Home
Class 12
PHYSICS
An imaginary space rocket launched from ...

An imaginary space rocket launched from the Earth moves with an acceleration `w^'=10g` which is the same in every instantaneous co-moving inertial reference frame. The boost stage lasted `tau=1.0` year of terrestrial time. Find how much (in per cent) does the rocket velocity differ from the velocity of light at the end of the boost stage. What distance does the rocket cover by that moment?

Text Solution

Verified by Experts

In the instantaneous rest frame `v=V` and
`w^'=(w)/((1-V^2/c^2)^(3//2))` (from 1.365a)
So, `=(dv)/((1-V^2/c^2)^(3//2)=w^'dt`
`w^'` is constant by assumption. Thus integration gives
`v=(w^'t)/(sqrt(1+((w^'t)/(c))^2)`
Integrating once again `x=c^2/w(sqrt(1+((w^'t)/(c))^2)-1)`
Promotional Banner

Topper's Solved these Questions

  • PHYSICAL FUNDAMENTALS OF MECHANICS

    IE IRODOV, LA SENA & SS KROTOV|Exercise Hydrodynamics|25 Videos

  • OSCILLATIONS AND WAVES

    IE IRODOV, LA SENA & SS KROTOV|Exercise Electromagnetic Waves, Radiation|36 Videos

  • THERMODYNAMICS AND MOLECULAR PHYSICS

    IE IRODOV, LA SENA & SS KROTOV|Exercise Transport Phenomena|38 Videos

Similar Questions

Explore conceptually related problems

The word fluid means a substance having particles which readily of its magnitude (a small shear stress, which may appear to be of negligible will cause deformation in the fluid). Fluids are charactrised by such properties as density. Specific weight, specific gravity, viscosity etc. Density of a substance is defined as mass per unit volume and it is denoted by. The specific gravity represents a numerical ratio of two densities, and water is commonly taken as a reference substance. Specific gravity of a substance in written as the ratio of density of substance to the density of water. Specific weight represents the force exerted by gravity on a unit volume of fluid. It is related to the density as the product of density of a fluid and acceleration due to gravity. Viscosity is the most important and is recognized as the only single property which influences the fluid motion to a great extent. The viscosity is the property by virtue of which a fluid offers resistance to deformation under the influenece if shear force. The force between the layers opposing relative motion between them are known as forces of viscosity. When a boat moves slowly on the river remains at rest. Velocities of different layers are different. Let v be the velocity of the level at a distance y from the bed and V+dv be the velocity at a distance y+dy . The velocity differs by dv in going through a distance by perpendicular to it. The quantity (dv)/(dy) is called velocity gradient. The force of viscosity between two layers of a fluid is proportional to velocity gradient and Area of the layer. F prop A & F prop (dv)/(dy) F= -etaA(dv)/(dy) ( -ve sign shown the force is frictional in nature and opposes relative motion. eta coefficient of dynamic viscosity Shear stress (F)/(A)= -eta(dv)/(dy) and simultaneously kinematic viscosity is defined as the dynamic viscosity divided by the density. If is denoted as v . The viscosity of a fluid depends upon its intermolecular structure. In gases, the molecules are widely spaced resulting in a negligible intermolecular cohesion, while in liquids the molecules being very close to each other, the cohesion is much larger with the increases of temperature, the cohesive force decreases rapidly resulting in the decreases of viscosity. In case of gases, the viscosity is mainly due to transfer of molecular momentum in the transerve direction brought about by the molecular agitation. Molecular agitation increases with rise in temperature. Thus we conclude that viscosity of a fluid may thus be considered to be composed of two parts, first due to intermolecuar cohesion and second due to transfer of molecular momentum. If the velocity profile is given by v=(2)/(3)y-y^(2)v is velocity in m//sec y is in meter above the bad. Determine shear stress at y=0.15m , & eta=0.863 Ns//m^(2)

