Physics Grade 10 Advanced level Mechanics and kinematics
Contents UNIT 2: Mechanics and Kinematics Core Standards... 3 Objectives..... 4 26.1 26.2 26.3 26.4 26.5 26.6 Motion in one dimension...... 5 Deriving equations of motion... 19 Forces and their effects..... 25 Resultant force..... 32 Friction...... 37 Static and dynamic friction..... 40 Questions..... 46 References........ 49 2
10A.26.1 Understand the concepts of displacement, speed, velocity and acceleration, represent them graphically and interpret graphs that represent them. 10A.26.2 Derive, from the definitions of velocity and acceleration, equations that represent uniformly accelerated motion in a straight line and use them to solve problems relating to the motion of objects under uniform acceleration. 10A.26.3 Know that a force acting on an object can cause deformation or velocity change 10A.26.4 Identify forces acting on a body, determine resultants, resolve forces into components and use the vector triangle to represent forces in equilibrium 10A.26.5 Show a qualitative knowledge of frictional forces and viscous forces, including air and water resistance, and distinguish between static and dynamic friction. 10A.26.6 Identify factors affecting friction and use the concepts of static and dynamic coefficients of friction. 3
By the end of the unit, students understand, manipulate and represent graphically the concepts of displacement, speed, velocity and acceleration to solve problems related to moving objects. They know that a force can cause a change in velocity or shape of an object, resolve multiple forces acting on an object and distinguish between dynamic and static friction. Students who progress further derive equations that represent uniformly accelerated linear motion and use them to solve problems. They know that the horizontal and vertical components of projectile motion are independent of one another. They identify factors affecting friction and use the static and dynamic coefficients of friction. 4
26.1 Motion in one dimension Grade 10 Unit AP.2 - Mechanics and Kinematics ا حروح في ت عذ احذ Wherever we look in the universe we find things that are moving. Animals, including humans, are clearly able to move and we can build machines such as cars, boats and aero planes for transport. However, we also find motion in less obvious places. 1. DISPLACEMENT اإلزاحح اإلزاحح ي لياش ا رغير في ا م لع Displacement measures the change in position Represented as x (if horizontal) or y (if vertical) x ورمس ا تا رمس ( x أفميح( أ ( y رأسيح ) Vector quantity (i.e. needs directional information) x f x i وميح مرد ( ذحراج رعريف اذدا ا( + or - is generally sufficient to indicate direction for one-dimensional motion 5
The following figure gives examples of determining displacements for a variety of situations. 2. VELOCITY ا سرعح ا مرد ح Average velocity is the ratio of the change of position to the time interval during which that changes occurred. ا غشػخ ا زغ خ ا ز عطخ غجخ ) ؼذي( رغ ١ ش ا لغ إ ا زغ ١ ش ف ا ض ا ز ر ف ١ زا ا زغ ١١ ش Consider the car in the figure. The car is moving along a highway in a straight line (the x-axis). Suppose that the positions of the car are x i at time t i and x f at time t f. In the time interval t t f t i, the displacement of the car is x x f x i. 6
The v avg, is defined as the displacement divided by the time interval during which the displacement occurred. ا غشػخ ا زغ خ ا ز عطخ : غجخ ) ؼذي( اإلصاحخ إ ا زغ ١ ش ف ا ض ا ز ر ذ ف ١ اإلصاحخ In SI, the unit of velocity is meters per second, abbreviated as m/s. The average velocity of an object can be positive or negative, depending on the sign of the displacement. (The time interval is always positive) ا غشػخ ا زغ خ ا ز عطخ ى أ رى عجخ ا عب جخ حغت إشبسح اإلصاحخ Example: v1 average x1 70m t 10s 7m s v2 average x2 60m t 10s 6m s 7
