Physics: Understanding Motion. Year 10 Core Science 2012. What do we need to learn?. How do we convert units? What do these terms mean? Distance, displacement, vector, scalar, speed, velocity, acceleration, force and momentum How can we describe and analyse motion?.
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Physics: Understanding Motion Year 10 Core Science 2012
What do we need to learn? How do we convert units? What do these terms mean? Distance, displacement, vector, scalar, speed, velocity, acceleration, force and momentum How can we describe and analyse motion?
What do we need to learn? How are changes in movement caused by the actions of forces? What are Newton’s 3 laws of motion? How do we explain and apply them to the real world? What is momentum and how does it apply to real life situations?
There’s lots to learn… What’s going to help us? Asking lots of Questions Conducting experiments Drawing graphs Applying the theory to real life situations
To make life easier for Physics students, situations or events which require mathematical analysis are often described as occuring in an ideal, frictionless world. In the ideal world an object under the influence of Earth’s gravity will accelerate at 9.8 ms-2 throughout its journey never reaching a terminal velocity. In the ideal world energy transformations are always 100% efficient, so that the potential energy of a pendulum at the top of its swing is all converted to Kinetic Energy (motion energy) at the bottom. In the ideal world perpetual motion machines are common place. 1.0 An Ideal World In the ideal world the laws of motion apply exactly, eg. objects which are moving will continue to move with the same speed unless or until something occurs to change this.
Physics language Some units we will be using. Length (m), time (s) Mass (kg), length (m), time (s) Mass (kg), length (m), time (s) Length (m), time (s) Standard International units are: meter, kilogram, second, ampere Why do we need standard units? When things go wrong…
Why do we need standard units? • It is important that scientists can share their data and findings. To do this, they use a common set of units. The SI unit for both distance and displacement is the metre (m) and the SI unit for speed is metres per second (m/s). • You may have seen ‘metres per second’ also written as ‘ms−1’. This expression is derived from the rule for calculating speed: • Speed = distance = metres time taken seconds • When shifting the ‘seconds’ from the denominator to the numerator of the fraction, the index (or power) becomes negative. Hence, the seconds are written with an index of −1 in ms−1 (we’ll learn more about this later…)
Scalars have magnitude (size) only Eg distance traveled is 300meters Other scalar quantities: Speed, mass, time, temp, energy Vectors have magnitude and direction. Eg distance traveled is 300m north Shown by a What’s the difference? Line showing magnitude arrow showing direction
Motion in motion What is the relationship between 100 and 27.78
To change units from m/s to km/h X 3.6 27.78m/s 100km/h ÷3.6
3.6 Fundamental skills Show that 1 ms-1 = 3.6 kmh-1 Two relevant conversion factors are: 1 km = 1000 m, 1 h = 3600 s 1km 1000m 1000m 1km 1h 3600 s 3600s 1h These can be written as: or and or Which ones to use ? Easy, you want to end up with km on the top line and h on the bottom 1m x1kmx3600s s 1000m 1h so 1 ms-1 = 3.6 kmh-1
So who is faster? • Did UsainBolt run the 100m faster than Michael Johnson ran the 400m? • Calculate the speed of the two men. Speed (m/s)= distance (m) ÷ time taken (sec)
100m-UsainBolt 9.58 seconds How many meters per second? 10.44 m/s How many km per hour? 37.59 km/h 400m Michael Johnson 43.18 seconds How many meters per second? 9.26 m/s How many km per hour? 33.34km/h World records So the faster runner was… Usain Bolt
Motion • Aim: To convert: meters per second (m/s or ms-1) to kilometers per hour (km/h or kmh-1) using a formula
Position & Displacement In order to specify the position of an object we first need to define an ORIGIN or starting point from which measurements can be taken. For example, on the number line, the point 0 is taken as the origin and all measurements are related to that point. 0 5 10 15 20 25 30 35 40 -40 -35 -30 -25 -20 -15 -10 -5 Numbers to the right of zero are labelled positive Numbers to the left of zero are labelled negative A number 40 is 40 units to the right of 0 A number -25 is 25 units to the left of 0
Position Questions • 1. What needs to be defined before the position of any object can be specified ? • A zero point needs to be defined before the position of an object can be defined • 2. (a) What distance has been covered when an object moves from position +150 m to position + 275 m ? • Change in position = final position – initial position • = +275 – (+150) = + 125 m. Just writing 125 m is OK • (b) What distance has been covered when an object moves from position + 10 m to position -133.5 m ? • Change in position = final position – initial position • = -133.5 – (+10) = - 143.5 m. Negative sign IS required
Distance & Displacement Distance is a measure of length travelled by an object. It has a Unit (metres). Displacement is the shortest possible length between the start and finish of the travelling object. Displacement is best defined as “How far from your starting point you are at the end of your journey” Distance is best defined as “How far you have travelled in your journey”
Distance & Displacement Distance is a scalar measurement. Remember: Scalar measurements are expressed only as a size, with no direction. Displacement is a vector measurement. Remember: Vector measurements are expressed as a size and a direction
Distance & Displacement Positive Direction At this point in the journey, Distance travelled = 2km and Displacement = + 2km 2 km The difference between distance & displacement is easily illustrated with a simple example. You are sent on a message from home to tell the butcher his meat is off. At the end of the journey, Distance travelled = 2 + 2 = 4km while Displacement = +2 + (-2) = 0 km
Let’s see if this makes sense… Lets read through pages 262-263 and attempt some questions
Distance • Is how far on object has traveled, from point A to point B. • Distance has only magnitude (scalar) • Eg the distance traveled by the runner was 9km
Displacement • Is the change in position or the shortest distance between two points. • Displacement has a magnitude and direction (vector) • Eg the runner ran 6km to the right and 3km down, (displacement 6.7km south east)
How far did the person travel? 6km start 3km Distance: 6 + 3 = 9km Displacement: 6.7km south east finish
Speed and Velocity So what’s the difference?
