Search Search. What's new. Log in. Install the app. JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding. You are using an out of date browser. It may not display this or other websites correctly. These notes are arranged in specific modules which is very helpful for students to save time in preparation for exams.
All these modules contain the most important formulas, equations, laws and calculations related to that module. Module 1 - Syllabus Analysis of thermodynamic cycles: Carnot, Otto, Diesel cycles, Derivation of efficiency of these cycles, Problems to calculate heat added, heat rejected, network and efficiency.
Feel free to comment and share this if you found it useful. Post a Comment 0 Comments. Post a Comment. Below Post Ad. This can be demonstrated graphically. The gradient of a line on the displacement time graph represents the velocity. The gradient of the velocity time graph gives the acceleration while the area under the velocity time graph gives the displacement. The area under an acceleration time graph gives the velocity.
It can be uniform, that is, with constant angular rate of rotation, or non-uniform, that is, with a changing rate of rotation.
Examples of circular motion are: an artificial satellite orbiting the Earth in geosynchronous orbit, a stone which is tied to a rope and is being swung in circles cf. Such change in direction of velocity involves acceleration of the moving object by a centripetal force, which pulls the moving object towards the center of the circular orbit. This law states that if the resultant force the vector sum of all forces acting on an object is zero, then the velocity of the object is constant.
Newton placed the first law of motion to establish frames of reference for which the other laws are applicable. The first law of motion postulates the existence of at least one frame of reference called a Newtonian or inertial reference frame, relative to which the motion of a particle not subject to forces is a straight line at a constant speed.
Thus, the net force applied to a body produces a proportional acceleration. If the direction of the force and the displacement do not coincide e. In situations where the force changes over time, or the path deviates from a straight line, equation 17 is not generally applicable although it is possible to divide the motion into small steps, such that the force and motion are well approximated as being constant for each step, and then to express the overall work as the sum over these steps.
Note that the result of the above integral de- pends on the path and only from the endpoints. This is typical for systems in which losses e. This quantity can be assigned to any particle, object, or system of objects as a consequence of its physical state. Energy is a scalar physical quantity. In the International System of Units SI , energy is measured in joules, but in some fields other units such as kilowatt-hours and kilocalories are also used.
Different forms of energy in- clude kinetic, potential, thermal, gravitational, sound, elastic and electro- magnetic energy. Any form of energy can be transformed into another form. When energy is in a form other than thermal energy, it may be transformed with good or even perfect efficiency, to any other type of energy, however, during this con- version a portion of energy is usually lost because of losses such as friction, imperfect heat isolation, etc.
Although the total energy of an isolated system does not change with time1 , its value may depend on the frame of reference. For example, a seated passenger in a moving airplane has zero kinetic energy relative to the air- plane, but non-zero kinetic energy and higher total energy relative to the Earth.
A closed system interacts with its surrounding with mechanical work W and heat transfer Q. There is no known exception to this lawit is exact so far as we know.
The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens.
It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same. The SI unit of power is the watt W , which is equal to one joule per second. The car has a 55kW motor 75hp and it can be assumed that during the journey this was the useful power. Problem 1. Worked problem 1. The two regimes of dry friction are static friction between non-moving surfaces, and kinetic friction sometimes called sliding friction or dynamic friction between moving surfaces.
Thus, in the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion. In this case, rather than providing an estimate of the actual frictional force, the Coulomb approximation provides a threshold value for this force, above which motion would commence. This maximum force is known as traction. The force of friction is always exerted in a direction that opposes move- ment for kinetic friction or potential movement for static friction between the two surfaces.
For example, a curling stone sliding along the ice experi- ences a kinetic force slowing it down. For an example of potential movement, the drive wheels of an accelerating car experience a frictional force pointing forward; if they did not, the wheels would spin, and the rubber would slide backwards along the pavement. Note that it is not the direction of move- ment of the vehicle they oppose, it is the direction of potential sliding between tire and road. In this case, the friction force exactly can- cels the applied force, so the net force given by the vector sum, equals zero.
It is caused mainly by the deformation of the object, the deformation of the surface, or both. Additional contributing factors include wheel radius, forward speed, sur- face adhesion, and relative micro-sliding between the surfaces of contact. It depends very much on the material of the wheel or tire and the sort of ground.
For example, rubber will give a bigger rolling resistance than steel. Also, sand on the ground will give more rolling resistance than concrete. A moving wheeled vehicle will gradually slow down due to rolling resistance including that of the bearings, but a train car with steel wheels running on steel rails will roll farther than a bus of the same mass with rubber tires running on tarmac.
The coefficient of rolling resistance is generally much smaller for tires or balls than the coefficient of sliding friction.
Crr b Description 0. In other words, the normal force is equal to the weight of the object being supported, if the wheel is on a horizontal surface. We can decompose the gravitational force into two vectors, one perpendic- ular to the plane and one parallel to the plane. Dashed line: the lift-up force given by A rope, cable, belt, or chain usually runs over the wheel and inside the groove, if present.
Pulleys are used to change the direc- tion of an applied force, transmit rotational motion, or realize a mechanical advantage in either a linear or rotational system of motion. It is one of the six simple machines.
Two or more pulleys together are called a block and tackle. The different types of pulley systems are: Fixed A fixed pulley has a fixed axle. A fixed pulley is used to change the direction of the force on a rope called a belt. Movable A movable pulley has a free axle. A movable pulley is used to multiply forces. Compound A compound pulley is a combination of a fixed and a movable pulley system.
The block and tackle is a type of compound pulley where several pulleys are mounted on each axle, further increasing the mechanical advantage.
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