Problem: During a race on level ground, Hamad runs with an average velocity of 6.02 m/s to the east. What is Hamad s displacement after 137 s? احسة اإلزاحح إرا أعطيد ا سرعح ا مر سطح ا سمه. Velocity is not the same as speed ا سرعح ا مرد ح يسد مث ا سرعح ا عذديح Velocity describes motion with both a direction and a numerical value (a magnitude). Speed has no direction, only magnitude. ا غشػخ ا زغ خ ب مذاس ارغب ا غشػخ ا ؼذد ٠ خ ب مذاس فمػ Average speed is equal to the total distance traveled divided by the time interval. ا غشػخ ا ؼذد ٠ خ ا ز عطخ رغب ا غبفخ ا ى ١ خ ا مط ػخ مغ خ ػ ا ض ا ى 8
Practice Lab: Grade 10 Unit AP.2 - Mechanics and Kinematics لياش ا سرعح MEASUREMENT OF VELOCITY Apparatus: األد اخ Ticker timer and tape, suitable low-voltage A c. power supply, trolley, runway, laboratory jack or stand. Procedure: ا خط اخ 1. Set up the apparatus as in the diagram. 2. Connect the ticker timer to a low-voltage power supply. 3. Give the trolley a small push to start it moving. 4. Adjust the angle of inclination of the runway until the trolley moves with constant velocity the spots on the tape are all equidistant. 5. Most ticker timers make 50 spots per second. Therefore the time interval between two adjacent spots is 0.02 s. 6. Measure the length s of ten adjacent spaces. 9
7. The time t is 10 0.02 = 0.2 s. 8. As the trolley was travelling at constant velocity we can say that 9. Repeat using pushes of varying strengths. 10. Tabulate results as shown. s v. t - رضجذ األد اد و ب ف ا شع - رذفغ ا ؼشثخ الحظخ ص ي حشوز ب غشػخ زظ ح ح ١ ش الحظ ا غبفبد ث ١ اي مبغ زغب ٠ خ ص رمبط ا غبفخ ث ١ ػششح مبغ ح ١ ش ا ا ض ث ١ و مػر ١ ٠ حذد ب ا غ بص ػ ذ ب ٠ ى حغبة ا غشػخ. Results: ا ىرائح s (m) t (s) v (m/s) مالحظاخ Notes: Ignore the initial five or six dots on the tape as this shows the initial acceleration due to the push. Ticker timers that use pre carbonated tape are recommended because the friction due to paper drag is reduced. Ensure that the voltage rating of the timer is not exceeded. Some timers make one hundred dots in one second. 10
3. Acceleration ايعح ح The quantity that describes the rate of change of velocity in a given time interval is called acceleration. ؼذي رغ ١ ش ا غشػخ ثب غجخ ض Acceleration has direction and magnitude. Thus, acceleration is a vector quantity. ا ؼغ خ ب ارغب ب مذاس. ز ه ا ؼغ خ و ١ خ زغ خ Acceleration is the rate of change of velocity with respect to time The magnitude of the average acceleration is calculated by dividing the total change in an object s velocity by the time interval in which the change occurs. 11
The units of acceleration in SI are meters per second per second, which is 2 written as meters per second squared ( m/s ). When measured in these units, acceleration describes how much the velocity changes in each second. Solved example: A shuttle bus slows down with an average acceleration of 2 1.8 m/s. How long does it take the bus to slow from 9.0 m/s to a complete stop? Solution: Given : v Unknown : t i 9.0 m/s, v f 0 m/s, a avg 1.8 m/s 2 a avg t v t v a avg v f a v avg i 0 9.0 1.8 5.0 s 12
Motion graphs Distance-time graphs ا رمثي ا ثياوي حروح ح ا غبفخ-ا ض On a distance-time graph, the slope of the line is numerically equal to the speed. ف ح ا غبفخ- ا ض ١ ا خػ ٠ غب ا غشػخ slope Slope of a line change in vertical coordinates change in horizantalcoordinates v Average speed avg x t x t f f x t i i If an object is not moving, a horizontal line is shown on a distance-time graph. إرا وب ا غغ عبو ٠ ض ثخػ أفم ػ ح ا غبفخ - ا ض Time is increasing to the right, but its distance does not change. It is not moving. We say it is At Rest. 13
