EP015 PHYSICS 1 SESSION 2023/2024 KOLEJ MATRIKULASI KEJURUTERAAN JOHOR
ACKNOWLEDGEMENTS Physics Unit KMKJ wish to thank everyone who has contributed in shaping and writing this TUTORIAL BOOK EP015 PHYSICS 1. Special thanks go to those for their many valuable suggestions and conscientiousness in completing this book. TOPIC 1: Physical Quantities and Measurements ENCIK EADY ESWADDY BIN CHE YAHYA TOPIC 2: Kinematics of Linear Motion CIK ANIS SAHIRA BINTI CHE RAMLI TOPIC 3: Dynamics of Linear Motion PUAN SHAZRINA BINTI NGATEMIN TOPIC 4: Work, Energy and Power PUAN SAHIRAH AKILAH BINTI MOHD SAH TOPIC 5: Circular Motion ENCIK EADY ESWADDY BIN CHE YAHYA TOPIC 6: Rotation of Rigid Body PUAN FARZANA BINTI HUSSIN TOPIC 7: Simple Harmonic Motion and Waves ENCIK ZAHIDI BIN HASHIM CIK NOOR AMALINA BINTI MOHD SHUKRI TOPIC 8: Physics of Matters PUAN HABIBAH BINTI SALLEH TOPIC 9: Kinetic Theory of Gases and Thermodynamics CIK SALASIAH BINTI HAMZAH Copyright © 2023 Physics Unit KMKJ Completed and updated: 13 July 2023
WEEK DATE TUTORIAL PRACTICAL REMARKS 16.7.2023 1.0 PHYSICAL QUANTITIES AND MEASUREMENTS 1.1 Dimensions of physical quantities 1.2 Scalars and vectors 20.7.2023 1.3 Significant figures and uncertainties analysis 23.7.2023 2.0 KINEMATICS OF LINEAR MOTION 2.1 Linear motion 2.2 Uniformly accelerated motion 27.7.2023 2.3 Projectile motion 30.7.2023 3.0 DYNAMICS OF LINEAR MOTION 3.8.2023 3.1 Momentum and impulse 6.8.2023 3.2 Conservation of linear momentum 3.3 Basic of forces and free body diagram 3.4 Newton's Laws of Motion 10.8.2023 13.8.2023 4.0 WORK, ENERGY AND POWER 4.1 Work 4.2 Energy and conservation of energy 17.8.2023 4.3 Power 20.8.2023 5.0 CIRCULAR MOTION 5.1 Parameters in circular motion 5.2 Uniform circular motion 24.8.2023 5.3 Centripetal force 27.8.2023 6.0 ROTATION OF RIGID BODY 6.1 Rotational kinematics 6.2 Equilibrium of a uniform rigid body 31.8.2023 6.3 Rotational dynamics 3.9.2023 6.4 Conservation of angular momentum 7.0 SIMPLE HARMONIC MOTION AND WAVES 7.9.2023 7.1 Kinematics of Simple Harmonic Motion (SHM) 17.9.2023 7.2 Graphs of Simple Harmonic Motion 7.3 Period of Simple Harmonic Motion 7.4 Properties of Waves 21.9.2023 7.5 Superposition of waves 24.9.2023 7.6 Application of standing waves 7.7 Doppler Effect 28.9.2023 1.10.2023 5.10.2023 8.10.2023 8.0 PHYSICS OF MATTERS 8.1 Stress and strain 8.2 Young's Modulus 12.10.2023 8.3 Hydrostatic pressure 15.10.2023 8.4 Fluid dynamics 8.5 Viscosity 8.6 Heat conduction 19.10.2023 8.7 Thermal expansion 22.10.2023 26.10.2023 29.10.2023 2.11.2023 5.11.2023 9.0 KINETIC THEORY OF GASES AND THERMODYNAMICS 9.11.2023 9.1 Kinetic theory of gases 12.11.2023 9.2 Molecular kinetic energy and internal energy 9.3 Molar specific heats 9.4 First Law of Thermodynamics 16.11.2023 9.5 Thermodynamics processes 19.12.2023 9.6 Thermodynamics work 23.11.2023 TOPIC 6 TOPIC 7 SCHEME OF WORK EP015: PHYSICS 1 SEMESTER 1 SESSION: 2023/2024 - 10 11 12 13 (19.7.2023) Awal Muharram - - - - - - - 14 - - - - - - - MID-SEMESTER BREAK (8.9.2023 - 16.9.2023) TOPIC 6 TOPIC 8 TOPIC 9 PRACTICAL TEST AND LAB REPORT TEST PRACTICAL TEST AND LAB REPORT TEST EXP 4: ROTATIONAL MOTION OF RIGID BODY PSPM I (4.12.2023 - 12.12.2023) 1 2 3 4 5 6 7 8 9 UPS 3 (7.11.2023) (12.11.2023 - 13.11.2023) Deepavali Holiday - STUDY WEEK (24.11.2023 -3.12.2023) 16 17 18 (31.8.2023) National Day (28.9.2023) Prophet's Birthday UPS 2 (3.10.2023) 15 - - POST-LAB EXP 4/ PRE-LAB EXP 5 EXP 5: SHM POST-LAB EXP 5/ PRE-LAB EXP 6 POST-LAB EXP 6 EXP 6: STANDING WAVES UPS 1 (22.8.2023) (23.8.2023) Hol Johor LECTURE POST-LAB EXP 2/ PRE-LAB EXP 3 EXP 3: ENERGY POST-LAB EXP 3/ PRE-LAB EXP 4 TOPIC 2 TOPIC 3 TOPIC 5 TOPIC 1 PRE-LAB EXP 1 EXP 1: MEASUREMENT AND UNCERTAINTY POST-LAB EXP 1/PRE-LAB EXP 2 EXP 2: FREE FALL AND PROJECTILE MOTION TOPIC 4
EP015 2 SULIT SULIT LIST OF SELECTED CONSTANT VALUES SENARAI NILAI PEMALAR TERPILIH Speed of light in vacuum c = 3.00 × 108 m s-1 Laju cahaya dalam vakum Permeability of free space ! = 4p × 10-7 H m-1 Ketelapan ruang bebas Permittivity of free space ! = 8.85 × 10-12 F m-1 Ketelusan ruang bebas Electron charge magnitude e = 1.60 × 10-19 C Magnitud cas elektron Planck constant h = 6.63 × 10-34 J s Pemalar Planck Electron mass me = 9.11 × 10-31 kg Jisim elektron = 5.49 × 10-4 u Neutron mass mn = 1.674 × 10-27 kg Jisim neutron = 1.008665 u Proton mass mp = 1.672 × 10-27 kg Jisim proton = 1.007277 u Deuteron mass md = 3.34 × 10-27 kg Jisim deuteron = 2.014102 u Molar gas constant R = 8.31 J K-1 mol-1 Pemalar gas molar Avogadro constant NA = 6.02 × 1023 mol-1 Pemalar Avogadro Boltzmann constant k = 1.38 × 10-23 J K-1 Pemalar Boltzmann Free-fall acceleration g = 9.81 m s-2 Pecutan jatuh bebas
