Module No. 17
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This document summarizes key concepts related to force, friction, and elasticity. It defines force as anything that can cause an object to change its movement. Friction is defined as the force that opposes the relative motion of two surfaces in contact. Elasticity is the property of solids to regain their original shape after a deforming force is removed. Key points include Newton's laws of motion, units of force, types of forces in nature, coefficients of static and kinetic friction, Hooke's law of elasticity, and applications of these concepts.
Module No. 17
- 1. 1 Module # 17 Force, Friction & Elasticity Force Force is that agency which moves or tends to move or stops or tends to stop the motion of a body. Alternatively, force is an agent which produces or tries to produce motion in the body, stops or tries to stop a moving body. Thus, force is that which changes a body's state of rest or of uniform motion in a straight line. Measurement of Force Force can be measured according to the second law of motion which gives the relationship as follows: F = ma Units of Force In MKS system or in SI system, the unit of force is newton and is denoted by N. A newton is the force required to give a mass of one kilogram an acceleration of one meter per second2 . 1 kg force = 9.81 Newtons &
- 2. 2 1 lb force = 4.45 Newtons Net Force Rate of change of momentum is called net force. Forces in Nature From our everyday observations, we realize that different kinds of forces come into play in different circumstances i.e. we come across various kinds of forces in nature. They are: (1) Gravitational force (2) Electrostatic force (3) Magnetic force (4) Electromagnetic force (5) Strong nuclear force (6) Weak nuclear force. The gravitational force is the weakest force in nature. The nuclear forces which hold the protons and neutrons in the nucleus are strongest in nature. These forces are attractive forces and are strong enough to overcome the electrostatic repulsive forces in the nucleus. During radioactive decay, the nucleus emits a - particle and a neutrino. The -particle and neutrino interact though a weak force.
- 3. 3 Unification of the Forces The unification of the various kinds of forces in nature has been a major theme in the history of physics. Some years earlier, magnetism and weak forces were listed separately and physicists counted four fundamental forces i.e. it was thought that the nature is controlled by only four forces. These four basic forces along with their relative strength are given in the table below. Table: The Four Forces in Nature Type Relative Strength Range Strong Nuclear Force 1 1.4 x 10-15 m limited to the nucleus Electromagnetic Force 10-2 Long range, can be screened by a conductor. Weak Nuclear Force 10-13 Almost zero Gravitational Force 10-40 Long range, cannot be screened by any known means.
- 4. 4 Three scientists, Dr. Abdus Salam, Sheldon Glashow and Steven Weinberg developed a unified theory of the electromagnetic and weak interactions, and in a sense, this presentation reduced the number of classes of forces from four to three. So, now, there are three basic forces in nature, namely, gravitational force, weak electromagnetic force and strong nuclear force. For their theory, linking the weak and electromagnetic forces, they received the 1979 Nobel Prize for Physics. That theory was confirmed experimentally in 1983 by a group working under the Italian physicist Carlo Rubbia, a Harvard professor working at CERN, the European Centre for Nuclear Research. The 1984 Nobel Prize for Physics went very quickly to Rubbia and his Dutch colleague Simon Van der Meer. There was a long held hope of Einstein to find a unified basis for these different forces, but, he was never able to realize this hope. Attempts similar to the unified theory have been made to understand all strong, electromagnetic and weak interaction on the basis of a single unified theory called a grand unified theory (GUT). Such theories are still speculative, and there are many unanswered questions. The entire area is a very active field of current research.