إرا وب ذ ا غبفخ ال رزغ ١ ش ةص ٠ بدح ا ض و ب ارغ ب ١ ٠ ب ٠ مبي أ ا غغ عبو. If an object is moving at a constant speed, it means it has the same increase in distance in a given time: إرا وب ا غغ زحشن ثغشػخ زظ خ فب ٠ مطغ غبفبد زغب ٠ خ ف أص خ زغب ٠ خ Time is increasing to the right, and distance is increasing constantly with time. The object moves at a constant speed. ا غبفخ رضداد ثبصد ٠ بد ا ض ا غغ ٠ زحشن ثغشػخ زظ خ. A steeper line indicates a larger distance moved in a given time. In other words, higher speed. و ب وب ١ ا خػ اوجش وب ذ ا غبفخ ا مط ػخ اوجش ف ا ض ا حذد. أ ا غغ ٠ ى أوضش عشػخ. 14
The following figure represents straight-line graphs of position-versus-time for three different objects. ا شع ا ج ١ ب ا زب ٠ ض حشوخ صالس أعغب. Object 1 has a constant positive speed because its position increases uniformly with time. Thus, the slope of this line is positive. Object 2 has zero speed because its position does not change (the object is at rest). Hence, the slope of this line is zero. Object 3 has a constant negative speed because its position decreases with time. As a result, the slope of this line is negative. ا غغ األ ي ٠ زحشن ثغشػخ صبثزخ عجخ ا غغ ا ضب عبو ا غغ ا ضب ش ٠ زحشن ثغشػخ صبثزخ عب جخ. 15
Speed-time graphs مىحى ا سرعح-ا سمه On a speed-time graph, the slope of the line is numerically equal to the acceleration. ف ح ا غشػخ- ا ض ١ ا خػ ٠ غب ا ؼغ خ Slope of a line change in vertical coordinates slope change in horizantalcoordinates Acceleration v a t v t f f v t i i A straight horizontal line on a speed-time graph means that speed is constant. It is not changing over time. ا خػ األفم ف ح ا غشػخ ا ض ٠ ؼ أ ا غشػخ زظ خ. ال رزغ ١ ش ث ش س ا ض. 16
This graph shows increasing speed. The moving object is accelerating. ا شع ا ج ١ ب ٠ ض ص ٠ بدح ف ا غشػخ ث ش س ا ض. إ ا غغ ٠ زحشن ثؼغ خ. A steeper line indicates a larger speed moved in a given time. In other words, higher acceleration. و ب وب ١ ا خػ اوجش وب ذ ا غشػخ اوجش ف ا ض ا حذد. أ ا غغ ٠ ى أوضش رغبسػب ( ػغ خ (. On a speed-time graph, the area under the line is numerically equal to the distance travelled. ف ح ا غشػخ ا ض ا غبحخ رحذ ا ح ر ض ا غبفخ ا مط ػخ. 17
Problem: The table below gives some data for a car: Speed (m/s) 0 10 20 30 40 50 60 Time (s) 0 1 2 3 4 5 6 Plot a speed-time graph for the car. ض ث ١ ب ١ ب ح عشػخ- ص Solution: 18
26.2 Deriving equations of motion Grade 10 Unit AP.2 - Mechanics and Kinematics اشرماق معادالخ ا حروح When velocity changes by the same amount during each time interval, acceleration is constant. ػ ذ ب رزغ ١ ش ا غشػخ ث فظ ا مذاسخالي فظ ا فزشاد ا ض ١ خ ا ؼغ خ رى زظ خ The relationships between displacement, time, velocity, and constant acceleration are expressed by the equations shown next. These equations apply to any object moving with constant acceleration. رغزخذ ا ؼبدالد زؼج ١ ش ػ ا ؼاللبد ث ١ اإلصاحخ ا ض ا غشػخ ا ؼغ خ These equations use the following symbols: x = displacement v i = initial velocity v f = final velocity t = time interval Equations for Constantly Accelerated Straight line motion 19
Solved example: A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.0 s later. Find the distance that the car travels during braking. حساب ا مسافح ا الزمح ر لف سيارج تمعرفح سرعر ا االترذائيح زمه. ا ر لف SOLUTION: Given : v Unknown : x i 42 m/s, v f 0 m/s, t 5 s x x x 1 ( vi v f ) t 2 1 (42 0)(5) 2 105 m 20
Acceleration due to gravity Grade 10 Unit AP.2 - Mechanics and Kinematics عد ح ا دارتيح األرضيح Free fall is the motion of a body when only the force due to gravity is acting on the body. ا غم غ ا حش: عم غ ايعغ رحذ رأص ١ ش ل ح احذح فمػ ق ج ا غبرث ١ خ األسظ ١ خ The acceleration on an object in free fall is called the acceleration due to gravity, or free-fall acceleration. ػغ خ ا غغ ف ا غم غ ا حش رغ ػغ خ ا غبرث ١ خ األسظ ١ خ أ ػغ خ ا غم غ ا حش. When there is no air resistance, all objects fall with the same acceleration regardless of their masses. ف حب خ ػذ ع د مب خ ا اء ع ١ غ األعغب رزحشن ث فظ ا ؼغ خ ب اخز فذ وز Acceleration due to gravity is constant during upward and downward motion. ػغ خ ا غبرث ١ خ األسظ ١ خ صبثزخ ع اء وب ذ ا حشوخ ألػ أ األعف 21
