD LAW For every ____________ there is an equal and opposite _______________. __________________________________________________________________________________________ Questions A seaplane of mass 2200 kg takes off from a smooth lake as shown. It starts from rest, and is driven by a CONSTANT force generated by the propeller. After travelling a distance of 500 m, the seaplane is travelling at a constant speed, and then it lifts off after travelling a further 100 m. The total force opposing the motion of the seaplane is not constant. The graph shows the TOTAL FORCE OPPOSING THE MOTION of the seaplane as a function of the distance travelled. Page 12 Drouin Secondary College VCE PHYSICS TOPIC: Motion Total Opposing Force (N) Opposing 10000 8000 6000 4000 2000 100 200 300 400 500 600 Distance Q6: What is the magnitude of the net force acting on the seaplane after it has travelled a distance of 500 m from the start ? Q7: What is the magnitude of the seaplane’s acceleration at the 200 m mark ? Q8: Estimate the work done by the seaplane against the opposing forces in travelling for a distance of 500 m. Page 13 Drouin Secondary College VCE PHYSICS TOPIC: Motion In Figure 2, a car of mass 1000 kg is being towed on a level road by a van of mass 2000 kg. There is a constant retarding force, due to air resistance and friction, of 500 N on the van, and 300 N on the car. The vehicles are travelling at a constant speed. Figure 2 Q9: What is the magnitude of the force driving the van? Q10: What is the value of the tension, T, in the towbar? Page 14 Drouin Secondary College VCE PHYSICS TOPIC: Motion The figure shows a cyclist with the bicycle wheels in CONTACT with the road surface. The cyclist is about to start accelerating forward. a FTR FRT Q11: Explain, with the aid of a clear force diagram, how the rotation of the wheels result in the cyclist accelerating forwards. 3.2 Newton’s Laws Restrictions & Consequences Page 15 Drouin Secondary College VCE PHYSICS TOPIC: Motion RESTRICTIONS The laws only apply at speeds much, much less than the speed of ___________. The laws apply equally in ALL inertial frames of reference. FRAME OF REFERENCE ? A frame of reference is best described as “your point of _________________.” An inertial frame of reference is one that is either _____________ or moving with constant _________________. A non inertial frame of reference is _____________________. CONSEQUENCES As far as Newton’s 1st law is concerned “rest” and “uniform motion” are the _________ state. You cannot perform any test which can show whether you are stationary or moving at constant velocity. The action and reaction law requires there to be ______ bodies interacting, the ACTION force acting on one body and the REACTION acting on the other. Deciding when an Action / Reaction situation exists can be done by answering the question: Does the second (reaction) force _________________ immediately the first (action) force disappears ? If the answer is yes, you have an action reaction pair. _______________________________________________________________ Questions A train is travelling at a constant velocity on a level track. Lee is standing in the train, facing the front, and throws a ball vertically up in the air, and observes its motion. Q12: Describe the motion of the ball as seen by Lee. Sam, who is standing at a level crossing, sees Lee throw the ball into the air. Page 16 Drouin Secondary College VCE PHYSICS TOPIC: Motion Q13: Describe and explain the motion of the ball as seen by Sam. 3.3 Forces In Two Dimensions. A force is a ________ or a pull. It can be a _____________ Force where direct contact is required for the effect of the force to be felt eg. - a punch in the nose or a vehicle colliding with a tree, or it can be a ___________ Force where direct contact is not necessarily required for the effect of the force to be felt eg. - the magnetic force or the force due to gravity. Force is NOT one of the 7 fundamental units of the S.I. System and thus it is a _____________ quantity. The unit for Force is kgms-2. This was assigned the name the NEWTON (N), in honour of Sir Isaac. Forces can act in any direction and the TOTAL, NET or RESULTANT force is the __________sum of all forces acting on a body. The body will then ___________________ in the direction of the RESULTANT FORCE, according to Newton 2. ________________________________________________________________________ Questions A cyclist is towing a small trailer along a level bike track (Figure 1). The cyclist and bike have a mass of 90 kg, and the trailer has a mass of 40 kg. There are opposing constant forces of 190 N on the rider and bike, and 70 N on the trailer. These opposing forces do not depend on the speed of the bike. The bike and trailer are initially travelling at a constant speed of 6.0 ms-1. Page 17 Drouin Secondary College VCE PHYSICS TOPIC: Motion Q14. What driving force is being exerted on the road by the rear tyre of the bicycle? 3.4 Momentum and Impulse. Newton called momentum the "quality of motion", and it is a measure of a body’s ____________________ motion – its tendency to continue moving in a particular direction. Roughly speaking, a body’s momentum indicates which way the body is heading and just how difficult is was to get the body moving with its current velocity. Momentum is the product of a body’s mass and velocity. Momentum is a _____________ quantity. Thus: p = mv p = Momentum (kgms-1) m = Mass (kg) v = Velocity (ms-1) The direction of the momentum is the same as the velocity’s direction. Impulse is called the “_______________ ________________” for the momentum. This means that in order to change the momentum of a body you need to exert a _______________ for some time in order to effect that momentum change. Impulse is the product of force and the time during which that force acts. Impulse is a _____________ quantity. Thus: I = Ft I = Impulse (Ns) F = Force (N) Page 18 Drouin Secondary College VCE PHYSICS TOPIC: Motion t = Time (s). Momentum arises from Newton's second law (F = ma). Substituting for a = v/t, the law becomes F = mv/t Rearranging we get: Ft = mv Or more often written as: Ft = p The product Ft is called the Impulse (I) of the force and mv represents the change in momentum (p) of the body. ________________________________________________________________________ Questions A small truck of mass 3.0 tonne collides with a stationary car of mass 1.0 tonne. They remain locked together as they move off. The speed immediately after the collision was known to be 7.0 ms-1 from the jammed reading on the car speedometer. Robin, one of the police investigating the crash, uses conservation of momentum to estimate the speed of the truck before the collision. Q15 : What value did Robin obtain? The calculated value is questioned by the other investigator, Chris, who believes that conservation of momentum only applies in elastic collisions. Q16: Explain why Chris’s comment is wrong. Page 19 Drouin Secondary College VCE PHYSICS TOPIC: Motion A car of mass 1000 kg travelling on a smooth road at 5.0 ms–1 collides with a truck that is stationary at a set of traffic lights. After the collision they are stuck together and move off with a speed of 2.0 ms–1 Q17 : How much momentum did the car transfer to the truck? Q18 : What is the mass of the truck? Q19: If the collision took place over a period of 0.3 s, what was the average force exerted by the car on the truck? Page 20 Drouin Secondary College VCE PHYSICS TOPIC: Motion A railway truck (X) of mass 10 tonnes, moving at 6.0 ms-1, collides with a stationary railway truck (Y), of mass 5.0 tonnes. After the collision they are joined together and move off as one. Q20: Calculate the final speed of the joined railway trucks after collision Q21: Calculate the magnitude of the total impulse that truck Y exerts on truck X 3.5 Elastic And Inelastic Collisions. All collisions (eg, cars with trees, cyclists with the footpath, neutrons with uranium atoms, bowling balls with pins etc.) fall into one of 2 categories: In _______________ collisions both momentum and kinetic energy are conserved In ________________ collisions, momentum is conserved but kinetic energy is not conserved. The smaller of the two groups are the elastic collisions which generally only occur on the atomic scale. By far the largest group of collisions are the inelastic collisions where the lost kinetic energy is converted to things like heat, sound, light. Questions Page 21 Drouin Secondary College VCE PHYSICS TOPIC: Motion A small truck of mass 3.0 tonne collides with a stationary car of mass 1.0 tonne. They remain locked together as they move off. The speed immediately after the collision was known to be 7.0 ms-1 from the jammed reading on the car speedometer. Robin, one of the police investigating the crash, uses conservation of momentum to estimate the speed of the truck before the collision at 9.3 ms-1 Q22: Use a calculation to show whether the collision was elastic or inelastic. A railway truck (X) of mass 10 tonnes, moving at 6.0 ms-1, collides with a stationary railway truck (Y), of mass 5.0 tonnes. After the collision they are joined together and move off as one at 4.0 ms-1. Q23: Explain why this collision is an example of an inelastic collision. Calculate specific numerical values to justify your answer. 3.6 Conservation of Momentum. The concept of momentum is particularly useful in analysing collisions. This is because of the law of conservation of momentum which states: In an isolated system, total Page 22 Drouin Secondary College VCE PHYSICS TOPIC: Motion momentum is _______________. Thus in a collision, the total momentum before equals the total momentum after. In collisions where momentum seems to have been lost, eg. a car hitting a tree and coming to rest, the conservation law means that the apparently "lost" momentum has in fact been transferred to the __________. Since the earth has such a large mass, the resulting change in its ___________________ is negligible. 3.6 The Physics of Crumple Zones & Air Bags A car crashes into a concrete barrier. The change in ____________ suffered by the car (and passengers) is a ____________ quantity. So, Impulse, (the product of F and t), is also _________. However, individual values of F and t can vary as long as their _______________ is always the same. So if t is made longer, consequently F must be smaller. Crumple Zones increase the time (t) of the collision. So, F is reduced and the passengers are less likely to be injured. The same logic can also be applied to Air Bags. The air bag increases the ____________ it takes for the person to stop. So the force they must absorb is ______________. So they are less likely to be seriously injured. A further benefit is this lesser force is distributed over a larger area. Questions In a car the driver’s head is moving horizontally at 8.0 ms -1 and collides with an air bag as shown. The time taken for the driver’s head to come to a complete stop is 1.6 x 10-1 s. This collision may be modelled as a simple horizontal collision between the head of mass 7.0 kg and the air bag. Q24: Calculate the magnitude of the average contact force that the air bag exerts on the driver’s head during this collision. Page 23 Drouin Secondary College VCE PHYSICS TOPIC: Motion Q25: Explain why the driver is less likely to suffer a head injury in a collision with the air bag than if his head collided with the car dashboard, or other hard surface. CHAPTER 4 4.1 Centre Of Mass In order to deal with large objects it is useful to think of all the mass of the object being concentrated at one point, this point is called the centre of ___________of the object. For regularly shaped objects eg. squares or rectangles, cubes or spheres the Centre of Mass of the object is in the geometric ___________ of the object For oddly shaped objects e.g. a boomerang, the centre of mass may be outside the perimeter of the object. Centre of Mass Page 24 Drouin Secondary College VCE PHYSICS TOPIC: Motion The Centre of Mass of an object is the point around which the object will ________ when a ____________ or Turning Force is applied to the object. 4.1 Centre of Mass - Systems For a system made up of two or more bodies, the position of the Centre of Mass may be determined by the use of the formula: XCM = (m1x1+ m2x2 + m3x3 + ...)/(m1 + m2+m3+ ...) XCM = Position of Centre of Mass (m) m1,m2 etc = Masses of individual objects (kg) x1,x2 etc = Distance of individual masses from a chosen reference point (m). 