MECHANICS for mech eenggineering students

MECHANICS for mech eenggineering students

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1. What is Physics? Physics is the most fundamental branch of physical science which deals with the study of matter and energy, and their relationship with each other. Physics is basically the study of how objects behave.

2. Mechanics is one of the main branches of physics which deals with the study and behavior of physical bodies when subjected to different types of forces or displacement, and the subsequent effect of bodies on the environment. Mechanics:

3. Types of mechanics Quantum Mechanics classical Mechanics Fluid Mechanics Kinematics (Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies, and systems of bodies without considering the forces that cause them to move.) Dynamics (Dynamics is the branch of physics developed in classical mechanics concerned with the study of forces and their effects on motion

4. Classical Physics believes in a single nature, only the particle nature of matter. It provides the macroscopic vision of matter. It is based upon Newtons laws of mechanics and Maxwells laws of electromagnetism. Quantum Physics believes in dual nature, both particle and wave nature of matter. It provides a microscopic vision of matter.

5. fundamentals to learn modeling and analysis of static equilibrium problems. Understand modeling and analysis of static equilibrium problems, with an emphasis on real-world engineering systems and problem solving. Draw free-body diagrams in analyzing static equilibrium engineering problems. Formulate static equilibrium equations for a rigid body.

6. Scalars and Vector Quantities Scalar Quantities: example,  length, speed, work, mass, density, etc. Vector Quantities: For example, displacement , force , torque , momentum , acceleration , velocity , etc.

7. Criteria Scalar Vector Definition A scalar is a quantity with magnitude only. A vector is a quantity with the magnitude as well as direction. Direction No direction Yes there is the direction Specified by A number (Magnitude) and a Unit A number (magnitude), direction and a unit. Represented by Quantity symbol Quantity symbol in bold or an arrow sign above Example Mass and Temperature Velocity and Acceleration Comparison between Scalars and Vectors

8. How to Draw a Vector A vector is drawn as an arrow with a head and a tail. The magnitude of the vector is often described by the length of the arrow. The arrow points in the direction of the vector. How to Write a Vector Vectors are generally written as boldface letters. They can also be written with an arrow over the top of the letter.

9. Isaac Newton (a 17th century scientist) put forth a variety of laws that explain why objects move (or don't move) as they do.

10. Newton's first law of motion is often stated as An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalenced force .   Newton’s first law of motion states that ” A body continues its state of rest or of uniform motion in a straight line provided no net force acts on it. Newton’s 1st law of motion deals with the inertial property of matter, therefore, newton’s 1st law of motion is known as the law of inertia .

11. Balanced Forces But what exactly is meant by the phrase unbalanced force ? What is an unbalanced force? consider a physics book at rest on a tabletop. There are two forces acting upon the book. One force - the Earth's gravitational pull - exerts a downward force. The other force - the push of the table on the book (sometimes referred to as a normal force ) - pushes upward on the book.     Since these two forces are of equal magnitude and in opposite directions, they balance each other. The book is said to be at equilibrium . There is no unbalanced force acting upon the book and thus the book maintains its state of motion . When all the forces acting upon an object balance each other, the object will be at equilibrium; it will not accelerate.

12. Unbalanced Forces Now consider a book sliding from left to right across a tabletop. it acquired its motion by sliding down an incline from an elevated position. The book is in motion and at the moment there is no one pushing it to the right. (Remember: a force is not needed to keep a moving object moving to the right .) The forces acting upon the book are shown below.  

13. The force of gravity pulling downward and the force of the table pushing upwards on the book are of equal magnitude and opposite directions. These two forces balance each other. Yet there is no force present to balance the force of friction. As the book moves to the right, friction acts to the left to slow the book down. There is an unbalanced force; and as such, the book changes its state of motion. The book is not at equilibrium and subsequently accelerates. Unbalanced forces cause accelerations . In this case, the unbalanced force is directed opposite the book's motion and will cause it to slow down.

14. A   force  is a push or pull upon an object resulting from the object's  interaction  with another object. Whenever there is an  interaction  between two objects, there is a force upon each of the objects. When the  interaction  ceases, the two objects no longer experience the force. Forces only exist as a result of an interaction.