EP015 3 SULIT SULIT LIST OF SELECTED CONSTANT VALUES SENARAI NILAI PEMALAR TERPILIH Atomic mass unit 1 u = 1.66 × 10-27 kg Unit jisim atom = 931.5 "#$ %! Electron volt 1 eV = 1.6 × 10-19 J Elektron volt Constant of proportionality = Pemalar hukum Coulomb Atmospheric pressure 1 atm = Tekanan atmosfera Density of water = 1000 kg m-3 Ketumpatan air 4 0 1 pe k = 9 2 2 9.0 10 Nm C- ´ 1.013 10 Pa 5 ´ r w for Coulomb’s law
EP015 4 SULIT SULIT LIST OF SELECTED FORMULAE SENARAI RUMUS TERPILIH 1. = + 2. = + & ' ' 3. ' = ' + 2 4. = & ' ( + ) 5. = 6. = ∆ 7. = ∆ = − 8. = . 9. = ⃗ ∙ ⃗ = cos 10. = & ' ' 11. = ℎ 12. (= & ' ' = & ' 13. = ∆ 14. 15. = %%%⃗• ⃗ = cos 16. ! = "! #= $ = 17. 18. 19. 20. 21. 22. 23. = % $ (& + ) 24. 25. 26. 27. 28. 29. 30. 31. ∑ = av W P t D D = 2 2 c mv F mv mr r === w w s r = q v r = w t a r = a o ww a = + t 2 o 1 2 qw a = +t t 2 2 o w w aq = + 2 t q = rF sin 2 I mr =å 2 solid sphere 2 5 I MR = 2 solid cylinder/disc 1 2 I MR = 2 ring I MR = 2 rod 1 12 I ML =
EP015 5 SULIT SULIT LIST OF SELECTED FORMULAE SENARAI RUMUS TERPILIH 32. 33. = sin 34. = cos = ±D' − ' 35. = −' sin = −' 36. = & ' '('− ') 37. = & ' '' 38. 39. 40. 41. 42. 43. 44. 45. ' = cos ( ± ) 46. 47. ( = (" $) 48. ( = ( $) <* + 49. ( = (" ,) 50. 51. = - ) 52. . = > "±"" "∓"# ? 53. 54. = ∆) )$ 55. 56. = % $ ∆ 57. 2 3 = % $ 58. 59. 60. 61. L I = w 1 2 2 2 E mA = w 2 2 f T p w p = = 2 l T g = p 2 m T k = p 2 k p l = v f = l y x t A t kx ( , sin ) = ± (w ) y A kx t = 2 cos sinw T v µ = F A s = Y s e = F P A ^ = P P P gh gauge abs atm = - = r P P gh abs atm = + r m V r =
EP015 6 SULIT SULIT LIST OF SELECTED FORMULAE SENARAI RUMUS TERPILIH 62. 63. 64. 65. 4 5= − > ∆* ) ? 66. 67. 68. 69. 70. 71. 72. #-6 = F〈$〉 73. 74. = % 7 #-6 $ 75. = % 7 #-6 $ 76. 77. 78. 79. 80. 81. ∆ = − 82. 83. 84. = ln 3% 3& = ln 8& 8% 85. = ∫ = (9 − :) 86. = ∫ = 0 Av Av 11 2 2 = 1 2 constant 2 P v gh + += r r D F rv = 6ph D aD L LT o = D bD A AT o = D gD V VT o = b a = 2 g a = 3 A m N n M N = = rms 3 3 kT RT v m M = = tr A 3 3 2 2 R K T kT N = = æ ö ç ÷ è ø 1 1 2 2 U fNkT fnRT = = CC R P V - = V Q C n T = D P V C C g = pV = constant g 1 TV constant - = g
EP015 7 SULIT SULIT
INDEX Topic Title of Chapter Page 1 Physical Quantities of Measurements 9 - 13 2 Kinematics of Linear Motion 14 - 21 3 Dynamics of Linear Motion 22 – 28 4 Work, Energy and Power 29 – 36 5 Circular Motion 37 – 42 6 Rotation of Rigid Body 43 – 50 7 Simple Harmonic Motion and Waves 51 – 61 8 Physics of Matter 62 – 72 9 Kinetic Theory of Gases and Thermodynamics 72 - 81
9 TOPIC 1 : PHYSICAL QUANTITIES AND MEASUREMENTS 1.1 DIMENSIONS OF PHYSICAL QUANTITIES 1.2 SCALARS AND VECTORS At the end of this topic, students should be able to: 1.1 DIMENSIONS OF PHYSICAL QUANTITIES 1. Define dimension 2. Determine the dimensions of derived quantities 3. Verify the homogeneity of equations using dimensional analysis 1.2 SCALARS AND VECTORS 4. Define scalar and vector quantities 5. Resolve vector into two perpendicular components (x and y axes) 6. Determine resultant of vectors
10 KOLEJ MATRIKULASI KEJURUTERAAN JOHOR KEMENTERIAN PENDIDIKAN MALAYSIA TUTORIAL 1 (PHYSICAL QUANTITIES AND MEASUREMENT) SECTION A 1. Which one of the following does not have the unit N m-2 ? A. Pressure B. Torque C. Stress D. The Young modulus 2. Dimension is defined as a A. technique or method which physical quantity can be expressed in terms of combination of basic quantities B. technique or method which basic quantity can be expressed in terms of combination of physical quantities C. technique or method to determine the homogeneity of equation D. technique or method to construct an equation 3. Which of the following is the correct dimension of k? A. M L2 T-1 B. M L2 T-2 C. L4 T-1 D. L2 T-1 4. Which pair of quantities below is correctly listed as a scalar and a vector? 5. Which of the following states are INCORRECT? A. A vector quantity has magnitude and direction B. A basic quantity is a quantity which cannot be derived from any other quantities C. A resultant vector quantity can be produced through additional, subtraction and multiplication D. A physical quantity can be derived through multiplication, division, differentiation and integration Scalar Vector A acceleration velocity B charge power C force momentum D Potential difference magnetic flux momentum = k x density