- 5. 5 Friction According to Newton's first law of motion, a body in motion will continue to move with constant velocity unless acted upon by an external net force. A body moving through a viscous medium such as air or water eventually comes to rest. Similarly, a body in motion on a solid surface eventually comes to rest. There are always forces which resist the motion of a body. These forces arise as a result of the interaction of the moving body with its environment. Such a force, which resists the motion of a body, is called a resistive force or a force of friction. Force of friction plays a very important role in our everyday life, for example, forces of friction allow us to walk or run and are necessary for the motion of wheeled vehicles. Thus, friction is the force which opposes the relative sliding motion of two surfaces in contact with one another. When a body is made to slide over the surface of another body, its motion is opposed by some force due to the roughness of the two surfaces. If we see the surfaces through microscope we observe that they are not smooth. When one surface is placed over another the elevations of one get interlocked with the depressions of the other. Thus they will oppose relative motion. Thus, the force which opposes the sliding motion of one surface
- 6. 6 over another is called force of friction or simply friction. Friction Good or Bad Whether friction proves to be useful or otherwise depends upon the circumstances under which it comes into action. Friction between rubber and concrete is certainly desirable, because it will be impossible to walk if the friction between the soles of the shoes and the ground were absent. Every mean of surface transportation is based upon friction between the wheels and the road. On the other hand, machines, clothes, shoes etc. wear out due to friction. Fluid Friction A body experiences a resistive force when it moves through a fluid, which can be either air/gas or liquid. Just as in the case of a body moving over a solid surface experiences a frictional force opposing its motion, similarly the fluid also exerts a frictional force on the body. The size, shape, orientation and velocity of an object determine the fluid friction on it. Swimmers and sky divers change their effective size and orientation of their bodies by bending, twisting or stretching their arms and legs in and out. This allows them to manipulate the fluid forces and consequently to control their speed and direction of motion.
- 7. 7 Hover Crafts and Friction Hover Crafts are those machines which are used for transportation over water, marshes and land. They make use of the comparatively low frictional forces offered by air at moderate speeds. Hover crafts have the ability to hover just above land or water. Hover crafts move very fast on a cushion of air that is formed between the bottom of the vehicle and the surface on which it hovers, irrespective of whether it is land or water. The air is continuously forced downward by the engines of the hover craft. These vehicles are now in regular use as ferries for short distance travel across channels and islands. They can attain speed over 150 km hr-1 as compared to the speed of the surface boats of around 60 km hr-1 . Rolling Friction When an object rolls over a surface, the force of friction is called the rolling friction. If a heavy spherical ball is allowed to roll, the ball appears partly sunk in the surface due to its weight or softness of the surface. Thus when it rolls it appears to move up an incline and so it experiences an opposing force called rolling friction. The rolling friction is much less than the sliding friction. For example, the rolling friction between steel is 1/100 of the sliding
- 8. 8 friction between them. Besides, in rolling the contact surface is much less than that in sliding friction. Limiting Friction When a certain force is applied to slide or move some body over another, then before the motion starts the force of friction increases as the applied force is increased. The maximum force of friction which just stops the body from moving is called limiting friction. This limiting friction is directly proportional to the normal reaction or the weight of the body. Let Fs is the magnitude of limiting friction and R is the normal reaction of the body having weight (W = mg), then mathematically we can write Fs R or Fs = R or Fs = mg (R = W = mg) Where is a constant of proportionality and depends on the nature of the surfaces of the bodies.