A Freely falling bodies undergo constant acceleration 2 2 Free-fall acceleration on Earth s surface is ( 9.81m/s 10 m/s ) at all points in the object s motion. Consider a ball thrown up into the air: Moving upward: velocity is decreasing, 2 acceleration is 9.81m/s Top of path: velocity is zero, acceleration is 9.81m/s 2 Moving downward: velocity is increasing, 2 acceleration is 9.81m/s سم ط األخسا ا حر ذحد ذأثير عد ح ثاترح Solved example: A ball is thrown vertically upward with a speed of 25.0 m/s from a height of 2.0 m. How long does it take the ball to reach its highest point? SOLUTION: Given : v Unknown: t i 25.0 m/s, v f v f 0 m/s, 0 25 10 t t v i 25 10 g 10 m/s g t 2.50 s 2 22
Practice Lab: MEASUREMENT THE ACCELERATION OF FREE FALL, g Apparatus: Millisecond timer, metal ball, trapdoor and electromagnet. Procedure: 1. Set up the apparatus. The millisecond timer starts when the ball is released and stops when the ball hits the trapdoor. 2. Measure the height h as shown, using a meter stick. 3. Release the ball and record the time t from the millisecond timer. 4. Repeat three times for this height h and take the smallest time as the correct value for t. 5. Repeat for different values of h. 23
1 h gt. 2 6. Calculate the values for g using the equation 2 Obtain an average value for g. Alternatively draw a graph of h against t 2 and use the slope to find the value of g. رغ ١ ض األد اد و ب ف ا شع م ١ ظ االسرفبع (h) غؼ ا ىشح ا ؼذ ١ خ رغمػ حغت ص ا غم غ, رؼبد ا خط اد وز ه االسرفبع -رغغ ا زبئظ ف ا غذ ي ا شفك ٠ ز ر ض ١ ا ؼاللخ ث ١ االسرفبع شثغ ا ض ث ١ ب ١ ب خالي ا ١ ا برظ رحغت ػغ خ ا غبرث ١ خ. Results: h (m) t (s) t (s) t (s) t (s) g (m/s 2 ) 1 2 3 Notes: Place a piece of paper between the ball bearing and the electromagnet to ensure a quick release. In some models of this apparatus, a pressure pad is used in place of the trapdoor; a manually operated spring-release mechanism may also be used in place of the electromagnet. 24
26.3 Forces and their effects Grade 10 Unit AP.2 - Mechanics and Kinematics ا م ذأثير ا What is a force? ب ا م ح What effects do forces have on materials and moving objects? ب رأص ١ ش ب ػ ا اد األعغب ا زحشوخ How do objects balance? و ١ ف رى األعغب زض خ A force is a 'push' or a 'pull'. We need to understand forces because they affect all the objects around us. Some forces only act when two objects are touching. These are called contact force acts on an object only by touching it. (Your hand and the desk exert forces only when they touch the book). Some forces act at a distance (long-range force). For example the gravitational pull of the Earth holds the Moon in orbit at a distance of over 350 000 km! All the pieces of metal and concrete in this bridge are acted upon by forces. This changes their shapes. Some pieces are in tension: the forces are stretching them. Other pieces are being compressed: the forces are squashing them. The weight of the bridge makes it bend in the middle. ا م ح دفغ عحت. ا غبرث ١ خ. حزبع ب ذساعخ ب ٠ ح ١ ػ ث ب ثؼط ا م رى ل رال ظ ةػع ب ػ ثؼذ وم ع ١ غ ى بد ا غغش ف ا شى ا شفك رزأصش ثم لذ رى شذ أ ظغػ وز ه ص خ ا ز ٠ غؼ ٠ ح ف ا زصف. 25
Forces change the speed of objects Grade 10 Unit AP.2 - Mechanics and Kinematics ا م ذغير سرعح األخسا Forces make things start to move. They also increase or decrease the object's speed. For example, a plane at rest on the runway will not start to move until its engines exert a force. Once it is moving, the force makes the plane accelerate. On landing, the plane has to exert a force in the opposite direction to make it slow down and stop. فب م رغؼ األش ١ بء رجذأ ا حشوخ أ رض ٠ ذ أ رم عشػز ب. وب طبئشح رى عبو خ حز رؤصش آالر ب ثم ح فزحشو ب ص رزغبسع. أ ب ف ا ج غ فب م رؼ ػىظ ا حشوخ زم ا غشػخ حز رمف. Forces change the direction of moving objects ا م ذغير اذداي حروح األخسا Moving objects tend to move in straight lines. They only change direction when a force acts. For example, a snooker ball moves in a straight line until it hits the 'cushion' at the edge of the table. When the ball meets the cushion, a force makes it bounce off in a different direction. The cue hitting the ball and the ball hitting the cushion are examples of contact forces. رحا ي األعغب ا حشوخ ف خػ غزم ١ ى ب رغ ١ ش ارغب حشوز ب ػ ذ ب رزأس ثم ح و ضبي ػ ر ه وشح ا غ وش ا ز رزحشن ثخػ غزم ١ حز رصطذ ثب عبدح ا غب ج ١ خ فزغ ١ ش ارغب حشوز ب. 26