5.0 m 1.0 m 1.0 m 30 kg 50 kg A A 30 kg block sits on a 50 kg beam . Where is the centre of mass of this system ? Since the block and the beam are uniform each will have its centre of mass at its geometric centre. All measurements are taken from point A, ie. this is the reference point for this system. XCM = [(50 x 2.5) + (30 x 3.5)] / [50 + 30] = 2.875 m Thus the centre of mass of this system is 2.875 m from A. 4.2 Weight. The effect of a Gravitational Field on a Mass is called its _____________. Page 25 Drouin Secondary College VCE PHYSICS TOPIC: Motion Weight is a FORCE and therefore a ______________ quantity. Mathematically: W = mg where W = Weight (N) m = mass (kg) g = Gravitational Field Strength (Nkg-1) Weight acts through the Centre of Mass of the body and is directed along the line joining the centres of the two bodies between which the Gravitational Field is generated. On Earth, the Gravitational Field of Strength ________ Nkg -1 gives any mass under its influence alone an acceleration of ________ ms-2 4.3 Reaction Force. Any stationary body under the influence of the Earth's gravitational field must have an equal and opposite force to that of gravity acting upon it. This force is called the ____________ Force. It only arises as the result of the action of another force and does not exist as an isolated force in its own right. R - Normal Reaction Force Centre of Mass Object, mass m Table top W = mg NOTES: 1. The Weight force W acts from the Centre of Mass downward toward the centre of the Earth. 2. The Normal Reaction Force acts from the boundary between the object and the table. It acts up through the Centre of Mass. 3. The Forces R and W should be co planer ie. they should sit on top of one another. This is impossible to show on the diagram, so they are slightly offset. 4. The Forces W and R are NOT an action - reaction pair. In the diagram above the two forces shown are NOT an action – reaction pair. This is because they do not meet the fundamental requirement for such a pair – when one disappears the other automatically disappears as well. Look closely. If the R force disappears ie. you take the table away, the W force still exists. thus these two are not an example of Newton 3. (although they are often used to illustrate Force of TABLE on OBJECT F TO These two forces are the action reaction pair in this situation Force of OBJECT on TABLE F OT Page 26 Drouin Secondary College VCE PHYSICS TOPIC: Motion Newton’s Third Law). 4.4 Bouncing Balls When a moving ball arrives at a hard surface it is the Normal Reaction Force (R) which provides the force needed to ________________ the ball to a stop and then accelerate away from the surface. R R a=g a=g a v a v W v v= 0 W W W 4.5 Friction Friction is the most unusual of all forces in that is cannot __________ an object moving, it can only slow down or ___________ an object once it is moving, or prevent it from starting to move. Slowing a moving object is the result of Dynamic Friction, while preventing an object from starting to move is the result of __________ Friction. It is usually the case that for the same pair of surfaces, static friction is greater than dynamic friction. In other words the force need to start an object moving is greater than the force needed to maintain its motion. Generally the size of the frictional force between two surfaces depends upon: (a) The __________________ of the surfaces (measured by the coefficient of friction ()) (b) the ________________ of the surfaces. The Frictional Force is NOT dependent upon the ____________ of contact. The size of the frictional force can be calculated from the equation: FR = R FR = Frictional force (N) Page 27 Drouin Secondary College VCE PHYSICS TOPIC: Motion = Coefficient of Friction (no units) R = Normal Reaction force (N) (numerically equal to Weight [mg]). Note: the normal reaction force is always directed at right angles to the surface on which Normal Reaction = R Fr (Friction) F (Pulling Force) Weight = mg the motion is occurring no matter the angle of that surface. 4.6 Friction Applications Friction is NOT always a hindrance to living on Earth, often it is vital for movement over the Earth’s surface. Consider the following situation: A vehicle’s rear (driving) wheel is in contact with a __________ (having friction) road surface. The frictional force between the tyre and the road is directed ___________, away from the direction of motion. This force cannot provide the forward propulsion. It is the _____________ force (arising from Newton 3), of the road on the tyre, Direction of Acceleration It is the REACTION FORCE which causes ACCELERATION Force of TYRE on ROAD Action Force Force of ROAD on TYRE Reaction Force directed forwards, which is providing the force for forward motion 4.6 Various Force Situations Page 28 Drouin Secondary College VCE PHYSICS Mass Stationary on Table Block mass = m R Mass falling with Air Resistance = C of M W = mg Lift – Accelerating Upwards FR a=0 +ve TOPIC: Motion a +ve R +ve W = mg ΣF = ma R – W = m(0) So, R = W a W = mg ΣF = ma W – FR = ma So, mg – FR = ma ΣF = ma R – W = ma So, R = mg + ma Mass is “heavier” by an amount = ma Lift – Accelerating Downwards +ve Inclined Plane – No Friction a a R R a mg Sin θ W = mg Mass is “lighter” by an amount = ma θ θ m2 ┴ to plane: R = mg Cos θ ║to plane: mg Sin θ = ma ║to plane: mg Sin θ - FR = ma Strings and Pulleys +ve T +ve W For m1 : T – FR = m1a For m2 : W – T = m2a Solve simultaneous equation to obtain acc. W = mg ┴ to plane: R = mg Cos θ T T mg Cos θ W = mg Connected Bodies with Friction a FR mg Cos θ ΣF = ma W – R = ma So, R = mg - ma m1 R mg Sin θ θ θ FR Inclined Plane – With Friction T m1 W = m1g For m1: a T – m1g = m1a m2 Pendulums θ For m2: m2g – T = m2a W = m2g Solve simultaneous equation to obtain acc. Restoring Force = mg Sinθ T T = mg Cosθ mg Sinθ W = mg mg Cosθ CHAPTER 5 5.0 Work. In Physics, the term Work has a very strict meaning. When a force moves an object through a distance, work has been done. Work is a ___________ quantity and is calculated from the equation: W = Fd Page 29 Drouin Secondary College VCE PHYSICS TOPIC: Motion W = Work (J [Joules]) F = Force (N) d = Distance (m). No work is done if the force has not caused the object to ___________. Provided the force remains constant the above formula may be used. BUT, If the force ______________ during the course of