Sound level at distance of 15 m is given as 20 dB
so intensity at this distance is given as
now if we move closer to some some distance the sound level is now 50 dB
now the intensity is given as
now we know that
so now the distance from friend must be 47 cm
Answer:
41.667 per cent of the total kinetic energy is translational kinetic energy.
Explanation:
As the spherical shell is rolling without slipping at constant speed, the system can be considered as conservative due to the absence of non-conservative forces (i.e. drag, friction) and energy equation can be expressed only by the Principle of Energy Conservation, whose total energy is equal to the sum of rotational and translational kinetic energies. That is to say:
Where:
- Total energy, measured in joules.
- Rotational kinetic energy, measured in joules.
- Translational kinetic energy, measured in joules.
The spherical shell can be considered as a rigid body, since there is no information of any deformation due to the motion. Then, rotational and translational components of kinetic energy are described by the following equations:
Rotational kinetic energy
Translational kinetic energy
Where:
- Moment of inertia of the spherical shell with respect to its center of mass, measured in
.
- Angular speed of the spherical shell, measured in radians per second.
- Radius of the spherical shell, measured in meters.
After replacing each component and simplifying algebraically, the total energy of the spherical shell is equal to:
In addition, the moment of inertia of a spherical shell is equal to:
Then, total energy is reduced to this expression:
The fraction of the total kinetic energy that is translational in percentage is given by the following expression:
41.667 per cent of the total kinetic energy is translational kinetic energy.