User:Rzmohsin

Mechanics Force Force may be defined as an agent which produces or tends to produce, destroy or tends to destroy the motion of a body. A force while action on a body may a. Change the motion of a body, b. Retard the motion of a body, c. Balance the forces already acting on a body, and d. Give rise to the internal stress in a body. In order to determine the effects of a force acting on a body, following characteristics of a force must be known. i. The magnitude of the force, ii. The line of action of the force, iii. The nature of the force, i.e. push or pull, and iv. The point at which the force is acting. Common symbols SI unit: Newton (N), MKS system of units Kilogram force (kgf) 1 kgf= 9.81 N Other units dyne, pound-force, poundal, kip In SI base units kg·m/s-2 F = m a Dimension M L T−2, Resolution of Force Any force can be resolved into the addition of two mutually perpendicular forces which are called components of force. The components of force are resolved along the x-axis and the y-axis of a given coordinate system. From Fig., we see that x-component: y-component:

In fact, the resultant force of a system can be found by resolving all the forces into their x and y-components, and then adding up the components in each direction. The following animation illustrates the tip-to-tail method of adding vectors, as well as the method of resolving components. Equilibrium A very basic concept when dealing with forces is the idea of equilibrium or balance. In general, an object can be acted on by several forces at the same time. A force is a vector quantity which means that it has both a magnitude (size) and a direction associated with it. If the size and direction of the forces acting on an object are exactly balanced, then there is no net force acting on the object and the object is said to be in equilibrium. Because there is no net force acting on an object in equilibrium, then from Newton's first law of motion, an object at rest will stay at rest, and an object in motion will stay in motion. Let us start with the simplest example of two forces acting on an object. Then we will show examples of three forces acting on a glider, and four forces acting on a powered aircraft. In Example 1 on the slide, we show a blue ball that is being pushed by two forces, labeled Force #1 F1 and Force #2 F2. Remember that forces are vector quantities and direction is important. Two forces with the same magnitude but different directions are not equal forces. In fact, F1 = - F2 for the coordinate system shown with the letter X below the ball. If we sum up the forces acting on the ball, we obtain the force equation on the left: F1 + F2 = F net = 0

where F net is the net force acting on the ball. Because the net force is equal to zero, the forces in Example 1 are acting in equilibrium. There is no net force acting on the ball in Example 1. Since the ball is initially at rest (velocity equals zero), the ball will remain at rest according to Newton's first law of motion. If the ball was travelling with a uniform velocity, it would continue travelling at the same velocity. In Example 2, we have increased the magnitude of Force #1 so that it is much greater than Force #2. The forces are no longer in equilibrium. The force equation remains the same, but the net force is not equal to zero. The magnitude of the net force is given by: F1 > - F2 F1 + F2 = F net |F net| = |F1| - |F2| where the "| |" symbols indicate the magnitude of the quantity included between the ends. The direction of the net force would be in the positive X direction because F1 is greater than F2. According to Newton's second law of motion, the ball would begin to accelerate to the right. Because there is a net force in Example 2, the forces are not in equilibrium.

Heat Heat: It is the energy in transition between the system and the surroundings by virtue of the difference in temperature. Heat is the energy that travels between two bodies at different temperature. In thermodynamics, heat is called a low grade energy and work is known as a high grade energy, the reason being the fact that work can completely be converted to heat but heat can never be entirely converted to work. Heat: When energy is exchanged between thermodynamic systems by thermal interaction, the transfer of energy is called heat. Heat transfer is the energy transfer due to temperature difference only. All other energy transfers can be termed as work transfer. Heat is energy in transit. The transfer of energy as heat occurs at the molecular level as a result of a temperature difference. The usual symbol for heat is Q. When energy is exchanged between thermodynamic systems by thermal interaction, the transfer of energy is called heat. The units of heat are therefore the units of energy, or joules (J) and calorie in the SI system. Heat is transferred by conduction, convection, and/or radiation. Work: Positive work is done by a system when the sole effect external to the system could be reduced to the rise of a weight. Work is the transfer of energy by any process other than heat. Work is the energy that causes displacement. Work = Force × displacement The work is the utilization of one’s energy into mechanical energy to produce an action. Work is the transfer of energy by any process other than heat. Like heat, the unit measurement for work is joules (J). There are many forms of work, including but not limited to mechanical, electrical, and gravitational work. Work is defined as the change in the volume (V) in liters within the system multiplied by a pressure (P). Assuming the system is at constant pressure, this equates to the following: W=PΔV Center of Gravity

