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Chapter 2: Q52P-b (page 45)
In the circuit shown in Figure 19.75, the emf of the battery is . Resistor has a resistance of , and resistor has a resistance of. A steady current flows through the circuit. (a) What is the absolute value of the potential difference across ? (b) What is the conventional current through ?
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Two metal rods are made of different elements. The interatomic spring stiffness of element A is three times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is three times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?
As shown in Figure 19.74, a spherical metal shell of radius has a charge (on its surface) and is surrounded by a concentric spherical metal shell of radius which has a charge (on its inner surface).
(a) Use the definition of capacitance: to find the capacitance of this spherical capacitor.
(b) If the radii of the spherical shells and are large and nearly equal to each other, show that can be written as (which is also the equation for the capacitance of a parallel-plate capacitor) where is the surface area of one of the spheres, and is the small gap distance between them .
A playground ride consists of a disk of mass and radius mounted on a low-friction axle (Figure 11.94). A child of mass runs at speed on a line tangential to the disk and jumps onto the outer edge of the disk.
(a.) If the disk was initially at rest, now how fast is it rotating? (b) What is the change in the kinetic energy of the child plus the disk? (c) where has most of this kinetic energy gone? (d) Calculate the change in linear momentum of the system consisting of the child plus the disk (but not including the axle), from just before to just after impact. What caused this change in the linear momentum? (e) The child on the disk walks inward on the disk and ends up standing at a new location a distance from the axle. Now what is the angular speed? (f) What is the change in the kinetic energy of the child plus the disk, from the beginning to the end of the walk on the disk? (g) What was the source of this increased kinetic energy?
On a straight road with the +x axis chosen to point in the direction of motion, you drive for 3 h at a constant 30 mi/h, then in a few seconds you speed up to 60mi/h and drive at this speed for 1 h.
(a) What was the x component of average velocity for the 4 h period, using the fundamental definition. Of average velocity, which is the displacement divided by the time interval?
(b) Suppose that instead you use the equation . What do you calculate for the x component of average velocity?
(c) Why does the equation used in part (b) give the wrong answer?
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