doing the work, (as in compressing a spring) the only way to calculate the size of the work done is to calculate the area under the graph of F vs d. Force Area = Work Done = 1/2 F x d d Distance 5.1 Work & Energy In the Physics world, Work and __________ are intimately related. Energy is very difficult to define. It is easy to say what energy can do but not so easy to say what it is. Thus energy is defined in terms of ______________. An object is said to possess energy if it has the ability or capacity to do work. Work is the “Transfer Mechanism” for Energy meaning that if some work has been done on an object the amount of energy it possesses has been changed. _________ DONE = ENERGY _____________________ __________________________________________________________________________________________ Questions A model rocket of mass 0.20 kg is launched by means of a spring, as shown in Figure 1. The spring is initially compressed by 20 cm, and the rocket leaves the spring as it reaches its natural length. The force-compression characteristic of the spring is shown in Figure 2. Page 30 Drouin Secondary College VCE PHYSICS TOPIC: Motion Q26 : How much energy is stored in the spring when it is compressed? Q27: What is the speed of the rocket as it leaves the spring? Q28: What is the maximum height, above the spring, reached by the rocket? You should ignore air resistance on the way up since the rocket is very narrow. Page 31 Drouin Secondary College VCE PHYSICS TOPIC: Motion When the rocket reaches its maximum height, the parachute opens and the system begins to fall. In the following questions you should still ignore the effects of air resistance on the rocket, but of course it is critical to the force on the parachute. This retarding force due to the parachute is shown as R in Figure 3, and its variation as a function of time after the parachute opened is shown in Figure 4. Q29: What is the acceleration of the rocket at a time 5 s after the parachute opens? In a storeroom a small box of mass 30.0 kg is loaded onto a slide from the second floor, and slides from rest to the ground floor below, as shown below. The slide has a linear length of 6.0 m, and is designed to provide a constant friction force of 50 N on the box. The box reaches the end of the slide with a speed of 8.0 m s–1 Q30: What is the height, h, between the floors? Page 32 Drouin Secondary College 5.2 VCE PHYSICS TOPIC: Motion Energy Types Kinetic Energy Kinetic energy is the energy possessed by a ________ body, sometimes called "the energy of motion". Kinetic Energy is a ________ quantity. It is calculated from the equation: K.E. = ½mv² K.E. = Kinetic Energy (J) m = Mass (kg) v = Velocity (ms-1) Gravitational Potential Energy Gravitational Potential Energy is the energy a body possesses due to its _______________ and thus is generally called the "energy of position". Potential Energy is a Scalar quantity. It is calculated from the equation: P.E. = mgh P.E. = Potential Energy (J) m = Mass (kg) g = Gravitational Field Strength (Nkg-1) h = Height (m) Page 33 Drouin Secondary College VCE PHYSICS TOPIC: Motion The value of the height (h) used in the equation depends upon the where the __________ for height is defined. This is usually, but not always, the surface of the earth. It is important to know where this zero point is defined to be before using the formula. Elastic Potential Energy The energy stored in ___________ materials (eg. Springs & rubber bands) Mathematically: Es = ½ kx2 where, Es = Elastic P. E. (J ) k = Spring Constant (N kg-1) x = Extension or Compression (m) Questions The box in the previous question then slides along the frictionless floor, and is momentarily stopped by a spring of stiffness 30 000 Nm–1 Q31: How far has the spring compressed when the box has come to rest? 5.3 Power. Power is the time rate of doing __________ and since; WORK DONE EQUALS ENERGY TRANSFERRED power can also be defined as the time rate of energy transfer. Power is a ___________ quantity. Thus: P = W/t = E/t P = Power ( W =Watts) W = Work (J) t = Time (s) It is also useful to note that since W = F.d, and v = d/t then; Page 34 Drouin Secondary College VCE PHYSICS TOPIC: Motion P = F.d/t = F.v This form of the power formula can be used to calculate power for a body moving at constant _____________. 5.4 Conservation Of Energy. The law of conservation of energy states: Energy can be neither ____________ nor _______________, but only transformed from one form to another. Most energy conversion processes result in the conversion of useful, Ordered Energy (energy that can easily be used to do work) into relatively useless Disordered Energy. This disordered energy is called Thermal Energy and is the energy we associate with temperature. It is sometimes called Internal Energy or "low grade, non recoverable" Heat. The percentage ____________________ of energy transfers is calculated from: %Eff = EOUT/EIN x 100/1 No energy transfer process can be 100% efficient in our friction ridden world. If 100% efficiency could be attained __________ motion machines would then be possible. 5.5 Seeing Energy With a little practice you can “__________ ” energy flow through a system just as an accountant can “watch” money flow through an economy. The most obvious form of energy is Kinetic Energy , the energy of _________. It is easy to see when kinetic energy is transferred to or from an object. As KE leaves the object it slows down: as in a car slowing down when you lift off the accelerator pedal. A water polo ball speeds up when you do work on it during the action of throwing, you are transferring ___________ from your body into the ball, where the energy shows up in the __________ of the ball. Page 35 Drouin Secondary College VCE PHYSICS TOPIC: Motion Potential Energy is more difficult to “see”. It can take many different forms, as shown in the table below. In each case nothing is moving; but because the objects still have a great potential to do work, they possess Potential Energy. Form of Potential Energy 1. Gravitational Potential Energy 2. Elastic Potential Energy 3. Electrostatic Potential Energy 4. Chemical Potential Energy 5. Nuclear Potential Energy Example A person standing at the top of a building A wound clock spring A cloud in a thunderstorm A firecracker Uranium CHAPTER 6. 