The point through which the whole mass of the body acts, irrespective of the position of the body, is known as center of gravity (c.g.) The plane geometrical figures like rectangle, triangle, circle, etc. have only area but no mass, the center of area of such figures is known as centroid’s or center of gravity of the area of the body. It may be noted that everybody has one and only one center of gravity, the center of gravity of simple figure:

1. The center of gravity of a uniform rod is at its middle point. 2. The center of gravity (G) of a rectangle (or parallelogram) lies at a point where its diagonals intersect. Fig 1.5 3. The center of gravity (G) of a triangle lies at a point where the three medians of the triangle intersect, Fig 1.6 Note: A median is a line joining the vertex and the middle point of the opposite side. 4. The center of gravity of a semi-circle lies at a distance of 4r/3π from its base measured along the vertical radius, Fig 1.7 5. The center of gravity of a hemisphere lies at a distance of 3r/8 from its base measured along the vertical radius, Fig 1.8 6. The center of gravity of a trapezium with parallel sides a and b, lies at a distance of h 2a + 3 measured from side b, Fig 1.9 3 a + b 7. The center of gravity of a right circular solid cone lies at a distance of h/4 from its base, measured along the vertical axis, Fig 1.10.

System of Forces When two or more than two forces act on a body, they are said to form a system of forces. Following are the various system of forces: 1. Coplanar forces: The forces, whose lines of action he on the same plane are known as coplanar forces. 2. Concurrent forces: The forces, which meet at one point are known as concurrent forces. 3. Coplanar concurrent forces, the forces, which meet at one point and their lines of action also lie on the same plane, are called coplanar concurrent forces. 4. Coplanar non-concurrent forces. The forces, which do not meet at one point but the lines of action lie on the same plane, are Known as coplanar non-concurrent forces. 5. Non-coplanar concurrent forces. The forces, which meet at one point but their lines of action do not lie on the same plane are known as non-coplanar concurrent forces. 6. Non-coplanar nan-concurrent forces. The forces, which do not meet at one point and their lines of actions do not lie on the same plane are called non-coplanar non-concurrent forces. Resultant Force It is a single force which produces the same effect as produced by all the given forces acting on a body, The resultant lorce may be determined by the following three laws of forces :

l. Parallelogram law offarces. It states that iftwo forces, acting simultaneously on a particle, be represented in magnitude and direction by the two adjacent Sides 0of a parallelogram, then their resultant may be represented in magnitude and direction by the diagonal of a parallelogram which passes through their points of intersection. For example, let us consider two forces P and Q acting at angle 0 at point 0 as shown in Fig. The resultant is given by,

R = P2 + Q2+ 2PQcosc

If the resultant (R) makes an angle α with the force P. then Q R

  Qsinθ							θ          α

tan α := P + Qcoseθ O P 2 Triangle law of forces. It states that if two forces, acting simultaneously on a particle, be represented in magnitude and direction by the two sides of a triangle taken in order, then their resultant may be represented in magnitude and direction by the third side of the triangle taken in opposite order. 3. Palygon law of forces. It states that if a number of forces, acting simultaneously on a particle be represented in magnitude and direction by the two sides of a triangle taken in order, then their resultant may be represented in magnitude and direction by the closing slide of the polygon taken in opposite order. Note 1 : if the resultunt of two or more intersecting forces may be found out by resolving all horzentally and vertically , in such cases resultant of forces is given by. R = (ΣH) 2 + (ΣV) 2 Where; ΣH = Sum of resolved pans in the horizontal direction, and ΣV = Sum of resolved parts in the vertical direction, If the resultant (R) makes an angle α with the horizontal, then tan α := ΣV / ΣH Note 2. If the resultant of a number of forces, acting on a particle, is zero then the particle will be in equilibrium Such a set of forces whose resultant is zero are known as equilibrium forces. The force which bring all forces in equilibrium is call equilibriant. It is equal to magniture of resultant force but opposite in direction. Note 3. If number of forces acting on a particle will be in equilibrium when ΣV = 0, ΣH = 0 Moment of a Force It is the turning effect produced by a force, on the body, on which it acts. The moment of a force is equal to the product of the force and the perpendicular distance of the point, about which the moment is required and the line of action of the force. Mathematically. the moment of a force F about point 0 as shown in Fig l .3, P