Speed & Velocity These two terms are used interchangeably in the community but strictly speaking they are different: Speed is the time rate of change of distance, i.e., Speed = Distance Time Velocity is the time rate of change of displacement, i.e., Velocity = Displacement Time
Speed & Velocity Speed is a SCALAR QUANTITY, having a unit (ms-1), but no direction. Thus a speed would be: 100 kmh-1 or, 27 ms-1 Velocity is a VECTOR QUANTITY, having a unit (ms-1) AND a direction. Thus a velocity would be: 100 kmh-1 South or - 27 ms-1
Instantaneous & Average Velocity The term velocity can be misleading, depending upon whether you are concerned with an Instantaneous or an Average value. The best way to illustrate the difference between the two is with an example. You take a car journey out of a city to your gran’s place in a country town 90 km away. The journey takes you a total of 2 hours. The average velocity for this journey, vAV = Total Displacement = 90 = 45 kmh-1 Total Time 2 Questions
Instantaneous & Average Velocity Recall: The average velocity for this journey, vAV = Total Displacement = 90 = 45 kmh-1 Total Time 2 However, your instantaneous velocity measured at a particular time during the journey would have varied between 0 kmh-1 when stopped at traffic lights, to, say 120 kmh-1 when speeding along the freeway. Average and Instantaneous velocities are rarely the same. Unless otherwise stated, all the problems you do in this section of the course require you to use Instantaneous Velocities. Questions
Speed and Velocity • Average speed- total distance by the total time • Velocity- is the displacement by the time taken Average Speed = total distance traveled (m) Total time taken (s) Velocity = displacement (m) time taken (s)
This car is travelling at a speed of 20m/s-1 This car is travelling at a velocity of 20m/s-1 east Speed vs. Velocity Speed is simply how fast you are travelling… Velocity is “speed in a given direction”…
Quick questions • A female runner completes a 400 m race (once around the track) in 21 seconds what is: • Her distance travelled (in km), • (b) her displacement (in km), • (c) her speed (in ms-1) and • (d) her velocity (in ms-1) ? (a) Distance = 0.4 km (b) Displacement = 0 km (c) Speed = distance/time = 400/21 = 19ms-1 (d) Velocity = displacement/time = 0/21 = 0 ms-1
The runner takes half and hour to finish 6km start 3km Distance= 9km Displacement= 6km Speed= 18km/hr Velocity= 12km/hr finish
Motion prac • Let’s collect some data. . . .
Motion by Graphs Distance (a) Time Displacement (b) Time Describe how the object moving?
Graphical Relationships Graphs are used to help give us an image of movement of an object Graphs “tell you a story”. You need to develop the skills and abilities to “read the story”. • There are two basic types of graphs used in Physics: • Sketch Graphs – give a “broad brush” picture or show the “trend”. • (b) Numerical Graphs – give the exact relationship between the two variables graphed and may be used to calculate other values.
Sketch Graphs Distance Displacement Velocity Displacement The Story: As time passes, the distance of the object from its starting point does not change. This is the graph of a stationary object Time Time Time Time Sketch graphs have labelled axes but no numerical values, they show a “trend” between the quantities. The Story: The object begins its journey at the origin at t = 0. As time passes its displacement increases at a constant rate (slope is constant). So time rate of change of displacement which equals velocity is constant. This is a graph of an object travelling at constant velocity The Story: As time passes its displacement gets larger at an increasing rate. This is the graph of an object moving with constant acceleration The Story: As time passes the velocity remains constant. This is a graph of an object travelling at constant velocity
Distance (a) Time Displacement (b) Time Sketch Graphs Distance versus time graph. As time passes displacement remains the same. This is the graph of a stationary object Displacement versus time graph. As time passes its displacement is increasing in a uniform manner. This is a graph of an object travelling at constant velocity.
Velocity (c) Time Displacement (d) Time Sketch Graphs Velocity versus time graph. As time passes the velocity of the object remains the same. This is a graph of an object travelling at constant velocity. Displacement versus time graph. As time passes its displacement gets larger at an increasing rate. This is a graph of an accelerating object.
What a graph can tell you. The graphs you are required to interpret mathematically are those where distance or displacement, speed or velocity or acceleration are plotted against time. The information available from these graphs are summarised in the table given below.
2) Horizontal line = • 4) Diagonal line downwards = • Diagonal line = • 3) Steeper diagonal line = Displacement-time graphs Remaining stationary Returning to the starting position 40 30 20 10 0 Distance (metres) Time/s 20 40 60 80 100 Moving forwards Moving forwards faster