The word fluid means a substance having particles which readily of its magnitude (a small shear stress, which may appear to be of negligible will cause deformation in the fluid). Fluids are charactrised by such properties as density. Specific weight, specific gravity, viscosity etc. Density of a substance is defined as mass per unit volume and it is denoted by. The specific gravity represents a numerical ratio of two densities, and water is commonly taken as a reference substance. Specific gravity of a substance in written as the ratio of density of substance to the density of water. Specific weight represents the force exerted by gravity on a unit volume of fluid. It is related to the density as the product of density of a fluid and acceleration due to gravity. Viscosity is the most important and is recognized as the only single property which influences the fluid motion to a great extent. The viscosity is the property by virtue of which a fluid offers resistance to deformation under the influenece if shear force. The force between the layers opposing relative motion between them are known as forces of viscosity. When a boat moves slowly on the river remains at rest. Velocities of different layers are different. Let v be the velocity of the level at a distance y from the bed and V+dv be the velocity at a distance y+dy . The velocity differs by dv in going through a distance by perpendicular to it. The quantity (dv)/(dy) is called velocity gradient. The force of viscosity between two layers of a fluid is proportional to velocity gradient and Area of the layer. F prop A & F prop (dv)/(dy) F= -etaA(dv)/(dy) ( -ve sign shown the force is frictional in nature and opposes relative motion. eta coefficient of dynamic viscosity Shear stress (F)/(A)= -eta(dv)/(dy) and simultaneously kinematic viscosity is defined as the dynamic viscosity divided by the density. If is denoted as v . The viscosity of a fluid depends upon its intermolecular structure. In gases, the molecules are widely spaced resulting in a negligible intermolecular cohesion, while in liquids the molecules being very close to each other, the cohesion is much larger with the increases of temperature, the cohesive force decreases rapidly resulting in the decreases of viscosity. In case of gases, the viscosity is mainly due to transfer of molecular momentum in the transerve direction brought about by the molecular agitation. Molecular agitation increases with rise in temperature. Thus we conclude that viscosity of a fluid may thus be considered to be composed of two parts, first due to intermolecuar cohesion and second due to transfer of molecular momentum. Ten litres of a liquid of specific gravity 1.3 is mixed with 6 litres of a liquid of specific gravity 0.8 the specific gravity of mixture is

A train of length l=350m starts moving rectilinearly with constant acceleration w=3.0*10^-2 m//s^2 , t=30s after the start the locomotive headlight is switched on (event 1), and tau=60s after that event the tail signal light is switched on (event 2). Find the distance between these events in the reference frames fixed to be train and to the Earth. How and at what constant velocity V relative to the Earth must a certain reference frame K move for the two events to occur in it at the same point?

An inquistive student, determined to test the law of gravity for himself, walks to the top of a building og 145 floors, with every floor of height 4 m, having a stopwatch in his hand (the first floor is at a height of 4 m from the ground level). From there he jumps off with negligible speed and hence starts rolling freely. A rocketeer arrives at the scene 5 s later and dives off from the top of the building to save the student. The rocketeer leaves the roof with an initial downward speed v_0 . In order to catch the student at a sufficiently great height above ground so that the rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by rocketeer's jet pack, which he turns on just as he catches the student, before the rocketeer is in free fall. To prevent any discomfort to the student, the magnitude of the acceleration of the rocketeer and the student as they move downward together should not exceed 5 g. The correct velocity - time graph for the rocketeer would be

An inquistive student, determined to test the law of gravity for himself, walks to the top of a building og 145 floors, with every floor of height 4 m, having a stopwatch in his hand (the first floor is at a height of 4 m from the ground level). From there he jumps off with negligible speed and hence starts rolling freely. A rocketeer arrives at the scene 5 s later and dives off from the top of the building to save the student. The rocketeer leaves the roof with an initial downward speed v_0 . In order to catch the student at a sufficiently great height above ground so that the rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by rocketeer's jet pack, which he turns on just as he catches the student, before the rocketeer is in free fall. To prevent any discomfort to the student, the magnitude of the acceleration of the rocketeer and the student as they move downward together should not exceed 5 g. The position - time graph for rocketeer would be (take the top of building as origin, and vertical downward direction as positive y-axis.)