15. all forces (interactions) between objects can be placed into two broad categories: contact forces forces resulting from action-at-a-distance Contact forces  are those types of forces that result when the two interacting objects are perceived to be physically contacting each other. Examples of contact forces include frictional forces, tensional forces, normal forces, air resistance forces, and applied forces. Action-at-a-distance forces  are those types of forces that result even when the two interacting objects are not in physical contact with each other, yet are able to exert a push or pull despite their physical separation. 

16. Contact Forces Action-at-a-Distance Forces Frictional Force Gravitational Force Tension Force Electrical Force Normal Force Magnetic Force Air Resistance Force   Applied Force   Spring Force

17. In the statement of Newton's first law , the unbalanced force refers to that force that does not become completely balanced (or canceled) by the other individual forces. If either all the vertical forces (up and down) do not cancel each other and/or all horizontal forces do not cancel each other, then an unbalanced force exists. The existence of an unbalanced force for a given situation can be quickly realized by looking at the free-body diagram for that situation .

18. What is a free-body diagram? A free-body diagram is a representation of an object with all the forces that act on it .

19. How to draw a free-body diagram? You can draw a free-body diagram of an object following these 3 steps: Sketch  what is happening Determine   the forces that act on the object Draw  the object in isolation with the forces that act on it

20. Step 1: Sketch what is happening This simply means that after you've read the problem once or twice, you sketch the object in its environment , and represent the main forces acting on the object (e.g. the push or the pull exerted by somebody, the friction force, etc.) so that you can clearly see what is going on. For example , if a block is pushed over the floor with friction, a sketch of what is happening could look like this: .

21. Step 2: Determine the forces that act on the object Carefully observe your sketch, and think about all the forces that are acting on the object. Returning to our example: the block is pushed , so a pushing force acts on the block; there is friction between the block and the floor, so a friction force acts on the block (opposing its motion); the block is subject to the force of gravity ; the floor exerts the normal force on the block in order to prevent the penetration of the block. Therefore, we come to the conclusion that 4 forces are acting on our block: push,  F friction force,  F f normal force,  N gravitational force  m g

22. Step 3: Draw the object in isolation with the forces that act on it Finally , draw the object on its own (omitting external elements like other objects, the floor, the ceiling, etc.) and the forces that are acting on it. In our example, we draw the block and the 4 forces that act on it:

23. Examples of drawing free-body diagrams Example 1 A box is pushed up an incline with friction which makes an angle of 20° with the horizontal. Let's draw the free-body diagram of the box. The first step is to sketch what is happening:

24. The next step is to look at the sketch , and enumerate all the forces to which the box is subject: upward push,  F force of friction,  F f normal force,  N force of gravity,  m g

25. The final step is to draw the box with the 4 forces that act on it :

26. Example 2 A mass hangs from a rope attached to the ceiling. Let's draw the FBD of the hanging mass. We begin with the sketch :

27. Looking at the sketch , we infer that there are only 2 forces acting on our mass: the force of gravity,  m g , which is pulling the mass downward the upward tension exerted by the rope,  T , which prevents the mass from falling Finally, we draw the mass and the two opposite vertical forces that act on it:

28. A sphere is hanging from two ropes attached to the ceiling. The first rope makes an angle of 30° with the ceiling, while the second rope makes an angle of 45° with the ceiling. Let's draw the free-body diagram of the sphere. Example 3 sketch what is happening:

29. sketch and think of all the forces that act on the sphere: tension exerted by the first rope,  T 1 tension exerted by the second rope,  T 2 force of gravity,  m g We draw the sphere with the 3 forces acting on it:

30. Newton's second law of motion pertains to the behavior of objects for which all existing forces are  not  balanced. The second law states that the acceleration of an object is dependent upon two variables - the  net force  acting upon the object and the mass of the object . The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.