أوشطح Activities 1- Place any object-a book, for example- in a student's outstretched hand and ask hat forces are acting on the book and the origin of each force. Downward-gravity; upward student's hand pushing up. 1- أ ٠ عغ ا طب ت عغ ب ػ ساحخ ٠ ذ وب ىزبة ا ط ت رحذ ٠ ذ ا م ا ؤصشح ادعب ب. 2- Student work in small groups to explore how an unbalanced force can produce acceleration. change the velocity using dynamics trolleys with ticker- timers or light gates. 2- ػ غ ػبد اعزخذا ا ذلبق ا ض أ ا ج اثبد ا ع ئ ١ خ ذساعخ رغ ١ ش عشػخ طع زحشن. حذج ا م ج The unit of force We measure force in units called Newton (N).These are named after the famous physicist Sir Isaac Newton. (1N resultant force acting on 1kg produces an acceleration of 1m/s 2 ).We can measure a force using a spring balance or Newton meter. رمبط ا م ح ث حذح ا ١ ر س ض )N( ا ١ ر ا احذ ا م ح ا ؤصشح ػ عغ وز ز احذ و ١ عشا رىغج ػغ خ مذاس ب 1m/s 2 27
Forces cause deformation on objects Grade 10 Unit AP.2 - Mechanics and Kinematics ا م ذسثة ذش ي ألخسا Forces can cause materials to stretch. When the forces are removed, the material may spring back to its original length. We call this elasticity. For example, a rubber band can be stretched to several times its length but it will still go back to its original size. Rubber is a very elastic material. Metal wires will also stretch and spring back into shape if the forces are small. However, if the forces are too large, the wire will be left permanently Stretched. This happens when we go beyond the material's elastic limit. ح ١ ش رؼ ا م ػ اعزطب خ ا اد ب ب ٠ ؼ د ظؼ األص ثض اي ا م ح ا ؤصشح ح ١ ش رغ ز ا خبص ١ خ ثب ش خ و ضبي ػ ر ه ا زأص ١ ش ثم ح ػ شش ٠ ػ ا طبغ وز ه األعالن ا ؼذ ١ خ ا بثط. ح ١ ش رغزط ١ إ حذ ؼ ١ ٠ غ حذ ا ش خ ا صادد ا م ح ا ؤصشح ػ زا ا حذ ٠ غزط ١ ثشى دائ د ا شع ع ط ي األص ػ ذ ص اي ا م ح ا ؤصشح. 28
Practice Lab: Forces on a spring ذمرير عم ي: ا م ا مؤثرج ع واتض Purpose: To determine the relationship between the forces applied to a spring and the vertical distance of its bend. ا ذف: دساعخ ا ؼاللخ ث ١ ا م ح ا ؤصشح ػ ا بثط اعزطب ز Equipments: 1-Meter stick 2-spring scale 3- Ruler 4- loads األد اخ: بثط- غطشح أصمبي-... Theory: The amount of bend or stretch in an elastic material depends on the applied force. This relationship was developed by the British scientist Sir Robert Hook (1635-1703). Hooke's law can be applied to elastic bands, springs, wooden meter sticks - anything that can bend or stretch. If we bend or stretch too far so called 'elastic limit' is exceeded and the object either breaks or stretches out of shape. Procedure: Hook s Law F = K x 1. Clamp one end of the meter stick to the desk. 2. Adjust the spring scale so that the pointer is on 0 Newton s. 3. Place the loop around the free end of the stick and hook the spring scale around the loop. 4. Pull with a force of 1 Newton and have a partner record the height of the end of the meter stick above the desk. 5. Repeat step 4. For 2 Newton s up to 7 Newton s. (don t exceed the elastic limit of 29
the spring) 6. Record you data in the table provided. ا خط اخ : 1- ثؼذ رضج ١ ذ ا بثط ظغ ػال خ ا صفش ثذ أصمبي. ٠ ز ظغ أصمبي حغت ا ز فش ف و شح ٠ غغ ف ا غذ ي ا شفك مذاس ا م ح ا ؤصشح مذاس االعزطب خ. 2-٠ ز ر ض ١ ا ؼاللخ ث ١ ا م ح االعزطب خ ث ١ ب ١ ب ا Data and Data Analysis: 1- Which variable is the independent variable? 2- Which variable is the dependent variable? 3- Draw a graph of your data on the grid provided. Draw a line of best fit through the points. Force (N) 1 2 3 4 6 Bending (mm) 30
