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Practice Exercises for Engineering Mechanics ZAHIDI BIN HIBADULLAH WAN ABD HALIM AMIR BIN WAN MUHAMMAD RUZILA BINTI MAT GHANI KOTA BHARU POLYTECHNIC
i Published and Distributed by: Mechanical Engineering Department Politeknik Kota Bharu KM. 24, Kok Lanas, 16450 Ketereh, Kelantan. Practice Exercises For Engineering Mechanics First Edition 2024 © 2024 Zahidi bin Hibadullah, Wan Abd Halim Amir bin Wan Muhammad, Ruzila binti Mat Ghani All right reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronics, mechanical, photocopying, recording or otherwise without prior permission of the publisher. Zahidi, Wan Abd Halim Amir & Ruzila Practice Exercises For Engineering Mechanics / Zahidi, Wan Abd Halim Amir & Ruzila
ii PREFACE Alhamdulillah, all praise be to God, with God's permission we were able to finish writing this question book. This question book was developed to give exposure to the students to familiarize themselves with the questions related to the engineering mechanic course. It is our intention to develop this question book, students' understanding will increase and make this course easier to learn and obtain good results in the exam. We would like to thank our colleagues and thank the organizations that helped us throughout the publication process, especially those who contributed in terms of ideas, time and advice. Hopefully this question book can help Mechanical Engineering students at Polytechnic, especially Polytechnic Kota Bharu
iii SYNOPSIS This question book contains Four (4) chapters which is Chapter 1: Basic Concepts of Engineering Mechanics, Force Vectors and Equilibrium, Chapter 2: Structure, Chapter 3: Kinematics of Particles and Chapter 4: Kinetics of Particles. Chapter one has 35 questions, chapter 2 has 15 questions, chapter 3 has 31 questions and chapter 4 has 23 questions. Questions consist of theory questions and calculation questions. As a reference each question is included with answers. This book is expected to help students answer related questions and then check their answers.
iv About the Authors Zahidi bin Hibadullah the author was born in 1970 in Kota Bharu, Kelantan. He received his primary and secondary education in Kota Bharu, Kelantan, Tumpat before enrolling at ITTHO, Johor in 1995. He has an academic qualification in Diploma of Mechanical Engineering (ITTHO, 97) and Mechanical Engineering degree with Honour in Education (OUM, 2006). Began his career as a lecturer at Polytechnic Sultan Abdul Halim Mu’adzam Shah (POLIMAS) in June 1997 until June 2014 and is now being served at the Polytechnic Kota Bharu (PKB). Experienced in teaching Mechanical Engineering related subjects such as Engineering Mechanics, AUTOCAD, Thermodynamics and Mechanical Workshop Practice Wan Abd Halim Amir bin Wan Muhammad the author was born in 1972 in Pasir Mas, Kelantan. He received his primary and secondary education in Kota Bharu, Kelantan before enrolling at UPM in 1994. He has an academic qualification in Degree of Agricultural Engineering (UPM, 98). Began his career as a lecturer at Polytechnic Kota Bharu (PKB) in 2001 until now. Experienced in teaching Mechanical Engineering related subjects such as Agricultural Mechanization, Agriculture Waste Management System and Agriculture Workshop Management Ruzila Binti mat Ghani was born on 2nd July 1977 in Kota Bharu Kelantan. She received her primary education at Sekolah Kebangsaan Seribong and secondary education at Sekolah Menengah Kubang Kerian. She studies in diploma of Mechanical Engineering and Bachelor of Science in Mechanical Engineering from University of Technology Malaysia (UTM). She has Master of Technical and Vocational Education from Tun Hussein Onn University College of Technology. Began her career as a lecturer at Politeknik Sultan Mizan Zainal Abidin (PSMZA) in 2001 and Politeknik Kota Bharu in 2005 until now.
