d through a railroad track
Answer:
1.28 m
Explanation:
Given;
Radius, r = 1.5 cm = 0.015 m
Time, t = 19 s
Average angular speed = 4.5 rad/s
Consider a point when the tape is moving at a constant velocity along the circumference of the circular reel of radius r. The linear velocity v at this point is given by;
v = rω ----(1)
Where
v is the linear velocity of the circular motion
r is the radius of the reel
ω is the the angular velocity.
At a point the tap undergoes a linear motion before passing round the reel of the cassette. The linear velocity v at this point is given by;
v = L/t ----(2)
where;
v is the velocity of the linear motion
L is the length of the tape (distance covered by the tape)
t is the time taken
Equating equation(1) and equation (2)
L/t = rω
L = rωt
Substituting the given values,
L = 0.015 × 4.5 × 19
L = 1.2825 m
L = 1.28 m
<u>We are given:</u>
Direction of motion: 25 degrees south of the east axis
Distance covered = 125 m
<u>East component of the Ball:</u>
<em>this component is denoted by green color in the image</em>
Once we drop a perpendicular from the end of the direction vector on the x-axis, we get a right angled triangle
The magnitude of the side of the triangle on the x-axis denotes the east component of the ball
Using trigonometry, we find that the east component of the ball is:
125 * Cos(25 degrees)
125 * 0.9 = 112.5 i (here, i denotes rightward direction on the x-axis)
<u />
<u>North Component of the Ball:</u>
<em>this component is denoted by blue color in the image</em>
Using trigonometry, we find that the North component of the ball is:
125* Sin(25 degrees) (-j) <em>[j denotes upward movement on the y-axis, since the vector is acting downwards, we have used '-j']</em>
125 * 0.42 (-j)
52.5 (-j) = -52.5 j
Therefore the direction vector of the ball is 112.5 i - 52.5 j
<em>where 112.5 i is the East Component and -52.5 is the North Component</em>
Answer:
5773.50269 Hz
23 A
Explanation:
= Inductance = 6 mH
= Capacitance = 5 μF
= Resistance = 3 Ω
= Maximum emf = 69 V
Resonant angular frequency is given by
The resonant angular frequency is 5773.50269 Hz
Current is given by
The current amplitude at the resonant angular frequency is 23 A
Interaction of Electromagnetic Radiation and Matter
It is well known that all matter is comprised of atoms. But subatomically, matter is made up of mostly empty space. For example, consider the hydrogen atom with its one proton, one neutron, and one electron. The diameter of a single proton has been measured to be about 10-15 meters. The diameter of a single hydrogen atom has been determined to be 10-10meters, therefore the ratio of the size of a hydrogen atom to the size of the proton is 100,000:1. Consider this in terms of something more easily pictured in your mind. If the nucleus of the atom could be enlarged to the size of a softball (about 10 cm), its electron would be approximately 10 kilometers away. Therefore, when electromagnetic waves pass through a material, they are primarily moving through free space, but may have a chance encounter with the nucleus or an electron of an atom.
Because the encounters of photons with atom particles are by chance, a given photon has a finite probability of passing completely through the medium it is traversing. The probability that a photon will pass completely through a medium depends on numerous factors including the photon’s energy and the medium’s composition and thickness. The more densely packed a medium’s atoms, the more likely the photon will encounter an atomic particle. <span>In other words, the more subatomic particles in a material (higher Z number), the greater the likelihood that interactions will occur </span>Similarly, the more material a photon must cross through, the more likely the chance of an encounter.
When a photon does encounter an atomic particle, it transfers energy to the particle. The energy may be reemitted back the way it came (reflected), scattered in a different direction or transmitted forward into the material. Let us first consider the interaction of visible light. Reflection and transmission of light waves occur because the light waves transfer energy to the electrons of the material and cause them to vibrate. If the material is transparent, then the vibrations of the electrons are passed on to neighboring atoms through the bulk of the material and reemitted on the opposite side of the object. If the material is opaque, then the vibrations of the electrons are not passed from atom to atom through the bulk of the material, but rather the electrons vibrate for short periods of time and then reemit the energy as a reflected light wave. The light may be reemitted from the surface of the material at a different wavelength, thus changing its color.
<span>X-Rays and Gamma Rays
</span>X-rays and gamma rays also transfer their energy to matter though chance encounters with electrons and atomic nuclei. However, X-rays and gamma rays have enough energy to do more than just make the electrons vibrate. When these high energy rays encounter an atom, the result is an ejection of energetic electrons from the atom or the excitation of electrons. The term "excitation" is used to describe an interaction where electrons acquire energy from a passing charged particle but are not removed completely from their atom. Excited electrons may subsequently emit energy in the form of x-rays during the process of returning to a lower energy state.
