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Answer:
T = mg/6
Explanation:
Draw a free body diagram (see attached). There are two tension forces acting upward at the edge of the cylinder, and weight at the center acting downwards.
The center rotates about the point where the cords touch the edge. Sum the torques about that point:
∑τ = Iα
mgr = (1/2 mr² + mr²) α
mgr = 3/2 mr² α
g = 3/2 r α
α = 2g / (3r)
(Notice that you have to use parallel axis theorem to find the moment of inertia of the cylinder about the point on its edge rather than its center.)
Now, sum of the forces in the y direction:
∑F = ma
2T − mg = m (-a)
2T − mg = -ma
Since a = αr:
2T − mg = -mαr
Substituting expression for α:
2T − mg = -m (2g / (3r)) r
2T − mg = -2/3 mg
2T = 1/3 mg
T = 1/6 mg
The tension in each cord is mg/6.
Answer:
The electronic transition of an electron back to a lower energy level generates an emission spectrum.
Explanation:
The atomic emission spectrum¹ of an element has its origin when an electronic transition² occurs. An electron in an atom or ion³will absorb energy coming from a source and pass to a higher energy level, the electron, upon returning to its base state will emit a photon⁴ or a series of photons.
Hence, that leads to the formation of an emission spectrum.
Remember that an electron has energy levels in an atom or ion, at which each energy level has a specific value.
The energy values will differ from one element to another. So, it can be concluded that each element has a unique pattern of emission lines.
Key terms:
¹Spectrum: Decomposition of light in its characteristic colors.
²Electronic transition: When an electron passes from one energy level to another, either for the emission or absorption of a photon.
³Ion: An atom electrically charged due to the gain or loss of electrons.
⁴Photon: Elementary particle that constitutes light.
Answer:
30,000 units, because total energy remains unchanged
Kinetic Energy = Energy of Motion