31. Newton's second law of motion can be formally stated as follows: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. This verbal statement can be expressed in equation form as follows: a = F net  / m The above equation is often rearranged to a more familiar form as shown below. The net force is equated to the product of the mass times the acceleration. F net  = m • a The acceleration is directly proportional to the  net force ; the  net force  equals mass times acceleration; the acceleration in the same direction as the  net force ; an acceleration is produced by a  net force . 

32. How to write force equations using components of an angled force Sometimes forces are angled and do not point along the coordinate axes. Let's analyze the specific example shown in Figure1 . An angled force can be broken down to horizontal and vertical components (see Figure 2 below). This allows us to apply Newton’s second law to the forces in the horizontal and vertical directions separately.

33. Given in the picture below, a horse is pulling the horsebox having 8 kg mass in it with a force of 40N; if the applied force has an angle of 37º to the horizontal; calculate the acceleration of the horse box.

34. two forces are called  action  and  reaction  forces and are the subject of Newton's third law of motion. Formally stated, Newton's third law is: For every action, there is an equal and opposite reaction. According to  Newton's third law , for every action force there is an equal (in size) and opposite (in direction) reaction force. Forces always come in pairs - known as "action-reaction force pairs." 

35. Work Work results when a force acts upon an object to cause a displacement (or a motion) or, in some instances, to hinder a motion. Three variables are of importance in this definition - force, displacement , and the extent to which the force causes or hinders the displacement . Work = Force • Displacement • Cosine(theta) W = F • d • cos θ

36. theta is the angle between the force and the displacement which it causes. If the force is in the same direction as the displacement, then the angle is 0 degrees. If the force is in the opposite direction as the displacement, then the angle is 180 degrees. If the force is up and the displacement is to the right, then the angle is 90 degrees.

37. Energy is a measurement of the ability of something to do work.  It is not a material substance. Energy can be stored and measured in many forms. Power Power is defined as the rate at which work is done upon an object. The equation for power shows the importance of time: Power = Work / time P = W / t Combining the equations for power and work can lead to a second equation for power. Power is W/t and work is F•d•cos (theta). Substituting the expression for work into the power equation yields P = F•d•cos (theta)/t. If this equation is re-written as P = F • cos (theta) • (d/t) The d/t ratio is the speed value for a constant speed motion or the average speed for an accelerated motion. Thus, the equation can be re-written as P = F • v • cos (theta)

38. two forces are called  action  and  reaction  forces and are the subject of Newton's third law of motion. Formally stated, Newton's third law is: For every action, there is an equal and opposite reaction. According to  Newton's third law , for every action force there is an equal (in size) and opposite (in direction) reaction force. Forces always come in pairs - known as "action-reaction force pairs." 

39. PROBLEMS

40. Given in the picture below, a horse is pulling the horsebox having 8 kg mass in it with a force of 40N; if the applied force has an angle of 37º to the horizontal; calculate the acceleration of the horse box.

41. Newton’s law and Centre of mass of a system of Particles

42. Torque:

43. Linear and Angular quantities

44. Centripetal force

45. Moment of inertia

46. Given in the picture below, a horse is pulling the horsebox having 8 kg mass in it with a force of 40N; if the applied force has an angle of 37º to the horizontal; calculate the acceleration of the horse box.

47. What are the magnitude and direction of vector

48. What are the components of a vector that has a magnitude 12 units and makes an angle of 126° with the positive x direction.

49. A plane is flying with a speed of 120 m/sec, it makes a turn to join a circular path leveling with the ground. What will be the radius of the circular path formed if the centripetal acceleration is equal to the acceleration due to gravity?

50. Suppose you are sitting in a room and felt the need to increase the speed of the fan, you increased the regulator and the blades accelerated at 2 rad /sec 2 . It accelerated for 3 seconds and the final angular frequency of the blades became 7 rad /sec. What was the initial angular frequency?

51. A satellite is moving at 2000 ms -1  in a circular orbit around a distant moon.   If the radius of the circle followed by the satellite is 1000 km, find: i ) the acceleration of the satellite ii) the time for the satellite to complete one full orbit of the moon in minutes

52. A particle starts to move in a circular direction with an angular speed of 5 rad s -1  . The radius of the circle of motion is 4 m, and the angular speed at time t is given by,