6.0 The Experience of Acceleration. Nothing is more central to the laws of motion than the relationship between force and _________________. Up to now we have looked at forces and noticed they can produce accelerations (Newtons 2nd Law). Now we will reverse the process – looking at accelerations and noticing that they require _____________. For you to accelerate, something must push or pull on you. Just where and how that force is exerted on you determines how you “_________” when you accelerate. The “backward” force you feel as a car accelerates is caused by your body’s ________________, its tendency not to want to accelerate. The car and your seat are accelerating forward, and since the seat back acts to keep you from falling “through” its surface, it provides a forward support force which causes you to accelerate forward. But the seat can’t exert a force uniformly throughout your body. Instead, it pushes only on your back and your back then pushes on your bones, internal organs and tissues to make them accelerate forward. The experience of the accelerating car seat is very similar to the experience of “gravity” when you stand still on the Earth’s surface. In this situation you feel “heavy” ie. you experience your ____________. Page 36 Drouin Secondary College 6.1 VCE PHYSICS TOPIC: Motion Fictitious Forces When the car seat is causing you to accelerate forward, you also feel “_______”; your body senses all the internal forces needed to accelerate its pieces forward, and you interpret these sensations as “weight”. This time you experience the weight directed toward the back of the car. The gravity-like “force” that you experience as you accelerate is truly indistinguishable from the force of gravity. No laboratory instrument can determine directly whether you are experiencing gravity or simply accelerating. However despite the convincing sensations, the backward heavy feeling in your gut as you accelerate forward is not due to a ________ force. This experience of acceleration is explained by the supposed action of a Fictitious Force. This Fictitious Force always points in the direction _____________ to the acceleration that causes it and its strength is proportional to the acceleration. 6.3 Apparent Weight a1 a2 Fictitious Force Fictitious Force a2 > a1 Apparent Weight Weight Gentle acceleration - small fictitious force Apparent weight mostly downward 6.2 Apparent Weight Weight Large acceleration - large fictitious force Apparent weight more backwards and down Circular Motion in Horizontal Circles. When left alone, no object will travel in a _________. Newton’s First Law says that an object experiencing no net force will move in a straight line at constant speed. Thus, in order to make an object travel in a circle ie. constantly change the direction of its velocity, a force must be constantly applied to it. This means the object is constantly __________________. Page 37 Drouin Secondary College VCE PHYSICS TOPIC: Motion Many objects, however, do execute circular motion, wheels, moons, planets, and electric motors all move is circles. The laws covering circular motion are derived from the laws covering straight line motion. The number of times an object spins around per second is called its Frequency. An object travelling around a circle completes one full spin in a time interval called a Period (T). Period and frequency (f) are the inverse of one another. Thus: T = 1/f T =Period (sec) f = Frequency (Hz or sec-1) Circumference = 2r r The distance covered in 1 period is the circumference of a circle (2R), thus the velocity of an object moving in a circle is given by the general expression distance/time or: v = 2R/T = 2Rf v = Velocity (ms-1) R = Radius (m) T = Period (s) f = Frequency (Hz) Since the direction of the velocity at any point is the tangent to the circle at that point, the direction of the velocity is constantly changing, thus an object travelling in a circular path is subject to a constant acceleration. The size of this acceleration is given by: a = v²/R Page 38 Drouin Secondary College VCE PHYSICS TOPIC: Motion r v r v Substituting for v = 2R/T, the acceleration equation becomes: a = 4²R/T² = 4²Rf² This acceleration acts toward the centre of the circle and is called the __________________ Acceleration. The term arising from the centre seeking nature of the acceleration. 6.5 Centripetal Force The fact that an acceleration exists requires there to be a force, in the same direction, which produces this acceleration. This force is called the ________________ Force and arises from Newton's Second Law. Thus: F = ma = mv²/R = m 4²R/T² Centripetal Force is, itself, not a _________ FORCE in its own right, but is supplied by other real, measurable forces. In the case below, the girl requires a Centripetal Force to travel her circular path The _______________ (T) of her muscular grip on the pivot pole of the ride provides the Centripetal Force. She, of course, will use the idea of a Fictitious Force, centrifugal force, to explain the “outward” pull she feels while on the constantly accelerating ride. Page 39 Drouin Secondary College VCE PHYSICS TOPIC: Motion Questions Mark Webber and his Formula 1 racing car are taking a corner at the Australian Grand Prix. A camera views the racing car head on at point X on the bend where it is travelling at constant speed. At this point the radius of curvature is 36.0 m. The total mass of the car and driver is 800 kg. Camera's head on view of racing car at point X 36.0 m X Camera Q32: On the diagram showing the camera’s view of the racing car, draw an arrow to represent the direction of the NET force acting on the racing car at this instant. Q33: Calculate the speed of the car. Page 40 Drouin Secondary College VCE PHYSICS TOPIC: Motion Q34: Referring to the racing car from the previous slide, explain: (a) Why the car needs a horizontal force to turn the corner. (b) Where this force comes from. The safe speed for a train taking a curve on level ground is determined by the force that the rails can take before they move sideways relative to the ground. From time to time trains derail because they take curves at speeds greater than that recommended for safe travel.Figure 5 shows a train at position P taking a curve on horizontal ground, at a constant speed, in the direction shown by the arrow. Q35: At point P shown on the figure, draw an arrow that shows the direction of the force exerted by the rails on the wheels of the train. The radius of curvature of a track that is safe at 60 km/h is approximately 200 m. Q36: What is the radius of curvature of a track that would be safe at a speed of 120 km/h, assuming that the track is constructed to the same strength as for a 60 km/h curve? Page 41 Drouin Secondary College VCE PHYSICS TOPIC: Motion Q37: At point Q the driver applies the brakes to slow down the train on the curve. Which of the arrows (A to D) indicates the direction of the net force exerted on the wheels by the rails? 