v TABLE OF CONTENTS TOPIC PAGES PREFACE SYNOPSIS ABOUT THE AUTHORS CHAPTER 1: BASIC CONCEPTS OF ENGINEERING MECHANICS, FORCE VECTOR AND EQUILIBRIUM 1 CHAPTER 2: STRUCTURES 11 CHAPTER 3: KINEMATICS OF PARTICLES 18 CHAPTER 4: KINETICS OF PARTICLES 26 SOLUTION 34 REFERENCES 191
CHAPTER 1 BASIC CONCEPTS OF ENGINEERING MECHANICS, FORCE VECTOR AND EQUILIBRIUM
1 1. Name FOUR (4) basic quantities in the field of mechanics. 2. Define Newton’s first law of motion and give TWO (2) examples of Newton’s first law of motion. 3. Explain the equilibrium using Newton’s second law of motion. 4. Define Newton’s first law of motion and Newton’s third law of motion. 5. Explain the condition for equilibrium of a particle and express the equation of equilibrium. 6. Define the terms below: i. Static ii. Dynamics 7. Define the terms below: i. Mass ii. Space 8. Differentiate between the quantity of scalar and vector quantities and give TWO (2) examples for each quantity. 9. Explain the condition for Equilibrium of particle. 10. State TWO (2) basic measurement quantities and the SI units. 11. Compare between scalar and vector. Give ONE example of each quantity. 12. Express a vector with magnitude of 3 N directed at 64°, counterclockwise from the x-axis in unit vector form.
2 13. Figure below shows a force = 38 acting on the particle O. Describe the components of the x and y axis. 14. Calculate the magnitude and angular directions represented by force 1 below: 1 = (60 − 50 + 40) 15. Refer to figure below, calculate: i. Force in component x and y axis and resultant force in terms of cartesian vector. ii. Magnitude of the resultant force, FR. 16. Express the value of the internal forces in cable CB, CE, and spring CD in figure below, if the mass of the ball is 70 kg.
3 17. Figure below shows the magnitude and direction of two forces acting on a ring bracket. Calculate: i. Magnitude of the resultant force. ii. Direction of the resultant force. 18. Figure below shows a load of 40 kg hanging in equilibrium on cable AO and BO. If the system is in equilibrium, calculate: i. Angle ii. Force at cable AO and BO 19. Based on figure below, if 2 = 35 and = 55° i. Calculate each force into component -x () and component -y (). ii. Calculate the magnitude of the resultant in cartesian vector form.
4 20. Figure below shows a plane force system at O. Calculate the magnitude of the forces, 1 and 2 if the system is in equilibrium. 21. Two cables AB and BC are tied together at B and a load of 25 kg is hung at B as shown in Figure below. Calculate the tension developed in cable AB and BC.
5 22. Referring to force diagram in figure below, calculate: i. Resultant force of each component ii. Magnitude of the resultant force. iii. Determine the direction of the resultant force. iv. Illustrate that direction using force diagram for resultant force. 23. Figure below shows the system in equilibrium. Represent the system in the form of free body diagram at: i. Point B ii. Point D
6 24. Determine the x and y components of each force acting on the screw eye shown in figure below. 25. Based on diagram below, if 1 = 700 and = 25°, calculate the magnitude and direction measured counterclockwise from the positive x axis of the resultant force produced from the three forces acting on the A ring. 26. By using parallelogram, calculate: i. The magnitude of the component force F in figure below and the magnitude of the resultant force if is directed along the positive y axis. ii. Predict what happen to the resultant force if the value of F is 400 N
7 27. A 10 kg block is suspended from pulley B and the sag of the cord is = 0.2 . Determine the force is cord ABC. Neglect the size of the pulley. 28. Calculate the magnitude of force T acting on the eyebolt and its angle , if the magnitude of the resultant force is 10 kN to be directed along the positive x axis.
8 29. Solve each force acting into x and y components. Express the force as a Cartesian vector. 30. Based on figure below, if 1 = 100 and ∅ = 30°, calculate the magnitude of the resultant force acting on the bracket and its direction measured clockwise from positive x-axis. 31. Based on figure below: i. Calculate the magnitude of the resultant of 1 and 2 in term of Cartesian vector. ii. Predict what will happen to the resultant force if the angle of 1 is increased to 60°.
