Three very large sheets are separated by equal distances of 15.0 cm (Fig. 22–47). The first and third sheets are very thin and nonconducting and have charge per unit area σ of +5.00 μ C/m 2 and −5.00 μ C/m 2 respectively. The middle sheet is conducting but has no net charge. ( a ) What is the electric field inside the middle sheet? What is the electric field ( b ) between the left and middle sheets, and ( c ) between the middle and right sheets? ( d ) What is the charge density on the surface of the middle sheet facing the left sheet, and ( e ) on the surface facing the right sheet? FIGURE 22–47 Problem 63.
Three very large sheets are separated by equal distances of 15.0 cm (Fig. 22–47). The first and third sheets are very thin and nonconducting and have charge per unit area σ of +5.00 μ C/m 2 and −5.00 μ C/m 2 respectively. The middle sheet is conducting but has no net charge. ( a ) What is the electric field inside the middle sheet? What is the electric field ( b ) between the left and middle sheets, and ( c ) between the middle and right sheets? ( d ) What is the charge density on the surface of the middle sheet facing the left sheet, and ( e ) on the surface facing the right sheet? FIGURE 22–47 Problem 63.
Three very large sheets are separated by equal distances of 15.0 cm (Fig. 22–47). The first and third sheets are very thin and nonconducting and have charge per unit area σ of +5.00 μC/m2 and −5.00 μC/m2 respectively. The middle sheet is conducting but has no net charge. (a) What is the electric field inside the middle sheet? What is the electric field (b) between the left and middle sheets, and (c) between the middle and right sheets? (d) What is the charge density on the surface of the middle sheet facing the left sheet, and (e) on the surface facing the right sheet?
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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