11 SECTION B 1.1 DIMENSIONS OF PHYSICAL QUANTITIES 1. Newton’s law of gravitation states that the force of attraction F between two particles of masses M and m at a distance r apart is where G is the gravitational constant. By using dimensional analysis, determine the SI unit for G. 2. The pressure of a liquid is given by P = ρgh. Calculate the pressure (in SI unit) if the density of water, ρ is 1 g cm–3, the acceleration due to gravity, g is 10 ms– 2, and the height of water, h is 50 cm ? (ANS: 5 × 103 Nm-2 or 5 × 103 Pa or 5 × 103 kgm-1 s -2) 3. a) Show that the expression v = at is dimensionally correct if in this expression v represents velocity, a is acceleration, and t an instant of time. b) The equation governing the rate of flow of fluid t v under streamline conditions through a horizontal pipe of length l and radius r is l pr t v 8 4 = where p is the pressure difference across the pipe and η is the viscosity of the fluid. Deduce the dimension for η. (ANS: ML-1T-1) 4. Change the following quantities into its SI unit. a) 50 mm2 b) 4.5 x 10-3 cm3 c) 100 g cm-3 d) 360 km hour-1 (ANS: 5.0 x 10- 5m2 , 4.5 x 10-9 m3 , 105 kg m-3 , 100 m s-1) 1.2 SCALARS AND VECTORS 1. FIGURE 1 shows two displacement vector A and B. FIGURE 1.1 Determine the magnitude and direction of the resultant displacement. (ANS: 1.68 km, 7.5° below negative x-axis) 3.7 km 40° 30° B 5.2 km A y x
12 2. Based on FIGURE 1.2 below, calculate the resultant vector of P and Q and its direction. FIGURE 1.2 (ANS: 53.68 ms-2, 69.96° above positive x-axis) 3. FIGURE 1.3 shows how two coplanar force F1 and F2, act on point O. FIGURE 1.3 a) Resolve the force along the x and y axes as well as determine the resultant force FR. b) Determine the direction of the resultant force FR. (ANS: 5.15 N, 50.28° below positive x-axis) 4. FIGURE 1.4 F1= 5 N F2= 10 N 20° 30° 50° T 70° 1 T2 W
13 FIGURE 1.4 a man hangs an object with weight, W using two strings connected to the ceiling and wall in the equilibrium state. If tension, T1 is 12 N, calculate tension, T2 and weight, W of the object. (ANS: 8.2 N, 12 N) SECTION C 1. Amirul is pulling a box of guava with a force of 20 N at 30° along an x-axis. Sahar then comes and pulls the box with a force of 35 N which makes an angle 110° with the Amirul’s force. Determine the resultant force on the box. (ANS: 33.86 N, θ = 74.3° from the negative x- axis) 2. Yazid drives from KL to Kuantan which is 240 km away in the direction 30° North of East. He then continues 200 km in the direction of 65° South of East to Mersing and finally 120 km at 10° West of South to Johor Bahru. Using the component method, calculate the distance and direction of Johor Bahru from KL. (ANS: 325.4 KM, 33.5 South of East) 3. A picture weighing 5 N was suspended from a hook on a wall by a cord with a breaking strength of 25 N. Initially, the picture was hung low as shown in figure (a), then the cord was shortened to hang the picture as shown in figure (b). When the picture was replaced, the cord broke immediately. Explain why the cord broke when supporting a much lighter load. 45° 5° Hook (a) (b) Hook
14 TOPIC 2 : KINEMATICS OF LINEAR MOTION 2.1 LINEAR MOTION 2.2 UNIFORMLY ACCELERATED MOTION 2.3 PROJECTILE MOTION At the end of this topic, students should be able to: 2.1 LINEAR MOTION a) Define: i. instantaneous velocity, average velocity and uniform velocity; and ii. instantaneous acceleration, average acceleration and uniform acceleration. b) Interpret the physical meaning of displacement-time, velocity-time and acceleration-time graphs. c) Determine the distance travelled, displacement, velocity and acceleration from appropriate graphs. 2.2 UNIFORMLY ACCELERATED MOTION a) Apply equations of motion with uniform acceleration: = + , = + 1 2 2 , 2 = 2 + 2, = 1 2 ( + ) 2.3 PROJECTILE MOTION a) Describe projectile motion launched at an angle, θ as well as special cases when = 0° b) Solve problems related to projectile motion.
15 KOLEJ MATRIKULASI KEJURUTERAAN JOHOR KEMENTERIAN PENDIDIKAN MALAYSIA TUTORIAL 2 (KINEMATICS OF LINEAR MOTION) SECTION A 1. A ball comes back to its starting point after bouncing off the floor. Its average velocity is ___. A. Zero B. Maximum C. Constant D. decreasing 2. Which one below is NOT the example of uniform velocity? A. Rotation of the Earth. B. A car moving on a straight road with constant speed. C. A bouncing ball. D. Movement of hands of a clock. 3. A woman step on the gas pedal of car when the traffic light turns green. Which one below is TRUE? Average velocity Average acceleration A increases constant B increases increases C increases zero D constant constant 4. Which one below is NOT the example of uniform accelerated motion? A. A skydiver jumping out of a plane. B. A stone dropped from the top of a building. C. A ball rolling down a slope. D. A bus driving in a heavy traffic.