9 32. If the mass of chandelier in figure below is 50 kg, determine the tension developed in BD and CD cable used to support the chandelier. 33. Figure below shown the three forces acting on the particle O. Calculate: i. Magnitude resultant force for these forces. ii. The direction of the resultant force counterclockwise from the positive x-axis. 34. Two forces 1 = 60 and 2 = 40 acting on the particle O as shown in figure below: i. Calculate magnitude of the resultant force of the forces as Cartesian vector form. ii. Predict what will happen to the resultant force if the angle of 2 is increased to 30°.
10 35. If the mass of bucket in figure below is 10 kg, determine the tension developed in EB and ED cable used to support the bucket.
CHAPTER 2 STRUCTURE
11 1. Describe the following term: i. The conditions for equilibrium ii. Plane truss 2. The truss is subjected to the loading as shown in figure below: i. Draw the free body diagram for the truss as show in figure. ii. Calculate the reaction force for each supporter. iii. Calculate the force in each member by using the method of joint and state the members are in tension or compression. 3. Figure below shows a truss on the floor with a supporter pin at A and supporter a roller at D. By using the method of section, i. Illustrate the free body diagram. ii. Find the reaction force at supporter A and D iii. Determine force in member BC, GF of the truss and state whether the member are in tension or compression.
12 4. A truss is a structure composed of member joined together at their end points. Figure below shows a truss member with load F = 500 N acting at joint C. i. Classify 2 method of analysing a truss. ii. Find internal forces in member AC. iii. Find external reaction at support B 5. Figure below shows a structure with load P = 1.6 kN acting at point A. From the structure given, find : i. The number of members in the structure. ii. Angle 1 2 . iii. Force in member AB and AC. 6. The truss is subjected to the loading as shown in figure below. i. Find the value of 1 and 2 for the truss in figure below. ii. Illustrate free body diagram and label all the force acting for the truss in figure below. iii. Find the reaction force at supporter A and C in figure below.
13 iv. Determine the force in all members and indicate if the member is in tension or compression. a) Member BD b) Member AD and AB c) Member BC, BD and DC 7. The truss is subjected to the loading as shown in Figure below: i. Illustrate free body diagram for the truss as shown in Figure below. ii. Find the reaction force for each supporter. iii. Determine the force in each member of the truss and state the members are in tension or compression. 8. The bridge in Figure below is subjected to the loading as shown below. By using method of section: i. Illustrate the free body diagram. ii. Find the reaction force at supporter A and E iii. Determine force in the part of frame HI, HB and BC of the truss.
14 9. Calculate the force in each member of the truss in figure below. State whether it is in tension or compression. 10. Calculate the forces of each member of the roof truss shown in Figure below and indicate if the members are in tension or compression.
15 11. Calculate the force of each member at BC, CF and EF of the truss as shown in fugure below and state whether the members are in tension or compression. 12. Based on figure below, determine the tension developed in cable CA and CB
16 13. Using the method of joints, determine: i. The force in each member of the truss and state whether the members are in tension or compression. ii. The magnitude of the external reactions at A and B and show the direction of the reaction. 14. The bridge in figure below is subjected to the loading shown. Identity whether the members IH, BH and BC of the truss are in tension or compression form.
17 15. The bridge in figure below is subjected to the loading shown. Calculate the force in the part of frame IH, BH and BC of the truss. Identity whether the parts of frame are in tension or compression. + ∑ = 0 2(4) + 2(8) + 4(12) − (16) = 0 8 + 16 + 48 − 16 = 0 72 − 16 = 0
CHAPTER 3 KINEMATICS OF PARTICLE
18 1. State the following terms: i. Displacement of particle ii. Acceleration iii. the time interval. 2. Give the definition and S.I. unit for accelerations. 3. Kinematics is a branch of dynamics. i. Define kinematics. ii. Compare velocity and speed in kinematics. 4. Define the following terms: i. Velocity ii. Speed iii. Angular velocity 5. Define the following terms: i. Constant velocity ii. Constant acceleration 6. Define the terms below. i. Kinematic ii. Kinetics 7. Figure below shows the sketch of a circular motion, interpret , , , .
