Answer:
Explanation:
Let us study the downward movement of cylinder which accelerates as well as rotates .
A)
If v be the linear downward velocity of cm of cylinder and ω be angular velocity of cylinder
v = ωr , when there is no slippage of string around cylinder.
B &C )
Total kinetic energy = Rotational + linear
= 1/2 Iω² + 1/2 m v²
1/2 x1/2 mr²ω² +1/2 m v²
= 1/4 mv² +1/2 m v²
= 3/4 m v²
For downward acceleration ,
mg - T = ma where T is tension in string.
Rotational movement
Torque = T x r
Tr = I α , I is moment of inertia and α is angular acceleration .
= I a/r
T = I a / r² , Putting this value of T in earlier equation
mg - I a / r² = ma
a (I / r² +m )= mg
a = mg / (I / r² +m )
For cylinders
I = .5 mr²
a = g / (.5 +1)
= g / 1.5
Completing the square gives the answer right away.
which indicates a maximum height of 87 when 
.
Answer:
a) W = - 6.825 J, b) θ = 1.72 revolution
Explanation:
a) In this exercise the work of the friction force is negative and is equal to the variation of the kinetic energy of the particle
W = ΔK
W = K_f - K₀
W = ½ m v_f² - ½ m v₀²
W = ½ 0.325 (5.5² - 8.5²)
W = - 6.825 J
b) find us the coefficient of friction
Let's use Newton's second law
fr = μ N
y-axis (vertical) N-W = 0
fr = μ W
work is defined by
W = F d
the distance traveled in a revolution is
d₀ = 2π r
W = μ mg d₀ = -6.825
μ = 
The total work as the object stops the final velocity is zero v_f = 0
W = 0 - ½ m v₀²
W = - ½ 0.325 8.5²
W = - 11.74 J
μ mg d = -11.74
we subtitle the friction coefficient value
( 
) m g d = -11.74
6.825 
= 11.74
d = 11.74/6.825 d₀
d = 1.7201 2π 0.400
d = 4.32 m
this is the total distance traveled, the distance and the angle are related
θ = d / r
θ = 4.32 / 0.40
θ = 10.808 rad
we reduce to revolutions
θ = 10.808 rad (1rev / 2π rad)
θ = 1.72 revolution
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.
A cyclist must lean into a turn to prevent tipping over in the other direction.The frictional force provides the centripetal force necessary to turn the cyclist to the left.But the frictional force also produces a clockwise torque that will cause the rider and the bicycle to tip clockwise to the right.The force is provided by the friction of the tires.