7 for this lab. 4- List the sources of error Question: 1- A spring is 80mm long. It stretches 12mm when a load of 1 N is applied. How long will the spring be when a load of 2N hangs from it? 31
26.4 Resultant force (The sum of two or more forces ( ا م ج ا محص ح ي ا دمع االذدا ي م ذيه أ أوثر Force is a vector quantity. 32
1- Two forces are equal when the two forces and direction are the same. For example the two forces F 1 and F 2 shown in the figure, are equal. Even though they don t begin or end at the same point, they have the same length and direction. 1- م ي ػ ل ر ١ أ ب زغب ٠ ز ١ إ وب ب فظ ا مذاس االرغب حز إ وب ذ مطخ ا جذا ٠ خ خز فخ و ب ف ا شى. 2- Forces of F 1 and F 2 acting in the same direction, add up to give a resultant force of F =F 1 +F 2 إرا وب ذ ا م رب رؤصشا ػ ا غغ ث فظ االرغب فب ا حص خ حبص ع ؼ ب. 3- Forces of F and F acting in opposite directions cancel out to give no resultant force at all: These forces are balanced. -2 3- إرا وب ذ ا م رب زغب ٠ زب مذاسا رؤصشا ف ارغب ١ زؼبوغ ١ فب حص خ رغب صفشا م ي أ ا م زض خ. 4- Forces of F 1 F 2 acting in the opposite direction, a resultant force of F =F 1 - F 2 33
4- إرا وب ذ إحذ ا م اوجش األخش فب حص خ حبص غشح ب ف ارغب األوجش. Note: When the two forces are at right angle the resultant force can determine by: F = F 1 2 + F 2 2 مالحظح: إ وب ذ ا م رب زؼب ذرب فزحغت ا حص خ ثبعزخذا ظش ٠ خ ف ١ ضبغ سط. Equilibrium and the Equilibrant االذسان ا م ج ا ري ذحمك االذسان Suppose two forces are exerted on an object and the sum is not zero how could you find a third force that, when added to the other two would add up to zero? Such a force, one that produces equilibrium, is called the equilibrant. To find the equilibrant, first find the sum of the two forces exerted on the object. This sum is the resultant force, F, the single force that would produce the same effect as the two individual forces added together. The equilibrant is thus a force with a magnitude equal to the resultant, but the opposite direction. Figure illustrates this procedure for two vectors, but any number of vectors could be used. إرا وب ذ حص خ ا م ال رغب صفشا أسد ب أ رى ا م ف حب خ ارضا فئ ب ع ١ ف ل ح صب ضخ غب ٠ خ مذاسا حص خ رؼبوغ ب ف االرغب ف ١ ى ا غغ ف ز ا حب خ ف حب خ ارضا و ب ف ا شى. 34
Question: 1- Each set of force vectors below is drawn to the same scale. For each situation, write its letter next to the correct number of the expression. a. Forces in set have same direction. ( ) b. Forces in set have same magnitude.( ) c. Forces in set are equal. ( ) 35
Question: 2- Forces of 12 N and 5 N both act at the same point, but their directions can be varied. a) What is their greatest possible resultant? b) What is their least possible resultant? c) If the two forces are at right angles, find the resultant. 36
26.5 Friction االحرىان Friction the resistive force that occurs when two surfaces contact each other. Friction makes it possible: ذمىىه ل ج االحرىان مه : ا غ ١ ش walk. To اعزخذا إغبساد غ ١ بساد vehicles. To use wheeled ا غ ط sit. To اإل غبن ثىزجه books. To hold To know further information about friction you may run this experiment: 37
ؼشفخ ا ض ٠ ذ ػ االحزىبن رأص ١ شار ب ٠ ى ه إعشاء ا زغشثخ ا ٢ ر ١ خ وش اط Activity Put an object on any ramp ( e.g. wooden beam) What do you think the forces acting on the object? What do you think the force that prevents the object to slide? Gradually try to increase the angle between the ramp and the floor. Expect when the object will start to move. 38