19 8. Visualize using suitable velocity-time graph. i. When the object starts to rest. ii. When the object is in acceleration. iii. when the object is in deceleration iv. When the object is in uniform motion. 9. A car with wheels of 500 mm in diameter each is travelling at 64 km/h. Determine the angular velocity of the wheels in rad/s. 10. A motorcycle moves with a wheel speed of 250 rpm. If the diameter of motorcycle wheel is 60 cm. i. Convert the velocity of motorcycle in km/h unit. ii. If the motorcycle moves for 10 minutes from rest, express the value of acceleration for the motorcycle in m/s2 . 11. The distance between building A and building B is 6.8 km. A car starts from rest at building A with a constant acceleration for 32 seconds, then a car travels with a constant velocity before it decelerates constantly and stops at building B in the last 15 seconds of the journey. If the total time taken is 7 minutes: i. Draw a velocity-time graph. ii. Calculate the constant velocity of the car in m/s iii. Calculate the acceleration of the car in m/s2 . iv. Calculate the distance traveled in the first 3 minutes of the journey. 12. A car starts from rest and accelerates uniformly until it reaches a velocity of 130 m/s in 65 seconds. Its velocity is maintained for 30 seconds and then it decelerates to stops within 35 seconds. i. Sketch the graph of velocity versus time. ii. Calculate the total distance of the journey. iii. Calculate the average velocity for the whole journey.
20 13. A car starts from rest and accelerates uniformly for 20 seconds until it reaches 22 m/s at the end of acceleration. Then the car moves constantly for 40 seconds, after that it accelerates for 10 seconds until it reaches 30 m/s and stops in 30 seconds. i. Draw a velocity-time graph for this trip. ii. Calculate the second acceleration. iii. Calculate each distance travelled by the car during first acceleration uniform velocity and deceleration. 14. The movement of a particle is expressed in relation of = 3 − 5 2 + 15 + 40 where s and t are in meters and second respectively. When = 2, express the answer in mathematical method. i. Displacement ii. Velocity 15. A man starts his exercise buy running from rest and accelerates uniformly for 40 seconds and reaches a velocity of 15 m/s at the end of the acceleration. Its velocity is maintained for a while and then it stops within 60 seconds with a constant deceleration. The total distance travelled by that man is 2.3 km. i. Sketch a graph of velocity (v) against time (t). ii. Calculate the acceleration of that running man. iii. Calculate the total time taken for the whole exercise sessions. iv. Calculate the deceleration of that running man. 16. A car with a velocity of 15 m/s accelerates to reach velocity of 80 m/s with an acceleration of 3.5 m/s2. This velocity is maintained for 35 seconds before deceleration until it stops within 25 seconds. i. Draw a velocity-time diagram for the trip. ii. Calculate the time taken during the acceleration. iii. Calculate the car deceleration. iv. Calculate total distance for the trip.
21 17. The movement of a particle is expressed in relation of = 5 3 − 4 2 + 3 + 12), where x and t are respectively in meters and seconds. If t = 8 seconds, determine i. Position. ii. Velocity. iii. Acceleration. 18. A ball is thrown downward from a 60m tower with an initial velocity of 20m/s, Determine the velocity at which it hits the ground and the time of travel. 19. A car travels in a straight line with initial velocity 10m/s and it accelerates uniformly at 2 m/s2 for 300m. Then, it travels at a constant velocity for 20 seconds. Finally, it slows at a constant deceleration for 15 seconds until it stops. i. Sketch a velocity-time graph. ii. Calculate the constant velocity of the car. iii. Calculate the deceleration of the car. iv. Calculate the total distance for the journey. 20. A car has an acceleration and a deceleration of 6 m/s. If it starts from rest and can have a maximum velocity of 60m/s, predict the shortest time it can travel for 1200m before it stops. 21. The coordinate of a car which is confined to move along a straight line is given by equation, = 2 3 − 24 + 6 where s is the distance travelled by the car measured in meter from an origin and t is the duration of travel in seconds. Calculate: i. The time required for the car to reach the velocity of 72 m/s from its initial condition at = 0. ii. The acceleration of the car when the velocity is 30 m/s. iii. The net displacement of the car during the interval from = 1 to = 4 .
