41 through 52 GO 43, 51 SSM 47, 51 Reflection by thin layers . In Fig. 35-42, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) The waves of rays r 1 and r 2 interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35-2 refers to the indexes of refraction n 1 , n 2 , and n 3 , the type of interference, the thin-layer thickness L in nanometers, and the wavelength λ in nanometers of the light as measured in air. Where λ is missing, give the wavelength that is in the visible range. Where L is missing, give the second least thickness or the third least thickness as indicated. Figure 35-42 Problems 41 through 52 Table 35-2 Problems 41 through 52: Reflection by Thin Layers. See the setup for these problems. n 1 n 2 n 3 Type L λ 41 1.68 1.59 1.50 min 2nd 342
41 through 52 GO 43, 51 SSM 47, 51 Reflection by thin layers . In Fig. 35-42, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) The waves of rays r 1 and r 2 interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35-2 refers to the indexes of refraction n 1 , n 2 , and n 3 , the type of interference, the thin-layer thickness L in nanometers, and the wavelength λ in nanometers of the light as measured in air. Where λ is missing, give the wavelength that is in the visible range. Where L is missing, give the second least thickness or the third least thickness as indicated. Figure 35-42 Problems 41 through 52 Table 35-2 Problems 41 through 52: Reflection by Thin Layers. See the setup for these problems. n 1 n 2 n 3 Type L λ 41 1.68 1.59 1.50 min 2nd 342
41 through 52 GO 43, 51 SSM 47, 51 Reflection by thin layers. In Fig. 35-42, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) The waves of rays r1 and r2 interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35-2 refers to the indexes of refraction n1, n2, and n3, the type of interference, the thin-layer thickness L in nanometers, and the wavelength λ in nanometers of the light as measured in air. Where λ is missing, give the wavelength that is in the visible range. Where L is missing, give the second least thickness or the third least thickness as indicated.
Figure 35-42 Problems 41 through 52
Table 35-2 Problems 41 through 52: Reflection by Thin Layers. See the setup for these problems.
A skateboarder with his board can be modeled as a particle of mass 80.0 kg, located at his center of mass. As shown in the figure below, the skateboarder starts from rest in a crouching position at one lip of a half-pipe (point). On his descent, the skateboarder moves without friction so
that his center of mass moves through one quarter of a circle of radius 6.20 m.
i
(a) Find his speed at the bottom of the half-pipe (point Ⓡ).
m/s
(b) Immediately after passing point Ⓑ, he stands up and raises his arms, lifting his center of mass and essentially "pumping" energy into the system. Next, the skateboarder glides upward with his center of mass moving in a quarter circle of radius 5.71 m, reaching point D. As he
passes through point ①, the speed of the skateboarder is 5.37 m/s. How much chemical potential energy in the body of the skateboarder was converted to mechanical energy when he stood up at point Ⓑ?
]
(c) How high above point ① does he rise?
m
A 31.0-kg child on a 3.00-m-long swing is released from rest when the ropes of the swing make an angle of 29.0° with the vertical.
(a) Neglecting friction, find the child's speed at the lowest position.
m/s
(b) If the actual speed of the child at the lowest position is 2.40 m/s, what is the mechanical energy lost due to friction?
]
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