- 9. 9 Methods of Reducing Friction 1. The various parts of the machines which are moving over one another are properly lubricated. A lot of research is being done all over the world to develop newer and newer lubricants to minimize friction in machines. Lubricants provide a film of fluid between the two moving surfaces and, therefore, tend to reduce the friction. 2. In machines the sliding of various parts is usually replaced by rolling and this is done by using ball bearing. Friction can be reduced by using ball bearings because they convert sliding friction into rolling friction. 3. Where sliding is unavoidable a thick layer of greasing material is used between the sliding surfaces. 4. The front of the fast moving objects e.g. car and aeroplane is made oblong to minimize air friction. Advantages of Friction Friction is necessary for our everyday activities 1 In the absence of friction, motion would not be possible i.e. it is not possible for a man to walk on earth without friction. When we walk we push the ground backward, the ground reacts and
- 10. 10 pushes us forward due to friction (in accordance with Newton’s 3rd Law of Motion). 2 Without friction it is impossible to stop a moving body (in accordance with Newton’s 1st Law of Motion). 3. In the absence of friction a horse will not be able to pull a cart / wagon (in accordance with Newton’s 3rd Law of Motion). 4 A nail stays in the wood because of friction similarly we can tie a knot because of this force. Disadvantages of Friction 1 Friction produces heat in various parts of the machines thus some useful energy is wasted as heat energy. 2 Vehicles like cars, buses and trains lose part of their useful energy in overcoming friction. Coefficient of Friction The ratios of the static and kinetic friction to the force pressing the surfaces together are called the coefficients of static and kinetic friction respectively. F = ------- R
- 11. 11 Where, is the coefficient of friction, F is the force of friction and R is the force pressing surfaces together. Co-efficient of Friction Never to Exceed One Value of co-efficient of friction cannot be greater than one because the force of friction increases with the increase of normal reaction (i.e. the force acting vertically upward). Therefore, we write Fs R OR Fs = R Where is the co-efficient of friction. If the value of is greater than one, then there will be an increase in the value of product R beyond Fs and the body will not move. In other words, we can say that when a force acts on a body, a part of acting force is used in balancing the friction force and the remaining portion causes motion in the body. Thus if value of becomes greater than one then the value of R will become so high that a body cannot move.
- 12. 12 The ratio of limiting friction to normal reaction is known as the co- efficient of friction. It is denoted by ‘’. Limiting friction Fs is directly proportional to the Normal Reaction i.e. Fs R OR Fs = R OR = Fs / R Thus is a constant of proportionality. The co-efficient of friction depends upon two factors. 1. Nature of surfaces. 2. Cleanliness and dryness of the surfaces. Elasticity Elasticity is the property of solid materials due to which they regain their original shape when an applied force is removed. Thus, the property of the matter by virtue of which it resists any force which tends to produce deformation in it is called elasticity. If we apply a force to pull a body like a rubber band (strip) or a spring, it is stretched. On removing the force, the rubber band or
- 13. 13 the spring regains its original length, that is, it returns to its original shape. The phenomenon of returning a solid body to its original shape and size after applied force is removed is known as elasticity. A wooden meter rod can be slightly bent into an arc and when the force applied is removed, it becomes straight again. The meter rod will break if it is bent too far. Thus, there is a limit to the applied force from which the rod will recover when the force is removed. This limit of the applied force is called the elastic limit. Its value is different for different materials. Once a body (material) crosses this limit, it will not regain its original shape even after the removal of the applied force. According to Kinetic or molecular theory of matter, the molecules in a solid are very close to each other and, therefore, there exist strong forces of attraction between them. When the applied force is removed, the attractive force between them pulls the molecules back again and the material is restored to its original shape. Materials have different elasticities depending upon the nature of the material.
- 14. 14 Elastic Potential Energy When work is done in compressing and stretching a spring against the elastic force, then, potential energy is stored in it. Such a potential energy is called elastic potential energy. It is to be noted here that potential energy is not always due to work against the force of gravity (which is called gravitational potential energy), e.g. if we wind our watch, then, its spring is tightened. During this process, some work is done. This energy is stored in the spring as its potential energy, which is then used to run the watch. Constant of Elasticity The ratio of stress and strain is equal to the constant value. This constant quantity is called constant of elasticity. Hook’s Law Robert Hook discovered that the strain produced is directly proportional to the stress exerted within elastic limits. This is known as Hook's law. Thus, stress strain
- 15. 15 In other words, the deformation of a material is proportional to the force applied to it, provided the elastic limit is not exceeded. Hence, if the deformation of a material is proportional to the force applied, then, the material is said to obey Hook's Law. Application of Hook's Law When a spring is fixed at one end and a force is applied to the other end, then, the extension of the spring is proportional to the applied force, provided the force is not large enough to stretch the spring permanently i.e. when an elastic spring is stretched by a force, then, the extension produced in the spring is proportional to the exerted force. This is known as Hook's law.