22 22. A ball is thrown vertically upward as shown in figure below with a speed of 15 m/s. Predict the time when it returns to its original position. 23. A shaft starts from rest and reaches velocity 250 rpm in 10 seconds. Calculate the angular acceleration of the shaft and the number of rotations within the time. 24. An object being thrown up from the top of 100 meters building from the ground with a velocity 20 m/s. Determine: i. The velocity of an object exactly when it hits the ground. ii. Time taken from it starts until it reaches the ground. 25. A car starts from rest with a constant acceleration of 1.25 m/s2 until it achieves 50 km/h. The velocity maintained as far as 1.2 km. When the brake is applied it stops with 10 second with constant deceleration. i. Calculate the total time taken during the journey. ii. Determine the total distance during the journey. 26. A car is travelling along a straight road at 30 km/h and the speed increases to 100 km/h in 20 s. Determine the distance travelled. The answer must be in SI unit. 27. A car starts from rest and accelerates uniformly for 50 seconds and reaches a velocity of 70 m/s at the end of the acceleration. Its velocity is maintained for a while and then it stops within 60 seconds with 60 seconds with constant deceleration. The total distance travelled by the car is 11.5 km. i. Sketch a velocity-time graph. ii. Calculate the acceleration of the car. iii. Calculate the time taken for the journey.
23 28. A vehicle moves in a straight road with a displacement defined by = (0.6 3 + 0.3 2 ) where t is in second and s is in meter. When = 6 , identify: i. Velocity. ii. Acceleration. iii. Predict whether the vehicle is in the motion of accelerating or decelerating within the duration time of {1 ≪ ≪ 6} . 29. A vehicle moves in a straight line such that for a short time its velocity is defined by = 0.9 2 + 0.6 m/s where t is in second. When t=3 s, determine: i. Displacement. ii. Acceleration. 30. A car starts from rest and accelerates uniformly for 70 seconds and reaches a velocity of 80 m/s at the end of the acceleration. Its velocity is maintained for a while and then it stops within 65 seconds with constant deceleration. The total distance travelled by the car is 12.2 km. i. Draw a velocity-time graph. ii. Determine the acceleration of the car. iii. Calculate the time taken for the journey. iv. Determine the deceleration of the car. 31. A train starts from rest at a station with constant acceleration of 2.5 m/s2 until it achieves velocity of 70 km/h. Then, the train decelerate until it stops in 10 s. Determine: i. Distance travelled by the train. ii. Deceleration of the train.
CHAPTER 4 KINETICS OF PARTICLES
25 1. State the following terms: i. Kinetic ii. Work 2. Define Newton’s second law of motion and give ONE (1) example in real life phenomenon. 3. The principles of relationship between work and energy can be used to solve some kinematics variables in kinetic related problems. i. Explain the relationship between work and energy. ii. Reprsent the relationship between work and energy in mathematical equantions. ∑ − = 1 2 2 − 1 2 2 4. Define the following terms: i. Potential Energy ii. Kinetic Energy 5. State the Newton’s Second Law and give TWO (2) examples of its application. 6. An object of mass 5 kg is dropped from a height of 35 m from a building. Based on the situation below, express the value of: i. The potential energy possessed by the object before it fell. ii. The kinetic energy possessed by the object before it fell. iii. The potential energy possessed by the object after it fell and touched the ground. iv. The kinetic energy possessed by the object after it fell and touched the ground. 7. The 75 kg crate shown in figure below rest on a horizontal surface for which the coefficient of kinetic friction is = 0.3. If the crate is subjected to a 600 N towing force as below:
26 i. Draw a Free Body Diagram (FBD). ii. Calculate the velocity of the crate after 5 second starting from rest. 8. Figure below shows a man is pushing a machine on a rough surface. Given that the pushing force 600 N, acted 48° from the negative x-axis. The total mass of the machine is 20 kg. If the kinetic friction, 0.4 ∶ i. Draw the free body diagram of forces that acted on the machine. ii. Calculate the normal force and friction force. iii. Calculate the acceleration of the machine. 9. A particle of 4 kg mass is being pulled across a smooth horizontal surface by a horizontal force. The force does 24 J of work in increasing the particle’s velocity from 5 m/s to v m/s. Express: i. The value of v after 15 seconds. ii. The value of the position for the particle after 15 seconds.