16 SECTION B 2.1 LINEAR MOTION 1. FIGURE 2.1 FIGURE 2.1 shows the velocity-time graph of an object moves from rest at point A and stops at point E after 20 s. Calculate the a) acceleration during the motion AB, BC, CD and DE b) acceleration at = 10 c) total distance travelled by the object d) total displacement of the motion e) average velocity for the whole journey A to E (ANS: . − , −. − , −. − , − , −. − , , −, −. − ) 2. FIGURE 2.2 shows a graph of position versus time for a certain particle moving along the x-axis is shown in. a) Find the average velocity in the time intervals from i. 0 to 2 s ii. 0 to 4 s iii. 2 to 4 s iv. 4 to 7 s v. 0 to 8 s b) Find the instantaneous velocity at the instants i. t = 3 s ii. t = 4.5 s iii. t = 7.5 s (ANS: − , . − , −. − , −. − , − , −. − , − , − ) v (ms-1 ) t (s) 0 6 12 -6 -12 A 5 10 15 20 B C D E FIGURE 2.2
17 3. The velocity versus time graph for an object moving along a straight path is shown in Figure 3. a) Find the average acceleration of the object during the time intervals: i. 0 to 5 s ii. 5 to 15 s iii. 0 to 20 s b) Find the instantaneous acceleration at: i. 2 s ii. 10 s iii. 18 s (ANS: − , . − , . − , − , . − , − ) 4. FIGURE 2.4 The graph in FIGURE 2.4 shows the motion of a body. a) Which part of the graph shows the body is moving with a maximum speed b) Calculate the maximum acceleration of the body. c) Calculate the average velocity of the body for the first 3 seconds. (ANS: − , . − ) 5. a) Hassan is driving at 108 ℎ −1 along a straight road. He suddenly sees a school girl who runs across the road 100 m ahead of his car. If his reaction time is 0.7 s and the maximum deceleration of the car is 4.5 −2 , determine the distance travelled by the car before it stops. Will the car stop before or after hitting the girl? b) When the brakes are applied, a car reduces its velocity from 30 −1 to 15 −1 after moving 75 m. In order to stop the car completely, what is the extra distance needed? (ANS: , ) FIGURE 2.3
18 6. A car which is initially at rest starts to move along a straight line with constant acceleration. It reaches a velocity of 60 −1 after travelling through a distance of 100 m. Determine the a) acceleration b) time taken to reach the velocity of 60 −1 c) velocity at = 3 (ANS: − , . , − ) 7. FIGURE 2.5 FIGURE 2.5 shows a rolling ball falls from the edge of a table with initial horizontal velocity, u of 60 −1 . The height of the table is 1 m. Calculate the a) time taken for the ball to reach point B. b) horizontal distance, x. c) magnitude and direction of its velocity at point B. (ANS: . , . , . − , . ° + − ) 8. FIGURE 2.6 A jet plane travelling horizontally at 1 × 102 −1 drops a rocket from a considerable height as shown in FIGURE 2.6. The rocket immediately fires its engines, accelerating at 20 −2 in the x-direction while falling under the influence of gravity in the y-direction. When the rocket has fallen 1 km, find : a) its velocity in the y-direction b) its velocity in the x-direction c) The magnitude and direction of its velocity (ANS: . × − , − , − , . ° + − ) u 1 m x B A
19 9. A leopard can jump to a height of 3.7 m when leaving the ground at an angle of 45° from the horizontal. Determine the initial speed must the leopard takes to reach that height. (ANS: . − ) 10. An archer stand on a cliff elevated at 50 m high from the ground and shoots an arrow at the angle of 30° above the horizontal with the speed of 80 ms-1. a) How long does it fly in the air? b) How far from the base of the cliff does the arrow fly until it hits the ground? c) Determine the speed of the arrow just before it hits the ground. (ANS: . , . , . − ) 11. A fireman 50 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of 30° above the horizontal as shown in Figure 2.7. If the speed of the stream as it leaves the hose is 40 −1 , at what height will the stream of water strike the building? (ANS: . ) 12. FIGURE 2.7 FIGURE 2.8
20 A playground is on the flat roof of a city school, 6 m above the street below (refer FIGURE 2.8). The vertical wall of the building is 7 m high, to form a 1 m high railing around the playground. A ball has fallen to the street below and a passerby returns it by launching at an angle of 53° above the horizontal at a point = 24 from the base of the building wall. The ball takes 2.2 s to reach a point vertically above the wall. a) Find the speed at which the ball was launched. b) Find the vertical distance by which the ball clears the wall. c) Find the horizontal distance from the wall to the point on the roof where the ball lands. (ANS: . − , . , . ) SECTION C 1. FIGURE 2.9 A particle starts from rest and accelerates as shown in Figure 9. Determine a) The particle’s speed at t = 10 s and at t = 20 s b) The distance travelled in the first 20 seconds. (ANS: − , − , . ) 2. An airplane taxiing at constant acceleration for a distance of 280 m. If it starts from rest and becomes airborne after 8 s, calculate its speed during take-off. (ANS: − ) 3. FIGURE 2.10 FIGURE 2.10 shows a ball being kicked from point P with initial velocity 16.5 −1 at 35°. On the way down, the ball hits the goal post at point Q, 3 m from the ground. The base of the goal post is located at point R.
21 a) Determine the time taken by the ball to reach Q. b) Calculate the horizontal distance PR. c) Determine the speed of the ball, kicked at the same angle, for it to hit R. (ANS: . , . , . − )
22 TOPIC 3 : DYNAMICS OF LINEAR MOTION 3.1 MOMENTUM AND IMPULSE 3.2 CONSERVATION OF LINEAR MOMENTUM 3.3 BASIC OF FORCES AND FREE BODY DIAGRAM 3.4 NEWTON’S LAWS OF MOTION At the end of this topic, students should be able to: 3.1 MOMENTUM AND IMPULSE a) Define momentum and impulse, = ∆ b) Solve problem related to impulse and impulse-momentum theorem, J = ∆p = mv– mu (remarks: 1D only). c) Use F-t graph to determine impulse. 3.2 CONSERVATION OF LINEAR MOMENTUM a) State the principle of conservation of momentum. b) Apply the principle of conservation of momentum in elastic and inelastic collisions in 2D collisions. c) Differentiate elastics and inelastic collisions. (remarks: similarities & differences). 3.3 BASIC OF FORCES AND FREE BODY DIAGRAM a) Identify the forces acting on a body in different situations: i. Weight, W ii. Tension, T iii. Normal force, N iv. Friction, f v. External force (pull or push), F b) Sketch free body diagram. c) Determine static and kinetic friction, ≤ ; ≤ 3.4 NEWTON’S LAWS OF MOTION a) State Newton’s Law of Motion. b) Apply Newton’s Law of Motion. (remarks: include static and dynamic equilibrium for Newton’s First Law Motion).
