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The stroke of a steam engine is 600 mm and the length of connecting rod is 1.5 m. The crank rotates at 180 r.p.m. Determine: (a) Velocity and acceleration of the piston when the crank has travelled through an angle of 40o from the inner dead centre. (b) The position of the crank for zero acceleration of the piston?
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The stroke of a steam engine is 600 mm and the length of connecting ro...
Velocity and acceleration of the piston at 40o from inner dead centre:
- Given data: Stroke = 600 mm = 0.6 m, Connecting rod length = 1.5 m, Crank rotation = 180 rpm
- First, calculate the distance travelled by the piston using the formula: Distance travelled by piston = Stroke + (Connecting rod length * cosθ)
- Substituting the values, we get: Distance = 0.6 + (1.5 * cos40) = 1.43 m
- Next, calculate the velocity using the formula: Velocity = Distance * angular velocity
- Angular velocity = (180 rpm * 2π) / 60 = 6π rad/s
- Substituting the values, we get: Velocity = 1.43 * 6π = 26.95 m/s
- Finally, calculate the acceleration using the formula: Acceleration = (Velocity^2) / (Connecting rod length)
- Substituting the values, we get: Acceleration = (26.95^2) / 1.5 = 485.1 m/s^2

Position of the crank for zero acceleration of the piston:
- For zero acceleration of the piston, the connecting rod and the piston must be perpendicular to each other.
- This occurs when the crank is at 90o from the inner dead centre.
- Therefore, the position of the crank for zero acceleration of the piston is at 90o from the inner dead centre.
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Passage 2Newtons surprising success at developing the laws of motion, as well as the development and refinement of other physical laws, led to the idea of scientific determinism. The first expression of this principle was in the beginning of the nineteenth century by Laplace, a French scientist. Laplace argued that if one knew the position and velocity of all the particles in the universe at a given time, the laws of physics would be able to predict the future state ofthe universe.Scientific determinism held sway over a great many scientists until the early twentieth century, when the quantum mechanics revolution occurred. Quantum mechanics introduced the world to the idea of the uncertainty principle, which stated that it was impossible to accurately measure both the position and the velocity of a particle at one time. Because Laplaces omniscience could never occur, even in theory, the principle of scientific determinism was thrown into doubt. However, quantum mechanics does allow for a reduced form of scientific determinism. Even though physicists are unable to know precisely where a particle is and what its velocity is, they can determine certain probabilities about its position and velocity. These probabilities are called wave functions. By use of a formula known as the Schrodinger equation, a scientist with the wave function of a particle at a given time can calculate the particles future wave function. These calculations can give the particles position or velocity, but not both. Thus, the physicist is in possession of exactly half ofthe information needed to satisfy Laplaces view ofdeterminism. Unfortunately, under modern physics theories, that is far as any researcher can go in predicting the future.Q. According to the passage, wave functions

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The stroke of a steam engine is 600 mm and the length of connecting rod is 1.5 m. The crank rotates at 180 r.p.m. Determine: (a) Velocity and acceleration of the piston when the crank has travelled through an angle of 40o from the inner dead centre. (b) The position of the crank for zero acceleration of the piston?
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The stroke of a steam engine is 600 mm and the length of connecting rod is 1.5 m. The crank rotates at 180 r.p.m. Determine: (a) Velocity and acceleration of the piston when the crank has travelled through an angle of 40o from the inner dead centre. (b) The position of the crank for zero acceleration of the piston? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The stroke of a steam engine is 600 mm and the length of connecting rod is 1.5 m. The crank rotates at 180 r.p.m. Determine: (a) Velocity and acceleration of the piston when the crank has travelled through an angle of 40o from the inner dead centre. (b) The position of the crank for zero acceleration of the piston? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The stroke of a steam engine is 600 mm and the length of connecting rod is 1.5 m. The crank rotates at 180 r.p.m. Determine: (a) Velocity and acceleration of the piston when the crank has travelled through an angle of 40o from the inner dead centre. (b) The position of the crank for zero acceleration of the piston?.
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