27 10. The 60 kg crate in figure below rests on a horizontal surface for which the coefficient of kinetic friction = 0.3. If the crate is subjected to a 400 N towing force as shown, calculate: i. The value of normal force and the friction force. ii. The value of an acceleration of the crate. iii. The velocity of the crate after 3 seconds starting from rest. 11. A 1000 kg container rest on a horizontal surface which the coefficient of kinetic friction is = 0.3.The container is subjected to 6000N towing force acting at angle of 45 0 as shown. 12. A particle of 2 kg mass is being pulled across a smooth horizontal surface by a horizontal force. The force does 39 Joule of work in increasing the particle's velocity from 5ms-1 to v ms-1 . Calculate. i. The value of v. ii. The value of an acceleration for the particle. iii. The position of the particle after 15 seconds.
28 13. A vehicle with a weight of 500 kg is driven downhill which is 6° incline and at a speed of 60 km/h as shown in Figure below. When the brakes are applied, it will cause a constant total braking force of 250 N. Based on this information: i. Draw a free body diagram for this vehicle. ii. Calculate the kinetic energy for this vehicle. iii. Calculate the work done by the vehicle. 14. A 1600 kg crate is pulled along the ground with a constant speed of a distance for 25 m, using a cable that makes a horizontal angle of 15°. Determine the tension in the cable. The coefficient of kinetic friction between the ground and the crate is = 0.55. 15. An object of 5 kg dropped from 16 m height. Calculate : i. Potential energy and kinetic energy possessed by the object before dropped. ii. Potential energy and kinetic energy possessed by the object after it dropped and landed on the ground. 16. Determine the velocity of the 105 kg crate as shown in figure below when it reaches the bottom of the chute at B. The initial velocity of the crate is 6 m/s at A and the friction force is 35 N.
29 17. An object weighs 2 kg falling from 10 m height. Calculate: i. Gravitational potential energy and the kinetic energy possessed by the object before it falls. ii. Gravitational potential and the kinetic energy possessed by the object right after it has touched the ground. 18. Based on figure below, determine the tension developed in the cable when the motor, M winds in the cable with a constant acceleration. Then, the 25 kg crate moves a distance, = 6 in 4 , starting from rest. The coefficient of kinetic friction between the crate and the plane is = 0.25. 19. The 150 kg box as shown -in Figure 4(c) is originally at rest on the smooth horizontal surface. If a towing force of 300N acting at an angle of 45 0 is applied to the box for 8 s, determine the final velocity using: i. Equation of motion ii. Principle of work and energy
30 20. An 80 kg block as shown in figure below rests on horizontal plane. Determine the magnitude of the force P required ti give the block an acceleration of 2.5 m/s2 to the right. The coefficient of kinetic friction between the block and the plane is = 0.25. 21. The 100 kg crate shown in figure below is originally at rest on a smooth horizontal surface. If a force of 200 N is applied to the crate for 6 s, calculate the final velocity using: i. Equation of motion. ii. Principle of work and energy. 22. A particle of 2 kg mass is being pulled across a smooth horizontal surface by a horizontal force. The force does 24 Joule of work in increasing the particle’s velocity from 5 m/s to v m/s. Calculate the value of v and the position of particle after 15 s.
31 23. A 50 kg crate rests on a horizontal plane for which the coefficient of kinetic () is 0.30. If the crate is subjected to a 400 N towing force as shown in figure below, determine the velocity of the crate in 5 s starting from rest.