23 KOLEJ MATRIKULASI KEJURUTERAAN JOHOR KEMENTERIAN PENDIDIKAN MALAYSIA TUTORIAL 3 (DYNAMICS OF LINEAR MOTION) SECTION A 1. Which of the following statements is true about the elastic collision between two objects? A. The momentum and total energy are conserved but the kinetic energy can be converted into other forms of energy. B. Both the momentum and total energy are conserved if and only if the mass of the two objects is identical. C. The kinetic energy is conserved whereas the total energy is reduced but can be increased. D. Momentum, kinetic energy and total energy must be conserved. 2. The purpose of an airbag or crumple zone in a car is to increase the time taken for the driver to stop. What is the advantage of this? A. It reduces the driver’s momentum. B. It reduces the driver’s energy. C. It reduces the force on the driver. D. It reduces the energy of the impact 3. A tennis player returns a serve. How does the force on the ball relate to its momentum? A. The force is the rate of change of momentum of the ball B. The force is the overall change of momentum multiplied by the time taken to cause the change C. The force is the momentum of the ball as it is hit D. The force is the momentum of the ball leaving the racket divided by the time taken to cause the change
24 4. An object will remain stationary on an inclined plane because… A. the static frictional force is acting upward along the inclined plane. B. The static frictional force is acting downward along the inclined plane. C. the dynamic frictional force is acting upward along the inclined plane. D. the dynamic frictional force is acting upward along the inclined plane. 5. If a nonzero net force is acting on an object, which of the following must we assume regarding the object’s condition? A. The object is at rest B. The object is moving with constant velocity C. The object is being accelerated D. The object is losing mass SECTION B 3.1 MOMENTUM AND IMPULSE 1. A 0.10 kg ball is thrown straight up into the air with an initial speed of 15 ms-1. Find the momentum of the ball a) at its maximum height and b) halfway to its maximum height. (ANS: a) 0 kgms-1 b) 1.061 kgms-1) 2. An object has a kinetic energy of 275 J and a momentum of 25.0 kg m s-1. Find a) the speed b) mass of the object. (ANS: a) 22 ms-1 b) 1.14 kg) 3. A force, F acting on an object of mass 2.0 kg varies with time t in the way as shown in FIGURE 3.1. The velocity of the object is 4.0 m s-1 before the application of the force. Determine the velocity of the object after applying the force for 0.2s. (ANS: 9 ms-1) t(s) 10 0 F(N) 0.2 FIGURE 3.1
25 3.2 CONSERVATION OF LINEAR MOMENTUM 1. A 75.0kg ice skater moving at 10.0 m s-1 crashes into a stationary skater of equal mass. After the collision, the two skaters move as a unit at 5.00 m s-1. Suppose the average force a skater can experience without breaking a bone is 4 500 N. If the impact time is 0.100 s, does a bone break? (ANS: 3750 N) 2. A 2 kg ball A moves to the right with velocity of 4 ms-1 collides with another 1 kg ball B moving in the opposite way with velocity of 0.5 m s-1 as shown in FIGURE 3.2. After the collision, both balls move at 300 and 150 from the horizontal. Calculate the final velocity of each ball after the collision. Assume the collision is an elastic. (ANS: 1.37 ms-1 , 5.3 ms-1) 3. A 600 g body, P is initially at rest. A 400 g body, Q which is initially moving with a velocity of 125 cm s-1 toward the right along the x-axis, strikes P. After the collision, Q has a velocity of 100 cm s-1 at an angle of 370 above the x-axis in the first quadrant. Both bodies move on a horizontal plane. Calculate: a) The magnitude and direction of the velocity of P after the collision. b) The loss kinetic energy during the collision. (ANS: a) 0.502 ms-1 , 53.21° below + x-axis, b) 0.0369 J) FIGURE 3.2
26 3.3 BASIC OF FORCES AND FREE BODY DIAGRAM 3.4 NEWTON’S LAWS OF MOTION 1. A 2.0 kg object is placed on a rough plane inclined at 30° with the horizontal as shown in FIGURE 3.3. It is released from rest and accelerates at 4.0 m s-2. Calculate the frictional force acting on the object. (ANS: 1.81 N) 2. A 3.0 kg cube is placed on a rough plane. The plane is then slowly tilted until the cube starts to move from rest. This occurred when the angle of inclination is 25°. Calculate the coefficient of static friction between the cube and the rough plane. (ANS: 0.466) 3. A 4.0 kg block A on a rough 30° inclined plane is connected to a freely hanging 1.0 kg block B by a mass-less cable passing over the frictionless pulley as shown in FIGURE 3.4. When the objects are released from rest, object A slides down the inclined plane with a friction force of 6.0 N. Calculate a) the acceleration of the objects b) the tension in the cable. (ANS: a) 4.69ms -2 b) 5.12 N) 300 FIGURE 3.3 300 A B 1 kg 4 kg FIGURE 3.4
27 4. A wooden block of mass 2.0 kg slides down with constant velocity on a inclined rough plane of 30° from the horizontal axis. a) Sketch a free body diagram to show forces acting on the wooden block. b) Calculate the kinetic frictional force between the wooden block and the rough inclined plane. (ANS: b) 9.81 N) SECTION C 1. FIGURE 3.5 FIGURE 3.5 shows a ball moving along x-axis with a speed of u1=17 ms-1 strikes an identical ball that is moving at a speed of u2=10 ms-1 along y-axis. After the collision, the balls stick together and moves at speed v with an angle from the horizontal x-axis . Calculate the speed of the balls, v after the collision. (ANS: 9.86 ms-1) 2. Three wooden blocks connected by a rope of negligible mass are being dragged by a horizontal force, F in FIGURE 3.6. Suppose that F = 1000 N, m1 = 3 kg, m2 = 15 kg and m3 = 30 kg. Determine a) the acceleration of blocks system. b) the tension of the rope, T1 and T2. Neglect the friction between the floor and the wooden blocks. (ANS: a) 20.8 ms -2 b) 936 N, 624 N) u1 u2 v FIGURE 3.6
28 3. A window washer pushes his scrub brush up a vertical window at constant speed by applying a force F as shown in FIGURE 3.7. The brush weights 10.0 N and the coefficient of kinetic friction is k= 0.125. Calculate a) the magnitude of the force F b) the normal force exerted by the window on the brush. (ANS: a) 14.6 N b) 9.38 N) FIGURE 3.7
29 TOPIC 4: WORK, ENERGY AND POWER 4.1 WORK 4.2 ENERGY AND CONSERVATION OF ENERGY 4.3 POWER At the end of this topic, students should be able to: 4.1 WORK a) State the physical meaning of dot (scalar) product for work: W = F • s Fs cos b) Define and apply work done by a constant force. c) Determine work done from a force-displacement graph. 4.2 ENERGY AND CONSERVATION OF ENERGY a) Define and use: a. Gravitational potential energy, U mgh b. Elastic potential energy for spring, kx Fx 2 1 2 1 2 c. Kinetic energy, 2 2 1 K mv b) State the principle of conservation of energy. c) Apply the principle of conservation of mechanical energy. d) State and apply work-energy theorem, W K 4.3 POWER a) Define and use average power, t W Pav and instantaneous power, P F • v