6.6 Centrifugal Force Centripetal Force & Acceleration Fictitious Force Girl's Path Velocity Despite its fictitious nature, centrifugal force creates a compelling sensation of gravity like _________. The girl on the ride feels as though gravity is pulling her outward as well as down and must hold the handle tight in order not to fall off. Fictitious forces, such as Centrifugal Force, do _________ contribute to the net force experienced by an object. Thus if the girl lets go she will fly off the ride in the direction of the linear velocity NOT in the direction of the fictitious force. A stationary object on Earth experiences a weight force of 1g. The fictitious centrifugal force experienced by 5 kg of clothes during the spin cycle in a washing machine, travelling in a 0.25 m radius circle at 20 ms-1 is about 163 g’s and they have an apparent weight of 815 kg. 6.7 Banked Corners Race track and road designers tend to build their tracks or roads with “__________” on the corners. This design feature is used to enhance the safety of the track or road allowing users to round corners at higher speeds (and with a greater margin of safety) than they could if the corner was not banked. Any vehicle travelling around a corner with velocity v needs a centripetal force (F C) acting toward the centre of the corner. Page 42 Drouin Secondary College VCE PHYSICS TOPIC: Motion FC v In the case of the flat, non banked, corner this centripetal force (F C) is supplied by the __________ of the road against the tyres (FRT) With the banked corner the centripetal force has an extra component - that being a component of the car’s ________ force acting toward the centre of the corner. This gives a _________ overall Centripetal Force (FC) larger than in the non banked case. The larger FC allows the car either a greater margin for safety or a faster speed around a banked corner compared to a flat corner of the same radius 6.8 Circular Motion – Vertical Circles Objects travelling in vertical circles are subject to the acceleration due to gravity, thus their speed will vary depending where in their motion observations are made. Analysis of this type of motion is based on energy considerations and the fact that the motion takes place in a uniform gravitational field. Page 43 Drouin Secondary College VCE PHYSICS TOPIC: Motion In theoretical situations, the TOTAL ENERGY REMAINS _________, but varies between Kinetic and Potential, depending on where in the circle you choose to look. PE = max KE = min KE PE KE = max KE Total Energy = KE + PE = a constant PE Body moving anticlockwise PE = min 6.9 PROJECTILE MOTION. Projectile motion is that motion which objects launched at some angle to the earth's gravitational field, undergo. It is a combination of two ________________ motions; (a) Horizontal motion which is constant ___________ motion. (b) Vertical motion which is constant __________________ motion. The horizontal motion has only one relevant equation: v = d/t The vertical motion, being constantly accelerated motion, is covered by the equations of motion with the acceleration being that due to gravity, usually g = 10 ms -2. It is vital that a positive direction is chosen and correctly assigned to the known and unknown values in the equations: v = u + at v² = u² + 2ax x = ut + ½at² The only common factor between the two motions is the t, the time of flight. Page 44 Drouin Secondary College VCE PHYSICS TOPIC: Motion Questions A B B H G Direction of Motion A C D H G C D X F E Y F E A car takes off from a ramp and the path of its centre of mass through the air is shown below.First model the motion of the car assuming that air resistance is small enough to neglect. Q38: Which of the directions (A - H), best shows the VELOCITY of the car at X ? Q39. Which of the directions (A - H), best shows the VELOCITY of the car at Y ? Q40: Which of the directions (A - H), best shows the ACCELERATION of the car at X ? Now suppose that AIR RESISTANCE CANNOT BE NEGLECTED. Q41: Which of the directions (A - H), best shows the ACCELERATION of the car at X ? A bushwalker is stranded while walking. Search and rescue officers drop an emergency package from a helicopter to the bushwalker. They release the package when the helicopter is a height (h) above the ground, and directly above the bushwalker. The helicopter is moving with a velocity of 10 ms–1 at an angle of 30° to the horizontal, as shown in Figure 1. The package lands on the ground 3.0 s after its release. Ignore air resistance in your calculations. Figure 1 Page 45 Drouin Secondary College VCE PHYSICS TOPIC: Motion Q42: What is the value of h in Figure 1? Q43: Assuming that the helicopter continues to fly with its initial velocity, where is it when the package lands? Which one of the statements below is most correct? A. It is directly above the package. B. It is directly above a point that is 15 m beyond the package. C. It is directly above a point that is 26 m beyond the package. D. It is directly above a point that is 30 m from the bushwalker. Q44: Which of the graphs below best represents the speed of the package as a function of time? Page 46 Drouin Secondary College VCE PHYSICS TOPIC: Motion Fred is playing tennis on the deck of a moving ship. He serves the ball so that it leaves the racket 3.0 m above the deck and travels perpendicular to the direction of motion of the ship. The ball leaves the racket at an angle of 8° to the horizontal. At its maximum height it has a speed of 30.0 ms-1. You may ignore air resistance in the following questions. Page 47 Drouin Secondary College VCE PHYSICS TOPIC: Motion Q45: With what speed, relative to the deck, did the ball leave Fred’s racket? Give your answer to three significant figures. Q46: At its highest point, how far was the ball above the deck? Page 48 Drouin Secondary College VCE PHYSICS TOPIC: Motion The ship is travelling straight ahead at a velocity of 10 ms-1 Q47: When the ball is at its highest point at what speed is it moving relative to the ocean? Q48: at what angle is the ball travelling relative to the direction of the ship’s travel? 