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Introduction to Basic Mechanics

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Introduction to Basic Mechanics Introduction to Basic Mechanics Learning Outcome When you complete this module you will be able to: Define basic terms used in the study of mechanics. Learning Objectives Here is what you will be able to do when you complete each objective: 1. Define mass, force, velocity, acceleration and weight. 2. Define pressure. 3. Define energy, work, and power. 1 AMEC 6006 INTRODUCTION Mechanics is a branch of physics that deals with forces and the effect of forces on bodies at rest and bodies in motion. The science of mechanics is therefore entailed when studying the forces acting upon a girder supporting a boiler, the leverage exerted in tightening a bolt with a wrench, the work done in pumping water to a supply tank or the work done in raising an elevator in its shaft. Each of these processes involves the action or movement of forces. There are two branches of mechanics, namely statics and dynamics. Statics deals with forces and their effects on rigid bodies at rest. Dynamics deals with motion and the effects of forces acting upon rigid bodies in motion. Newton’s Laws of Motion Many of the problems in mechanics deal with forces and motion, and it is important for the student to know and understand the laws of motion. These laws were summarized by Newton as follows: 1. Every body will continue in its state of rest, or uniform motion in a straight line, unless it is acted upon by an external force. 2. The rate of change of motion is proportional to the force producing the change and takes place in the direction in which the force acts. 3. To every action, there is an equal and opposite reaction, or, when one object exerts a force on a second object, the second object exerts a reactive force of equal magnitude and opposite direction on the first object. MASS, FORCE, VELOCITY, ACCELERATION, AND GRAVITY Mass, force, velocity, and acceleration are all related and must be clearly defined and understood. Mass Mass is the quantity of matter a body contains. The unit of mass in the SI system has been chosen as the kilogram (kg). Force Force may be defined as any action on a body which tends to change its size or shape, its state of rest, or its state of motion. In the SI system, the unit of force is called the newton (N). 2 AMEC 6006 Acceleration and Velocity To understand what acceleration is, it is useful to understand what velocity is. Velocity is the rate of change of position: that is, it is the change in position that occurs during a given time. The unit of velocity in the SI system is the metre per second (m/s). Example 1: If a body moves on the x-axis pictured below from the 10 m position to the 30 m position in 4 seconds, then it would have changed position by 20 m in 4 seconds. What was its velocity? Solution: X X 0 10 m 30 m origin Velocity = change in position time = 20m 4s = 5m/s (Ans.) Now acceleration can more easily be defined. Acceleration is the rate of change of velocity: that is, it is the change in velocity that occurs during a given time. The unit of acceleration in the SI system is the metre per second squared (m/s2). Example 2: If a body is moving toward the right at a velocity of 10 m/s, and 4 seconds later it is found to be moving to the right at a velocity of 30 m/s, then it would have changed velocity by 20 m/s (30 m/s - 10 m/s) during the 4 seconds. What would its rate of acceleration have been? v = 10 m/s v = 30 m/s time = NOW time = NOW + 4 seconds 3 AMEC 6006 Solution: Acceleration = change in velocity time = 20 m/s 4s = 20 m/s 4 s = 5 m x 1 s s = 5 m/s2 (Ans.) Note: A velocity of 5 m/s means that a body’s position will change by 5 m during the elapse of 1 second (that is, a rate of change of position of 5m/s). An acceleration of 5 m/s/s = 5 m/s2 means that a body’s velocity will change by 5 m/s during the elapse of 1 second (that is, a rate of change of velocity of 5 m/s per second, or 5 m/s2). 