30 KOLEJ MATRIKULASI KEJURUTERAAN JOHOR KEMENTERIAN PENDIDIKAN MALAYSIA TUTORIAL 4 (WORK, ENERGY AND POWER) SECTION A 1. The work done is 0 J if A. The body shows displacement in the opposite direction of the force applied. B. The body shows displacement in the same direction as that of the force applied. C. The body shows a displacement in perpendicular direction to the force applied. D. The body masses obliquely to the direction of the force applied. 2. A ball is dropped from a height of 10 m. A. Its potential energy increases and kinetic energy decreases during the falls B. Its potential energy is equal to the kinetic energy during the fall. C. The potential energy decreases and the kinetic energy increases during the fall. D. The potential energy is zero and kinetic energy is maximum while it is falling. 3. According to the work-energy theorem, total change in energy is equal to the _____ A. total work done. B. half of the total work done. C. total work done added with frictional losses. D. square of the total work done. 4. The spring will have maximum potential energy when A. it is pulled out B. it is compressed C. it is pulled out and compressed D. neither (A) nor (B)
31 5. A trolley is pulled along a smooth horizontal track by a constant force. Which of the following graphs best describe the variation of the trolley’s kinetic energy, K with time, t if air resistance is negligible? A B C D SECTION B 4.1 WORK 1. FIGURE 4.1 FIGURE 4.1 shows four situations in which a force is applied to an object. In all four cases, the force has the same magnitude, and the displacement of the object is to the right and of the same magnitude. Rank the situations in order of the work done by the force on the object, from most positive to most negative. 2. A 500 kg helicopter ascends vertically from the ground with an acceleration of 2 m s-2 over a 5.0 s interval. Calculate the : a) work done by the lifting force. (ANS: 1.48 x 105 J) b) work done by the gravitational force. (ANS: -1.23 x 105 J) c) net work done on the helicopter. (ANS: 2.50 x 104 J) K t K t K t K t
32 3. A block of mass 25.0 kg is pulled 1.2 m along a frictionless horizontal table by a constant force of 36 N directed at 35° above the horizontal. Determine the total work done on the block. (ANS: 35.4 J) 4. A horizontal constant force of 480 N is applied to an object of mass 30 kg on a rough inclined plane 50° to the horizontal. If the force of friction is 50 N, how much work is done to push object through at distance of 2 m up the plane. (ANS: 66.2 J) 5. FIGURE 4.2 The force acting on a particle varies as in FIGURE 4.2 above. Find the work done by the force as the particle moves a) From x = 0 m to x = 8 m (ANS: 24 J) b) From x = 8 m to x = 10 m (ANS: - 3 J) c) From x = 0 m to x = 10 m (ANS: 21 J) 6. FIGURE 4.3 shows an object of mass 5.0 kg moving along a straight line is acted upon by a force as shown in the force-displacement graph. Determine the total work done on the object. (ANS: 0.65 J) FIGURE 4.3 F (N) s (cm) 10 -5 4 8 12 10
33 4.2 ENERGY AND CONSERVATION OF ENERGY 1. A spring is extended by 20 cm when a force of 150 N is applied to it. This spring is suspended vertically with a load of 8 kg attached at its lower end. Calculate the a) spring constant, k (ANS: 750 N m-1) b) elongation of the spring, x (ANS: 0.1 m) c) energy stored in the spring. (ANS: 3.75 J) 2. A 25 kg boy slides down a 1.2 m inclined plane making an angle of 30° with the horizontal. If he starts from rest at the top of plane and reaches the end of the plane with a speed of 2.0 m s-1, find the work done by the friction. (ANS: 97.15 J) 3. FIGURE 4.4 An object of mass 2.0 kg is placed 30 cm directly above the top end of a vertical spring as shown in FIGURE 4.4. It is then released from that height. The spring constant k = 20 Nm-1. a) Calculate the speed of the object just before it strikes the spring. b) Determine the maximum compression, x. (ANS: 2.43 ms-1, 0.768 m) 4. A mechanic pushes a 2.50 × 103 kg car from rest to a speed of v, doing 5000 J of work in the process. During this time, the car moves 25.0 m. Neglecting friction between car and road, find a) the final speed, v. (ANS: 2 ms-1) b) the net force on the block. (ANS: 200 N) 5. A 2000 kg car moves down a level highway under the actions of two forces. One is a 1000 N forward force exerted on the drive wheels by the road and the other is 950 N resistive force. Use the work-kinetic energy theorem to find the speed of the car after it has moved a distance of 20 m, assuming it starts from rest. (ANS: 1.0 ms-1)
34 4.3 POWER 1. A car accelerates from 0 to 100 km per hour in 3 minutes. If the mass of the car is 1500 kg, determine the power delivered by its engine. (ANS: 3.22 × 103 W) 2. A construction worker used a motor-driven cable to pull a 70 kg crate of bricks up a 30° inclined slope of length 60 m. Assuming the slope is smooth and the man is pulling at constant speed of 2 m s-1, determine the a) work done by the man. (ANS: 20.6 kJ) b) power of the motor. (ANS: 686.7 W) 3. A 1.5 × 103 kg car starts from rest and accelerates uniformly to 18.0 m s-1 in 12.0 s. Assume that air resistance remains constant at 400 N during this time. Find a) the average power developed by the engine in hp. (ANS: 32 hp) b) the instantaneous power output of the engine at t =12.0 s, just before the car stops accelerating. (ANS: 64 hp) (Given that, 1hp = 746 W) 4. A 1000 kg elevator carries a maximum load of 800 kg. A constant frictional force of 4000 N retards its motion upward. What is the minimum power (in kW and in hp) must the motor deliver to lift the fully loaded elevator at a constant speed of 3 ms-1? (Given that, 1hp = 746 W) (ANS: 65.1 kW @ 87.3 hp)
35 SECTION C 1. FIGURE 4.5 An object of mass 2 kg travels along horizontal floor under the action of force, F. FIGURE 4.5 shows the graph of force, F against displacement, s. The speed of the object at s = 0 is 10 ms-1. Determine the kinetic energy of an object at s = 10 m. (ANS: 132.5 J) 2. FIGURE 4.6 A ball of mass m=1.80 kg is released from rest at a height h =65.0 cm above a light vertical spring of force constant k as in FIGURE 4.6(a). The ball strikes the top of the spring and compresses it a distance d = 9.0 cm as in FIGURE 4.6(b). Neglecting any energy losses during the collision, find a) the speed of the ball just as it touches the spring (ANS: 3.57 m s-1) b) the force constant of the spring. (ANS: 3.22 kN m-1)
36 3. FIGURE 4.7 Two objects (m1 = 5 kg and m2 = 3kg) are connected by a light string passing over a light, frictionless pulley as in FIGURE 4.7 above. The 5 kg object is released from rest at a point h = 4 m above the table. a) Determine the speed of each object when the two pass each other. b) Determine the speed of each object at the moment the 5kg object hits the table. c) How much higher does the 3kg object travel after the 5kg object hits the table? (ANS: 3.13 m s-1 , 4.33 m s-1 ,1.0m) 4. FIGURE 4.8 A 500 g block is shot on the surface in FIGURE 4.8 with an initial speed of 0.5 ms1. How far will it go if the coefficient of friction between it and the surface is 0.15? (ANS: 0.085 m) 5. A 0.25 hp motor is used to lift a load at the rate of 5.0 cms-1. Determine the mass of the load at this constant speed? [1 hp = 746 W] (ANS: 380.22 kg) 6. At sea level, a nitrogen molecule in the air has kinetic energy of 6.2 x 10-21 J. Its mass is 4.7 x 10-26 kg. If the molecule could shoot straight up without striking other air molecules, how high would it rise? (ANS: 13447 m)
37 TOPIC 5 : CIRCULAR MOTION 5.1 PARAMETERS IN CIRCULAR MOTION 5.2 UNIFORM CIRCULAR MOTION 5.3 CENTRIPETAL FORCE At the end of this topic, students should be able to: 5.1 PARAMETERS IN CIRCULAR MOTION a) Define and use angular displacement, period, frequency, and angular velocity. 5.2 UNIFORM CIRCULAR MOTION a) Describe uniform circular motion b) Convert units between degrees, radian, and revolution or rotation. 5.3 CENTRIPETAL FORCE a) Define centripetal acceleration and centripetal force b) Solve problems related to centripetal force for uniform circular motion cases: horizontal, vertical and conical pendulum.
