Answer:
Time according to earth clock (T0) = 0.22 years (Approx)
Explanation:
Given:
Time taken by light = 4.5 years
Time taken by ship = 5 years
Speed of light = c
Speed of ship (v) = 90% of c = 0.9c
Find:
Time according to earth clock (T0) = ?
Computation:
Time dilation is ,
Time according to earth clock (T0) = 0.22 years (Approx)
Answer:
a) 16.32 m/s
b) 640 N
Explanation:
A) mass of rocket m_r = 1000 g = 1 kg
initial speed of rocket u_r = 15 m/sec
initial speed of ball is u_b = 18 m/sec
final speed of ball is v_b = 40 m/sec
Let m_b be the mass of the ball= 60 g and v_r be the final velocity of the rocket
from law of conservation of momentum
momentum of the system remains zero
m_r×(u_r-v_r)+m_b(16-42) = 0
1×(15-v_r) = -0.060(18-40)
15-v_r = -1.32
v_r = 15+1.32 = 16.32 m/sec.
B) Average force that the rocket exert's on the ball is F_avg can be calculated as
contact time t=7.00 ms
F_avg = m(v-u)/t = 0.06×(40+18)/0.007 = 640 N
Width of the fringes gets decreased if the distance between the slits is increased and thus we get narrower fringes.
What is Young's double-slit experiment?
- In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena.
- This type of experiment was first performed, using light, by Thomas Young in 1802, as a demonstration of the wave behavior of light.
- A wave is split into two separate waves (the wave is typically made of many photons and better referred to as a wave front (not to be confused with the wave properties of the individual photon)) that later combine into a single wave.
- Changes in the path-lengths of both waves result in a phase shift, creating an interference pattern.
- A coherent light source, such as a laser beam, illuminates a plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate.
- The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles. However, the light is always found to be absorbed at the screen at discrete points, as individual particles (not waves); the interference pattern appears via the varying density of these particle hits on the screen.
- Furthermore, versions of the experiment that include detectors at the slits find that each detected photon passes through one slit (as would a classical particle), and not through both slits (as would a wave).
- However, such experiments demonstrate that particles do not form the interference pattern if one detects which slit they pass through. These results demonstrate the principle of wave-particle duality.
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The resultant vector is 5.2 cm at a direction of 12⁰ west of north.
<h3>
Resultant of the two vectors</h3>
The resultant of the two vectors is calculated as follows;
R = a² + b² - 2ab cos(θ)
where;
- θ is the angle between the two vectors = 45° + (90 - 57) = 78⁰
- a is the first vector
- b is the second vector
R² = (3.7)² + (4.5)² - (2 x 3.7 x 4.5) cos(78)
R² = 27.02
R = 5.2 cm
<h3>Direction of the vector</h3>
θ = 90 - 78⁰
θ = 12⁰
Thus, the resultant vector is 5.2 cm at a direction of 12⁰ west of north.
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