ما ي ل ج االحرىان Friction? What is It s the force that tries to stop materials sliding across each other. ر ه ا م ح ا ز رحب ي إ ٠ مبف ا اد ا ز رزحشن ف ق ثؼع ب ا جؼط There is friction between your hands when you rub them together and friction between your shoes and the ground when you walk along. Friction prevents machinery from moving freely and heats up its moving parts. ر حظ ل ح االحزىبن ث ١ ٠ ذ ٠ ه ػ ذ د ى ب ثجؼط وز ه ر حظ ب ػ ذ ا غ ١ ش ػ ذ ب ٠ ال ظ حزائه األسض ػ د ا غ ١ ش Friction is not always a nuisance. It gives shoes and tyres grip on the ground, and it is used in most braking systems. In cars, for example, rubber pads are pressed against the wheels to slow them down. ال رؼزجش ل ح االحزىبن دائ ا ا ضػظ وز ه ف ظب وبثح ا غ ١ بساد ف ا ز رؼط حزائه إغبساد ع ١ بسره ا ضجبد ػ األسض رغزخذ 39
Static and dynamic friction ل ج االحرىان ا ساوىح ا حرويح To initiate motion of the box the man must overcome the Force of Static Friction Upon sliding, the baseball player will come to a complete stop due to the Force of Kinetic Friction When the block below is pulled gently, friction stops it moving. As the force is increased, the friction rises until the block is about to slip. This is the starting or static friction. ػ ذ عزة ا ىؼت ا خشج ث طف فئ ل ح االحزىبن ر غ رحشو رظ رمب حشوذحز رغزث ثم ح أوجش ٠ جذأ ف ا حشوخ. رغ ز ا م ح االثزذائ ١ خ ثم ح االحزىبن ا غبو خ With a greater downward force on the block, the static friction is higher. Once the block starts to slide, the friction drops: moving (i.e. dynamic friction is less than static friction). ػ ذ ب ٠ جذأ ا ىؼت ا خشج ف ا حشوخ فئ ل ح االحزىبن رظ رحب ي مب خ ا حشوخ ى ثم ح أل رغ ػ ذئز ثم ح االحزىبن ا حشو ١ خ ( رى أل ل ح االحزىبن ا غبو خ ) 40
Static friction is greater than.. dynamic friction Dynamic friction heats materials up. When something is moved against the force of friction, its energy of motion (called kinetic energy) is changed into thermal energy (heat ). Brakes and other machinery must be designed so that they get rid of this thermal energy. Otherwise their moving parts may become so hot that they seize up 41
وش اط Activity 2 2 We can compare between the static and dynamic friction by doing the خالي زا ا شبغ ٠ ى ب مبس خ ل ح االحزىبن ا غبو خ ا حشو ١ خ activity. following Put a wooden block on a wooden plane. Gradually pull the block by a spring balance using ascending magnitudes of force ( 2N, 4N,.. )( keep increasing the force unless the block start to slide) Record the results in the table below ( static friction). When the block start to slide try to keep its velocity at constant value ( dynamic friction ) and record the results in the table. Draw a graph between the applied forces and friction force. force friction 42
Factors affect friction ا ع ام ا مؤثرج ع ل ج االحرىان وش اط Activity 3 3 In the diagram up use different blocks with different weights. Record the maximum static friction in each case in the table below (1). From the results you recorded, what do you observe? Now change the plane with different planes with different materials like what in the table below (2). What is the relation between the kind of material and the friction produced? اعزخذ ىؼجبد ثأ صا خز فخ عغ ألص ل ح احزىبن ف و حب خ ف ا غذ ي )1( خالي ا زبئظ ا غغ خ برا رالحظ ا ٢ غ ١ ش ا غطح ا غز اعزجذ ثأعطح اد خز فخ عغ زبئغه ف ا غذ ي )2( ب ا ؼاللخ ث ١ ع ا اد ل ح االحزىبن ا برغخ Weight friction Material friction Table (1) Table (2) 43
Viscous force ل ج ا س خح Now we know that the resistance due to contact between two solid surfaces is called friction. But when the resistance arises from air or water we describe it as viscous force. ل ح االحزىبن ا برغخ ػ ا اء أ ا بء ر صف ثم ح ا ض عخ مثاي Example: When a Parachutist jump from the aero plane he starts to fall freely. As the velocity increases, so does the upward viscous force until it equals the downward force of gravity, giving a resultant force of zero so that no further acceleration takes place. ػ ذ ب ٠ مفض ا ظ ١ ا طبئشح رجذأ أعغب ثب غم غ ا حش و ب صادد عشػخ ا غم غ صادد ؼ ب ل ح ض عخ ( احزىبن ) ا اء إ أ رزغب ل ح ا غبرث ١ خ ل ح االحزىبن رصجح حص خ ا م صفشا ا ػ ذ ب ال ل ١ خ ػغ خ ػ ذ ب. 44