38 KOLEJ MATRIKULASI KEJURUTERAAN JOHOR KEMENTERIAN PENDIDIKAN MALAYSIA TUTORIAL 5 (CIRCULAR MOTION) SECTION A 1. Which of these statements is incorrect about uniform circular motion? A. The speed is always constant B. The velocity is changing with time C. The object is speeding up or slowing down D. The direction of the velocity is changing with time 2. The blades of a table fan make 25 revolutions in one minute. What is the angular velocity of the blades? A. 1.31 rad s-1 B. 2.62 rad s-1 C. 78.5 rad s-1 D. 157 rad s-1 3. The three hands on a clock are called the hour hand, the minute hand and the second hand. What is the angular velocity of the second hand? A. 0.105 rad s-1 B. 1.05 rad s-1 C. 5.1 rad s-1 D. 1.5 rad s-1 4. When a particle travels in a circle of radius f, with speed v, its acceleration is A. r v 2 towards the centre B. r v 2 away from the centre C. Zero D. rv2 towards the centre 5. A particle moving in a horizontal circle with constant angular velocity will have A. constant linear momentum but varying energy B. constant energy but varying linear momentum C. neither linear momentum nor energy constant D. both energy and linear momentum constant
39 SECTION B 5.4 CENTRIPETAL FORCE 1. A gramophone rotates at 331 rev min-1 and has a radius of 0.15 m. What is a) its angular velocity b) the speed of a point on its circumference c) the centripetal acceleration of a point on its circumference (ANS: 34.66 rad s -1 , 5.2 ms-1 , 180.27 ms-2 ) 2. Calculate the centripetal acceleration of an object at the Equator due to rotation of the Earth. The radius of Earth is 6.37 x 106 m. (ANS: 0.034 ms-2) 3. A mass moves in a horizontal circle with a constant speed of v1. When the same mass moves in the same circular path with a speed of v2, the new centripetal force is half that of the first. What is the value of v1/v2 ? (ANS: 0.034 ms-2) 4. A 2 kg ball attached to a 2.5 m string is whirled in a vertical circle with a constant speedof 6 ms-1. a) Determine the centripetal force of the ball b) Calculate the tension of the string at the highest and lowest point of the circle. (ANS: 28.8 N , 9.18 N , 48.42 N) 5. A 4 kg object is attached to a vertical rod by two strings as shown in FIGURE 5.1 below. FIGURE 5.1 The object rotates in a horizontal circle at constant speed 6.00 m/s. Find the tension in a) the upper string b) the lower string (ANS: 108.63 N , 56.3 N)
40 6. FIGURE 5.2 FIGURE 5.2 above shows a 200 g ball attached to a horizontal rod by two string, each of length 0.5 m. The ball is whirled with a speed 10.0 m s-1 around the rod axis. Determine the tension in the strings when the ball is at a) the lowest point, b) the highest point. (ANS: 57.2 N, 54 N) 7. A 5000 kg truck is making a turn at a corner of radius 55 m. The road is flat and the coefficient of kinetic friction between the tyres and the road is 0.58. a) Sketch and label a free body diagram for the truck b) Calculate the maximum velocity of the truck without skidding c) Calculate the maximum angular velocity of the truck d) Calculate the maximum centripetal acceleration of the truck (ANS: 17.69 ms-1 , 0.321 rad s -1 , 28449 N) 8. A 0.2 kg, 50 cm pendulum is swirled horizontally at an angle of 37° with the vertical as shown in the FIGURE 5.3. FIGURE 5.3 a) Sketch and label a free body diagram for the pendulum bob b) Calculate the tension of the string c) Calculate the speed of the pendulum (ANS: 2.46 N , 1.49 ms-1) 0.5 m 0.5 m 0.8 m
41 9. A ball of mass 0.35 kg is attached to the end of a horizontal cord and is rotated in a circle ofradius 1.0 m on a frictionless horizontal surface. If the cord will break when the tension in itexceeds 80 N, determine a) The maximum speed of the ball b) The minimum period of the ball. (ANS: 15.12 ms-1 , 0.42 s) 10. FIGURE 5.4 shows a child riding on a Ferris Wheel “Eye on Malacca” of 4.5 m in diameter, rotating at constant speed. FIGURE 5.4 a) Draw the free body diagram and write equations for forces acting on the passenger at position A and B. b) What is the maximum angular speed so that the passenger is not thrown out form the chair? (ANS: 2.09 rad s-1) SECTION C 1. A turntable rotates at 45 revolutions per minute and then at 3 1 33 revolutions per minute. What is the ratio of the accelerations of a point on the rim of the turntable? (ANS: 1.83) 2. Find the centripetal acceleration of a sample which is at a distance of 5.0 cm from the axis of rotation of a centrifuge rotating at a constant speed of 2000 revolutions per minute. (ANS: 2.19 x 103 m s-1)
42 3. One end of a string of length 100 cm is fixed and the other end has a bob of mass 100 g attached to it. A conical pendulum is formed when the bob moves in a horizontal circle. a) If θ is the angle between the string and the vertical, show that the number of revolutions made by the bob per minute is n = cos 30 l g b) The string breaks when the tension in it exceeds 3.0 N. Calculate the maximum value for the angle θ. (ANS: 70° 54’)