6.10 Projection Angles There are two basic types of projectile motion: (a) Objects projected horizontally from a position some distance above the earth's surface. V horiz V horiz V vert V horiz V vert V vert V horiz V vert Page 49 Drouin Secondary College VCE PHYSICS TOPIC: Motion (b) Objects which are projected at an angle to the horizontal from the surface of the earth. These objects have a path which can be divided into two equal parts, one to the point of maximum height and the other from the point of maximum height back to earth. The two parts are mirror images of one another. V horiz V vert = 0 V vert V horiz V horiz V vert INITIAL VELOCITIES FOR ANGLED PROJECTILES Initial Horizontal Velocity = Horizontal component of Initial Velocity = VCos Initial Vertical Velocity =Vertical component of Initial Velocity = V Sin Initial Velocity (V) V V vert = V Sin V horiz = VCos 6.11 Projectiles – Time, Height & Range An object is fired from ground level with a velocity v at an angle θ to the horizontal v h θ Range (R) Page 50 Drouin Secondary College VCE PHYSICS TOPIC: Motion 1. Time to reach Maximum Height (h) Upward is +ve. u = v sin θ use eqns of motion: v=0 v = u + at a = -g 0 = v sin θ – gt s=? t = v sin θ t=? g 2. Total Time of Flight Total time = (time to reach h) x 2 = 2 v sin θ g 3. Maximum Height Upward is +ve u = v sin θ v=0 use eqns of motion a = -g v2 = u2 + 2as s=h 0 = v2 sin2θ – 2gh t = v sin θ h = v2 sin2θ g 2g 4. Range of Projectile Horizontally vH = dH / t vH = v cos θ R = 2v sinθ x v cos θ dH = R g t = 2v sinθ 2 = v x 2 sin θcos θ g g = v2 sin 2θ g 5. Maximum Range occurs when sin 2θ = 1 2θ = 900 or θ = 450 6.12 Real Life Projectiles The mathematical analysis of projectile motion ignores the effects of __________, in particular air resistance. The real world trajectory differs from the theoretical trajectory in three main ways. (1) The actual range (horizontal distance) covered in the real world is less because of the reduction of the horizontal component of velocity due to air resistance. (2) The actual height achieved will be less, due to the effect of air resistance on the upward vertical velocity. (3) The object will fall more steeply than it rises, the path of the projectile is no longer symmetrical around its highest point. Page 51 Drouin Secondary College VCE PHYSICS TOPIC: Motion CHAPTER 7 7.0 POTENTIAL ENERGY IN ELASTIC MATERIALS. Elastic materials display ______________ behaviour. This means that when they are deformed, stretched or compressed, they change their _____________ and when the force used to deform them is removed they return to their original condition. Such materials are able to store energy when deformed and release that energy when allowed to return to original condition. The mathematical relation between force and extension is called Hooke's Law which states F = -k∆x F = Restoring Force (N) k = Spring constant of material (Nm-1) ∆x = Compression or Extension (m) The negative sign indicates that the restoring force F acts in the _________________ direction to the extension or compression ∆x A plot of the Compressive (or Extensive) force vs extension will be a straight line with Force Slope = k (Spring Constant) Area = Elastic Potential Energy Extension slope equal to the Spring Constant (k). 7.1 Potential Energy in Elastic Materials Elastic materials store ___________ when they are deformed and release that energy when they return to their original condition. Page 52 Drouin Secondary College VCE PHYSICS TOPIC: Motion The amount of energy stored can be found from the Elastic Potential Energy Formula: ES = ½kx2 where ES = Elastic P. E. (J ) k = Spring Constant (Nm-1) x = extension and or compression (m) For materials which display “irregular” behaviour, the Potential Energy stored can only be found from the area under the Force vs Extension (or Compression) graph. “REGULAR” ELASTIC BEHAVIOUR Force “IRREGULAR” ELASTIC BEHAVIOUR Slope = Spring constant (k) Force F F Extension Extension x x Area = ½Fx = ½kx2 = Energy stored up to extension x CHAPTER 8 8.0 Law of Universal Gravitation ________________ is the most well known of all the Natural Forces. We live with the effects of gravity every day and would lead completely different lives if gravity was not present. It is gravity alone which gives us our sense of “up and down”. Gravity is a ___________________ force, it acts at a distance. It is ALWAYS an ___________________ force. Gravity arises from the interaction of ____ masses. The size of the gravitational force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them. Page 53 Drouin Secondary College VCE PHYSICS Mathematically: TOPIC: Motion Fg = GM1M2 R2 where Fg = Gravitational Force (N) Constant = (6.67 x 10-11 Nm2kg-2) G = Universal Gravitational M1, M2 = masses (kg) R = Separation of the masses (m) EACH of the bodies experiences the ___________ FORCE even though they may have vastly different masses. ________________________________________________________________ Questions Newton was the first person to quantify the gravitational force between two masses M and m, with their centres of mass separated by a distance R as F= GMm R2 where G is the universal gravitational constant, and has a value of 6.67 × 10-11 N m2 kg-2. For a mass m on the surface of Earth (mass M) this becomes F = gm, where g = GM R2 ________________________________________________________________________ Questions Q49: Which one of the expressions (A to D) does not describe the term g? A. g is the gravitational field at the surface of Earth. B. g is the force that a mass m feels at the surface of Earth. C. g is the force experienced by a mass of 1 kg at the surface of Earth. D. g is the acceleration of a free body at the surface of Earth. The radius of the Earth’s orbit in its circular motion around the Sun is 1.5×1011 m Q50: Indicate on the diagram, with an arrow, the direction of the acceleration of Earth. Page 54 Drouin Secondary College VCE PHYSICS TOPIC: Motion Q51: Calculate the mass of the Sun. Take the value of the gravitational constant G = 6.67 × 10–11 N m2 kg–2. Nato III is a communication satellite that has a mass of 310 kg and orbits Earth at a constant speed at a radius R = 4.22 x 107 m from the centre of Earth. Q52: What is the speed of Nato III in its orbit ? R Nato III Earth Q53: Which ONE of the following statements (A - D) about Nato III is correct ?A: The net force acting on Nato III is zero and therefore it does not accelerate. B: The speed is constant and therefore the net force acting on Nato III is zero. C: The is a net force acting on Nato III and therefore it is accelerating. D: There is a net force acting on Nato III, but it has zero acceleration 8.1 Gravitational Attraction What Gravitational Force do the Earth and the Moon experience because of their proximity Earth to one another ? Moon Mass of Earth ME = 5.98 x 1024 kg Mass of Moon MM= 7.34 x 1022 kg Page 55 Drouin Secondary College VCE PHYSICS TOPIC: Motion Q54: What is the magnitude of the force exerted by Earth on a water molecule of mass 3.0 × 10-26 kg at the surface of Earth? Nato III is a communication satellite that has a mass of 310 kg and orbits Earth at a constant speed at a radius R = 4.22 x 107 m from the centre of Earth. Q55: Calculate the magnitude of the Earth’s gravitational field at the orbit radius, R = 4.22 x 107 m, of Nato III. Give your answer to 3 sig figs. You MUST show your working. G = 6.67 x 10-11 Nm2kg-2 Me = 5.98 x 1024 kg. 8.2 Circular Orbits under Gravity On the large scale of planets, moons, stars and other bodies in the universe, their motions are determined by the gravitational attractions between them. If, for example, a moon travels in a circular orbit around its host planet, it must be subject to a ___________________ Force. This Centripetal Force must be supplied by some kind of interaction between the planet and its moon. This interaction is the GRAVITATIONAL ATTRACTION between the Planet and its Moon. Page 56 Drouin Secondary College VCE PHYSICS TOPIC: Motion Thus the Centripetal Force (FC) needed for circular motion is supplied by the Gravitational attraction (Fg) between the planet and its moon. 8.3 Mathematics of Circular Orbits The Centripetal Force (FC) the moon is subject to is given by: FC = MMv2/R Remember the velocity of an object travelling in a circle is: v = 2R/T v2 = 4 2R2/T2 Substituting for v2 we get: FC = MM 42R2/T2 This Centripetal Force is supplied by the Gravitational Force between the Planet and the Moon: FG = GMMMp/R2 GMMMP/R2 = MM42R2/T2 Rearranging we get: R3/T2 = GMP/42 The terms G, MP, and are all constants so their ratio is constant. The ratio R3/T2 is also a constant 8.4 Kepler’s Law Johannes Kepler (1570 - 1630) discovered the laws governing planetary motion which describe the movement of the planets in our solar system. In 1615 Kepler discovered that the ratio of the of the cube of the average sun - planet distance (R3) to the square of its period (T2) was a constant for _______ planets in our solar system, this became known as Kepler’s Third Law. His other 2 laws establish planets’ speeds and the elliptical nature of planet orbits. In the previous section we found the ratio R3/T2 was a constant, (its value is roughly 3.0 x 1018 ). Page 57 Drouin Secondary College VCE PHYSICS TOPIC: Motion The 3rd law: R3/T2 = GMP/42 can be rewritten as: 3 R= GMPT2 42 Notice that the radius of orbit of any satellite, while it does depend on the mass of the planet around which it circulates, _______ depend its own mass. This is true of any satellites whether man made of naturally occurring. ________________________________________________________________ Questions A satellite in a circular orbit of radius 3.8 × 108 m around Earth has a period of 2.36 × 106 s. Q56: Calculate the mass of Earth. You must show your working. 8.5 Satellites in Space A satellite moving through space will often use the gravitational field of a planet, like Jupiter or star like our Sun to help propel it through space. At point A, the satellite comes under the influence of the gravitational field of the planet. The field does Work ON the satellite, accelerating it toward the planet. By the time it has reached B, the satellite has increased its Kinetic Energy, and hence its Speed, sufficiently to pass around, rather than crash into, the planet. The satellite flies past the planet leaving with greater speed, having “___________” some of the energy stored in the planet’s field. Page 58 Drouin Secondary College VCE PHYSICS TOPIC: Motion This is the normal way of sending satellites to the outer planets and even outside our solar system. 8.6 Energy Transfers in Gravitational Fields The Gravitational Field vs Distance graph for Jupiter showing positions A and B for the satellite is shown. g(Nkg-1) RJ B A Distance R (m) Since Work Done = Energy Transferred, the area under the graph represents the work done by the field on, and the change in energy possessed by, “1 kg of satellite mass” in moving from A to B. In exam questions, the area normally needs to be found by the “counting the squares” method. Area gives: 1. Work by the field on 1 kg of satellite moving from A to B. 2. The increase in Kinetic Energy possessed by 1 kg of satellite in moving from A to B. 3. The loss in Potential Energy of 1 kg of satellite moving from A to B For the satellite with a mass >1 kg, total energy possessed = area x mass Page 59 Drouin Secondary College VCE PHYSICS TOPIC: Motion Questions The Russian space station MIR (Russian meaning - peace) was in a circular orbit around the Earth at a height where the Gravitational Field Strength is 8.7 Nkg-1 Q57: Calculate the magnitude of the gravitational force exerted by Earth on the astronaut of mass 68 kg on MIR When the astronaut wishes to rest he has to lie down and strap himself into bed. Q58: What is the magnitude of the force that the bed exerts on the astronaut before he begins to fasten the strap ? Newspaper articles about astronauts in orbit sometimes speak about zero gravity when describing weightlessness. Q59: Explain why the astronaut in the orbiting MIR is not really weightless. Page 60