F =P x l O The unit of moment depends upon the units of force and l perpendicular distance If the force is in newtons and the perpendicular distance in metres, then the unit of moment will be newton-metre (briefly written as N~m). Parallel Forces The forces, whose lines of action are parallel to each other, are said to be parallel forces: If the parallel forces act in the same direction then these are known as like parallel forces. When the parallel forces act in opposite directions. then these are known as unlike parallel forces. Couple The two equal and opposite forces. whose lines of action are different, form a couple, as shown in Fig. The perpendicular distance (x) between the lines of action of P two equal and opposite forces is known as arm of the couple The magnitude of the couple ( i. e. moment of a couple) is the product of one of the forces and the arm of the couple. Mathematically, x P

Moment of acouple = P x x A little consideration will show, that a couple does not produce any translatory motion (i.e.motion in a straight line), but a couple produces a motion of rotation of the body on which it acts. Types of Friction Different types of motion of the object gives rise to different types of friction. Generally, there are 4 types of friction they are Static friction, sliding friction, Rolling friction, Fluid friction. Following are type of friction. Static Friction Static friction exists between a stationary object and the surface on which it is resting. It prevents an object from moving against the surface. Examples: static friction prevents an object like book falling from the desk even if the desk is slightly tilted, it helps us to pick up an object without slipping through our fingers. When we want to move an object first we must overcome the static friction acting between the object and the surface on which the object is resting.

Sliding Friction Sliding friction occurs between objects as the slide against each other. It acts in the direction opposite to the direction of motion. It prevents the object from moving too fast. It is also called as kinetic friction. Examples: A book sliding from an inclined desk, A kid sliding on a slide. When sliding friction is acting there must be another force existing to keep the body in moving, in case of the book sliding from the desk the other force acting is gravitational force.

Rolling Friction Rolling friction is the resistive force that slows down the motion of a rolling ball or wheel. It is also called rolling resistance. When a force or torque is applied to a stationary wheel, there is a small static rolling friction force holding back the rolling motion. However, resistance from static sliding friction is what really causes the wheel to start rolling. Rolling friction hinders the motion of an object rolling on a surface, that means it slows down the motion of an object rolling on a surface. Examples: It slows down a ball rolling on a surface and it slows down the motion of tire rolling on the surface. Like sliding friction here also another force is required to keep the object in motion, in case of pedaling bicycle the bicyclist provides the force which is required for the bicycle to be in motion. Fluid Friction (Air Friction) Here on Earth, we tend to take air resistance (aka. “drag”) for granted. We just assume that when we throw a ball, launch an aircraft, deorbit a spacecraft, or fire a bullet from a gun, that the act of it traveling through our atmosphere will naturally slow it down. But what is the reason for this? Just how is air able to slow an object down, whether it is in free-fall or in flight? air friction is experienced by the objects moving through the open air. air friction acts between the object and the air through which it is moving. It is also called drag. This force depends upon the object's shape, material, speed with which it is moving and the viscosity of the fluid. Viscosity is the measure of the resistance of the air to flow and it differs from one density another. Examples: It slowdowns the motion of airplane flying in the air, here the engine of the airplane helps the plane to overcome the fluid friction and move forward.

NOTE: sliding friction, rolling friction, and air friction are types of dynamic friction.