43 TOPIC 6: ROTATION OF RIGID BODY 6.1 Rotational Kinematics 6.2 Equilibrium of A Uniform Rigid Body 6.3 Rotational Dynamics 6.4 Conservation of Angular Momentum At the end of this topic, students should be able to: 6.1 ROTATIONAL KINEMATICS a) Define and use: i. angular displacement, θ ii. average angular velocity, ωav iii. instantaneous angular velocity, ω iv. average angular acceleration, αav v. instantaneous angular acceleration, α b) Analyse parameters in rotational motion with their corresponding quantities in linear motion: c) Solve problem related to rotational motion with constant angular acceleration: 6.2 EQUILIBRIUM OF A UNIFORM RIGID BODY a) State the physical meaning of cross (vector) product for torque, b) Apply torque c) State conditions for equilibrium of rigid body, and d) Solve problems related to equilibrium of a uniform rigid body. (remarks: limit to 5 forces) 6.3 ROTATIONAL DYNAMICS a) Define and use moment of inertia, b) Use the moment of inertia of a uniform rigid body (sphere, cylinder, ring, disc, and rod) c) Determine the moment of inertia of a flywheel d) State and use net torque,
44 6.4 CONSERVATION OF ANGULAR MOMENTUM a) Explain and use angular momentum, b) State and use principle of conservation of angular momentum.
45 KOLEJ MATRIKULASI KEJURUTERAAN JOHOR KEMENTERIAN PENDIDIKAN MALAYSIA TUTORIAL 6 (ROTATION OF RIGID BODY SECTION A FIGURE 6.1 1. FIGURE 6.1 shows a heavy uniform plank of length L is supported by two forces F1 and F2 at a point at a distance L/4 and L/8 from its ends. Determine the ratio of F2 : F1. A. 1 : 3 B. 2 : 3 C. 3 : 2 D. 2 : 6 2. Two forces are acting on an object. Which of the following statements is correct? A. The object is in equilibrium if the forces are equal in magnitude and opposite in direction. B. The object is in equilibrium if the net torque on the object is zero. C. The object is in equilibrium if the forces act at the same point on the object. D. The object is in equilibrium if the net force and the net torque on the object are both zero. 3. Which of the following does not affect the moment of inertia of a rotating rigid body? A. Mass B. Shape C. Angular acceleration D. Mass distribution
46 4. An ice skater is spinning with his arms folded inwards. Later the ice skater stretches his arms outwards. Which of the following pairs of quantities will increase? A. period of rotation and moment of inertia. B. kinetic energy and moment of inertia. C. angular momentum and period of revolution. D. angular momentum and kinetic energy. SECTION B 6.1 ROTATIONAL KINEMATICS 1. A rotating wheel decelerates uniformly and makes N revolutions before stopping. The time taken is T. What is the initial angular velocity of the wheel? [Ans: 2N/T] 2. A motorcycle wheel with a radius 0.3 m rotates freely about a fixed axis. A steady force of 10 N is applied tangentially for the wheel’s rim for 2 s. If the wheel moves from rest and its moments of inertia about the axis is 0.5 kg m2, what is the final angular velocity? [Ans: 12 rad s-1 ] 3. A rigid body rotates about a fixed axis through a point in the body, with uniform angular velocity of 600 rpm. The velocity then decreases at a constant retardation to 300 rpm. in 6.0 s. Determine: a) the angular acceleration b) the number of revolutions the body has turned through in the 6.0 s c) the extra time needed by the body to come to a stop if it continues to slow down at the same rate. [Ans: -5.2 rad s-2, 45 revolutions, 6.0 s] 6.2 EQUILIBRIUM OF A UNIFORM RIGID BODY 1. a) State the conditions for a particle that is acted upon by a system of forces for it to be in equilibrium. FIGURE 6.2
47 b) FIGURE 6.2 shows a 1 m rod of mass 2 kg is pivoted at point P. A load of mass 6 kg is suspended at one end and another load of mass M is suspended at Q. If the system is in equilibrium, determine the value of M. FIGURE 6.3 c) FIGURE 6.3 shows a 10 kg uniform beam with 2.0 m long is pivoted at the centre. A 20 N force is exerted 0.5 from centre of the beam. If the beam is in equilibrium, determine F. [Ans: 1.2 kg, 13 N] 2. FIGURE 6.4 below shows a uniform ladder 3 m long and has a mass of 30 kg. The ladder is at rest with its upper end against a smooth vertical wall and its lower end on rough ground. The ladder is placed at the angle of 50° with the horizontal, to maintain its position. FIGURE 6.4 a) Draw a free-body diagram of this system and show the forces acting on it. b) Calculate the reaction forces at A and B. c) Calculate the least coefficient of friction between the ground and the ladder. [Ans: 294.3 N, 123.4 N, 0.42]
48 6.3 ROTATIONAL DYNAMICS 1. FIGURE 6.5 FIGURE 6.5 shows a string wound around a wheel with the free end of the string tied to the ceiling. The mass of the wheel is 0.5 kg and its radius are 40 cm. When the wheel is released, it will fall downwards and, at the same time, rotate. If the moment of inertia of the wheel about its axis of rotation is 0.2 kg m2. Calculate the linear acceleration of the wheel and also the tension of the string. [Ans: 2.80 m s-2, 3.5 N] 2. FIGURE 6.6 a) FIGURE 6.6 shows a solid cylinder of radius 18.0 cm is free to rotate about a smooth horizontal axle. A mass of 0.38 kg hangs from a string wound around the cylinder. When the system released from rest, the mass takes 2.0 s to fall through a height of 5.0 m. What is the moment of inertia of the cylinder? [Ans: 3.60 x 10-2 kg m2] b) The cylinder is then replaced by a hollow cylinder of the same mass and dimensions. Discuss qualitatively the effect on the speed of the mass after the mass has fallen through a height of 5.0 m.