Questions: 1- Describe and explain the motion of a skydiver falling from rest. 2- Name 2 sports where friction is helpful and needed. Explain Name 2 sports where friction is reduced for better performance. Explain 45
Questions 1- Simpson drives his car with an average velocity of 48.0 km/h to the east. How long will it take him to drive 144 km on a straight highway? حغبة ص لطغ غبفخ ؼ خ ث ؼشفخ ا غشػخ. 2- What is the average speed of a car which travels 400 m in 20 s? حغبة ا غشػخ ث ؼشفخ ا غبفخ ا ض 2 3- A car traveling at 7.0 m/s accelerates uniformly at 2.5 m/s to reach a speed of 12.0 m/s. How long does it take for this acceleration to occur? حغبة ا غبفخ إرا ػشفذ ا ؼغ خ ا غشػز ١ االثزذائ ١ خ. ا بئ ١ خ 4- Omar accelerates his skateboard uniformly along a straight path from rest to 12.5 m/s in 2.5 s. What is Omar s acceleration? حغبة ا ؼغ خ إرا رحشن ا غغ عى غشػخ بئ ١ خ خالي ص ؼ 5- A person pushing a stroller starts from rest, uniformly accelerating at a rate of 2 0.500 m/s. What is the velocity of the stroller after it has traveled 4.75m? حغبة ا غشػخ ا بئ ١ خ ث ؼشفخ ا ؼغ خ غبفخ ا حشوخ ظط ثذا عى. 46
6- Use the graphs below to answer questions A-C. اعزخذ ا شع ا ج ١ ب ١ خ اعت ػ األعئ خ اي رب ١ خ a. Which graph represents an object moving with a constant positive velocity? b. Which graph represents an object at rest? c. Which graph represents an object moving with constant positive acceleration? 7- A plane starting at rest at one end of a runway undergoes a uniform acceleration 2 of 5 m/s for 15 s before takeoff. a. What is its speed at takeoff? b. How long must the runway be for the plane to be able to take off? حغبة عشػخ الالع غبئشح وز ه غ ي ذسط ا طبس ا بعت 8- A car accelerates uniformly from rest to a speed of 6.6 m/s in 6.5 s. Find the distance the car travels during this time. حغبة ا غبفخ غغ رحشن عى ث ؼشفخ ا ض ا غشػخ ا بئ ١ خ. 47
2 9- A car with an initial speed of 6.5 m/s accelerates at a uniform rate of 0.92 m/s for 3.6 s. Find the final speed and the displacement of the car during this time. حغبة ا غشػخ ا بئ ١ خ ا غبفخ ا مط ػخ ث ؼشفخ ا غشػخ االثزذائ ١ خ ا ؼغ خ ا ض. 10- A car accelerates uniformly in a straight line from rest at the rate of a- What is the speed of the car after it has traveled 55 m? b- How long does it take the car to travel 55 m? 2 2.3 m/s حغبة ا غشػخ ا بئ ١ خ ص ا ص ب ث ؼشفخ ا ؼغ خ ا غبفخ ا مط ػخ ػ ب أ ا غغ رحشن عى 11- A worker drops a wrench from the top of a tower 80.0 m tall. What is the velocity when the wrench strikes the ground? حغبة عشػخ ص عغ غطح األسض عمػ اسرفبع ؼ. 12- How far above the floor would you need to drop a pencil to have it land in 1 s? ب االسرفبع ١ غمػ عغ ألسض ٠ ص خالي صب ١ خ احذح. 13- A spring stretches by 10cm when a force of 20N is applied. When a force of 22N is used, the spring stretches by 11 cm. What would be the extension for forces of? 1) 10N 2) 1N 3) 15N حغبة اعزطب خ بثط رحذ رأص ١ ش ل خز فخ 14- The 225-N force is exerted on the crate toward the north and the 165-N force is exerted toward the east. Find the magnitude of the resultant force. حغبة حص خ م ر ١ زؼب ذر ١. 48
15- What are the components of a vector of magnitude 1.5 N at an angle of 35 from the positive x-axis? حغبة ا شوجبد األفم ١ خ ا ؼ د ٠ خ م ح ض خ ثب شع ا ج ١ ب. Resources: Books: 1-Holt Physics (Raymond A. Serway, Ph.D., Jerry S. Faughn, Ph.D.) 2- Complete physics (Stephen Pople) 3- Physics first (George Bethell & David Coppock) 3- Glencoe Physics (Paul W.Zitzewitz) Websites: 1. http://physics.slss.ie 2. http://science-class.net 3. http://ffden- 2.phys.uaf.edu/211_fall2002.web.dir/ben_townsend/staticandkineticfriction.htm 4. http://www.westminster.edu/acad/sim/pdf/sstaticandkineticfriction.pdf 49