32 Solutions
33 CHAPTER 1 BASIC CONCEPTS OF ENGINEERING MECHANICS, FORCE VECTOR AND EQUILIBRIUM 1. Name FOUR (4) basic quantities in the field of mechanics. Answer: i. Length. ii. Time. iii. Mass. iv. Force. 2. Define Newton’s first law of motion and give TWO (2) examples of Newton’s first law of motion. Answer: Newton’s first law of motion states that an object in motion will continue in its state of motion (both in magnitude and direction), and an object at rest will remain at rest in an isolated system unless acted upon by an external force. 3. Explain the equilibrium using Newton’s second law of motion. Answer: From the Newton’s second law of motion, ∑ = . To maintain the equilibrium, it is necessary to satisfy the Newton’s first law of motion, ∑ = 0, where = 0 and therefore the particle’s acceleration, = 0. 4. Define Newton’s first law of motion and Newton’s third law of motion. Answer: Newton’s first law: A particle originally at rest or moving in a straight line with constant velocity will remain in this state if it is not subjected to unbalanced force. Newton’s third law: The mutual forces of action or reaction between two particles are equal.
34 5. Explain the condition for equilibrium of a particle and express the equation of equilibrium. Answer: Equilibrium equations for a particle is defined as a particle is in equilibrium if the resultant of all forces acting on the particle is equal to zero. ∑ where the component also ∑ = 0, ∑ = 0 6. Define the terms below: i. Static ii. Dynamics Answer: Static: related to the balance of a body whether it is at rest or moving with a constant velocity Dynamics: related to bodies that have acceleration 7. Define the terms below: i. Mass ii. Space Answer: i. Mass Mass is a measure of the amount of material ill a body. The standard unit of mass measurement is the kilogram (kg). ii. Space Space is a geometric region in which even involving bodies occur. The concept of length is needed to locate the position of a point in space and thereby to describe the size of physical system. The standard unit of length measurement is the meter (m).
35 8. Differentiate between the quantity of scalar and vector quantities and give TWO (2) examples for each quantity. Answer: Scalar Quantity is any positive or negative physical quantity that can be completely specified by its magnitude. Example: mass, time, length, speed, distance, kinetic energy, power Vector Quantity is any physical quantity that requires both a magnitude and a direction for its complete description. Example: force, moment, displacement, velocity, force, weight. 9. Explain the condition for Equilibrium of particle. Answer: A particle is said to be in equilibrium when the forces acting on it are zero. ∑ = 0 10. State TWO (2) basic measurement quantities and the SI units: Answer: Measurement Quantity Unit (SI) Time S Length m Mass kg Temperature K
36 11. Compare between scalar and vector. Give ONE example of each quantity. Answer: Scalar is quantity, which is only has magnitude, while vector has a magnitude and its direction. Example: Length, Mass, Time etc Example: Force, Velocity, Acceleration, etc. 12. Express a vector with magnitude of 3 N directed at 64°, counterclockwise from the x-axis in unit vector form. Answer: The x-coordinate is the magnitude times the cosine of the angle, while the y-coordinate is the magnitude times the since of the angle. Magnitude = 3 N, = 64° = 3 cos 64° = 1.315 = 3 sin 64° = 2.296 The resultant vector is 1.315 + 2.296
37 13. Figure below shows a force = 38 acting on the particle O. Describe the components of the x and y axis. Answer: = tan−1 4 3 = 53.13° = 38 cos 53.13° = 22.8 = 38 sin 53.13° = 30.4
38 14. Calculate the magnitude and angular directions represented by force 1 below: 1 = (60 − 50 + 40) Answer: 1 = (60 − 50 + 40) Magnitude of 1 = √ 2 + 2 + 2 1 = √(60) 2 + (−50) 2 + (40) 2 1 = √3600 + 2500 + 1600 1 = √7700 1 = 87.75 Direction of 1: cos 1 = cos 1 = 60 87.75 1 = cos−1 0.684 1 = 46.86° cos 1 = cos 1 = −50 87.75 1 = cos−1 −0.5698 1 = 125° cos 1 =
39 cos 1 = 40 87.75 1 = cos−1 0.4558 1 = 62.88° Draw the model for force 1 with the aid of diagram on an , , .