An inquistive student, determined to test the law of gravity for himself, walks to the top of a building og 145 floors, with every floor of height 4 m, having a stopwatch in his hand (the first floor is at a height of 4 m from the ground level). From there he jumps off with negligible speed and hence starts rolling freely. A rocketeer arrives at the scene 5 s later and dives off from the top of the building to save the student. The rocketeer leaves the roof with an initial downward speed v_0 . In order to catch the student at a sufficiently great height above ground so that the rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by rocketeer's jet pack, which he turns on just as he catches the student, before the rocketeer is in free fall. To prevent any discomfort to the student, the magnitude of the acceleration of the rocketeer and the student as they move downward together should not exceed 5 g. What should be the initial downward speed of the rocketeer so that he catches the student at the top of 100 the floor for safe landing ?

An inquistive student, determined to test the law of gravity for himself, walks to the top of a building og 145 floors, with every floor of height 4 m, having a stopwatch in his hand (the first floor is at a height of 4 m from the ground level). From there he jumps off with negligible speed and hence starts rolling freely. A rocketeer arrives at the scene 5 s later and dives off from the top of the building to save the student. The rocketeer leaves the roof with an initial downward speed v_0 . In order to catch the student at a sufficiently great height above ground so that the rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by rocketeer's jet pack, which he turns on just as he catches the student, before the rocketeer is in free fall. To prevent any discomfort to the student, the magnitude of the acceleration of the rocketeer and the student as they move downward together should not exceed 5 g. Just as the student starts his free fall, he presses the button of the stopwatch. When he reaches at the top of 100th floor, he has observed the reading of stopwatch as 00:00:06:00 (hh:mm:ss:100 th part of the second). Find the value of g. (correct upt ot two decimal places).

An inquistive student, determined to test the law of gravity for himself, walks to the top of a building og 145 floors, with every floor of height 4 m, having a stopwatch in his hand (the first floor is at a height of 4 m from the ground level). From there he jumps off with negligible speed and hence starts rolling freely. A rocketeer arrives at the scene 5 s later and dives off from the top of the building to save the student. The rocketeer leaves the roof with an initial downward speed v_0 . In order to catch the student at a sufficiently great height above ground so that the rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by rocketeer's jet pack, which he turns on just as he catches the student, before the rocketeer is in free fall. To prevent any discomfort to the student, the magnitude of the acceleration of the rocketeer and the student as they move downward together should not exceed 5 g. In Q.1, what would be the approximate retardation to be given by jet pack along for safe landing?

IE IRODOV, LA SENA & SS KROTOV-PHYSICAL FUNDAMENTALS OF MECHANICS-Relativistic Mechanics
  1. The rod AB oriented parallel to the x^' axis of the reference frame K^...

    Text Solution

    |

  2. The frame K^' moves with a constant velocity V relative to the frame K...

    Text Solution

    |

  3. An imaginary space rocket launched from the Earth moves with an accele...

    Text Solution

    |

  4. From the conditions of the foregoing problem determine the boost time ...

    Text Solution

    |

  5. How many times does the relativistic mass of a particle whose velocity...

    Text Solution

    |

  6. The density of a stationary body is equal to rho0. Find the velocity (...

    Text Solution

    |

  7. A proton moves with a momentum p=10.0GeV//c, where c is the velocity o...

    Text Solution

    |

  8. Find the velocity at which the relativistic momentum of a particle exc...

    Text Solution

    |

  9. What work has to be performed in order to increase the velocity of a p...

    Text Solution

    |

  10. Find the velocity at which the kinetic energy of a particle equals its...

    Text Solution

    |

  11. At what values of the ratio of the kinetic energy to rest energy can t...

    Text Solution

    |

  12. Find how the momentum of a particle of rest mass m0 depends on its kin...

    Text Solution

    |

  13. A beam of relativistic particles with kinetic energy T strikes against...

    Text Solution

    |

  14. A sphere moves with a relativistic velocity v through a gas whose unit...

    Text Solution

    |

  15. A particle of rest mass m0 starts moving at a moment t=0 due to a cons...

    Text Solution

    |

  16. A particle of rest mass m0 moves along the x axis of the frame K in ac...

    Text Solution

    |

  17. Proceeding from the fundamental equation of relativistic dynamics, fin...

    Text Solution

    |

  18. A relativistic particle with momentum p and total energy E moves along...

    Text Solution

    |

  19. The photon energy in the frame K is equal to epsilon. Making use of th...

    Text Solution

    |

  20. Demonstrate that the quantity E^2-p^2c^2 for a particle is an invarian...

    Text Solution

    |