2 m/s 5 m/s is just a shorthand way of writing 5 s Relationship Between Mass, Force, and Acceleration For all cases: Force = mass x acceleration If the unit of mass in the SI system is the kg and the units of acceleration are m/s2, then Force = mass (kg) x acceleration (m/s2) = kg m/s2 In the SI system, this unit of force, kg m/s2, is called a newton (N). That is, 1 N = 1 kg x 1 m/s2 4 AMEC 6006 This means: (1) If a force of 1 N is applied to a mass of 1 kg, then that mass will accelerate at 1 m/s2. or (2) If a mass of 1 kg is observed to be accelerating at 1 m/s2, then there must be a force of 1 N acting upon the mass. or (3) If an unknown mass is found to be accelerating at 1 m/s2 under the influence of a 1 N force, then that mass must be 1 kg. Example 3: A mass of 1000 kg is to be accelerated at 15 m/s2. What force is required? Solution: Force = mass (kg) x acceleration (m/s2) = 1000 kg x 15 m/s2 = 15000 kg m/s2 = 15000 N = 15 kN (Ans.) Since the newton is a relatively small unit, the kilonewton (kN) is often used. 1 kN = 1000 N 5 AMEC 6006 Acceleration Due to Gravity If a body is within the earth’s field of gravity, there is an attraction to the earth’s centre due to this “pull” of gravity. Bodies which are allowed to fall, will fall towards the earth at an increasing velocity due to the force of gravity. The velocity will be found to increase by approximately 9.81 m/s during the elapse of each second of time. This is referred to as the acceleration due to gravity. Acceleration due to gravity = change in velocity time = 9.81 m/s 1 s = 9.81 m/s2 This acceleration, together with its value, should be remembered, as it is of great importance when dealing with mechanics problems. Force of Gravity Since the acceleration due to the earth’s gravity may be taken as 9.81 m/s2, then the force of the earth’s gravity acting on a mass of 1 kg will be: Force (N) = mass (kg) x acceleration (m/s2) = 1 kg x 9.81 m/s2 = 9.81 kg m/s2 = 9.81 N The direction of this force will be downward (i.e., toward the earth). Thus, a mass of 1 kg on the earth’s surface will be subjected to a downward force (the force due to gravity) of 9.81 N. 6 AMEC 6006 Example 4: A body has a mass of 200 kg. What will be the magnitude of the force due to the earth’s gravity acting upon this mass? Solution: Force (N) = mass (kg) x acceleration (m/s2) Acceleration due to gravity = 9.81 m/s2 Force = 200 kg x 9.81 m/s2 = 1962 kg m s2 = 1962 N (Ans.) Weight: A Controversial Term The mass of a body is unchanging, and does not vary according to its location. The force of gravity on a body varies from location to location, depending on the value of the acceleration due to gravity. The value, 9.81 m/s2, is only an average value for the acceleration due to the earth’s gravity on the surface of the earth. It is much less at a height of 50 km above the earth’s surface. It is for this reason that the SI system expresses the quantity of material (e.g., meat or concrete) in terms of the kilogram (an unchanging mass unit) rather than the newton (counterpart to the pound in the Imperial system). The newton is a unit of measurement of the imprecise concept “weight” (which is an inexact word often used to denote the force of gravity on the material). In fact, the term “weight” has sometimes been used to mean “mass” and sometimes to mean “force of gravity”. In engineering courses, a clear distinction must be made between “mass” and “force of gravity”. Therefore, the Canadian Standards Association recommends that the term “weight” be avoided. However, in everyday life, we have gone from the Imperial system of “weighing” things in terms of the force of gravity on them (in pounds), to the SI system of “weighing” things in terms of their mass (in kilograms). It can be shown that a mass of 1 kilogram at a place on the earth where the acceleration of gravity is 9.81 m/s2, will have a gravitational force exerted on it that is approximately 2.2 pounds. It is for this reason that we use the conversion for convenience in everyday life that 1 kg = 2.2 lbs. However, the left side of the equation is a mass and the right side is a force, which are two very different physical concepts! 7 AMEC 6006 PRESSURE AND FORCE Force has previously been defined as the action on a body which tends to change its size or shape, its state of rest, or its state of motion.
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