91影视

A certain ohmic resistor has a resistance of $\mathbf{40}\mathbf{}\mathbf{惟}$.A second resistor is made of the same material but is three times as long and has half the cross-sectional area. What is the resistance of the second resistor? What is the effective resistance of the two resistors in series?

In the circuit shown in Figure 19.75, the emf of the battery is $\mathbf{7}\mathbf{.}\mathbf{9}\mathbf{}\mathbf{V}$. Resistor ${\mathit{R}}_{\mathbf{1}}$ has a resistance of $\mathbf{23}\mathbf{}\mathbf{惟}$ , and resistor ${\mathit{R}}_{\mathbf{2}}$ has a resistance of $\mathbf{44}\mathbf{}\mathbf{惟}$ . A steady current flows through the circuit. (a) What is the absolute value of the potential difference across ${\mathit{R}}_{\mathbf{1}}$? (b) What is the conventional current through ${\mathit{R}}_{\mathbf{2}}$?

In the circuit shown in Figure 19.75, the emf of the battery is $\mathbf{7}\mathbf{.}\mathbf{9}\mathbf{}\mathbf{V}$. Resistor ${\mathit{R}}_{\mathbf{1}}$ has a resistance of $\mathbf{23}\mathbf{}\mathbf{惟}$, and resistor ${\mathit{R}}_{\mathbf{2}}$has a resistance of$\mathbf{44}\mathbf{}\mathbf{惟}$. A steady current flows through the circuit. (a) What is the absolute value of the potential difference across ${\mathit{R}}_{\mathbf{1}}$? (b) What is the conventional current through ${\mathit{R}}_{\mathbf{2}}$?

In Figure 19.76 the resistance ${\mathit{R}}_{\mathbf{1}}$ is $\mathbf{10}\mathbf{}\mathbf{惟}$, ${\mathit{R}}_{\mathbf{2}}$is$\mathbf{5}\mathbf{}\mathbf{惟}$ , and ${\mathit{R}}_{\mathbf{3}}$ is $\mathbf{20}\mathbf{}\mathbf{惟}$. If this combination of resistors were to be replaced by a single resistor with an equivalent resistance, what should that resistance be?

In the circuit shown in Figure 19.77 the emf of the battery is $\mathbf{7}\mathbf{.}\mathbf{4}\mathbf{}\mathbf{V}$. Resistor ${\mathit{R}}_{\mathbf{1}}$has a resistance of $\mathbf{31}\mathbf{}\mathbf{惟}$, resistor ${\mathit{R}}_{\mathbf{2}}$ has a resistance of $\mathbf{47}\mathbf{}\mathbf{惟}$, and resistor localid="1662203602529" ${\mathit{R}}_3$has a resistance of localid="1662203617219" $\mathbf{52}\mathbf{}\mathbf{惟}$. A steady current flows through the circuit.

(a)What is the equivalent resistance of ${\mathit{R}}_{\mathbf{1}}$and${\mathit{R}}_{\mathbf{2}}$ ? (b) What is the equivalent resistance of all three resistors? (c) What is the conventional current through${\mathit{R}}_{\mathbf{3}}$

A ball is kicked on Earth from a location$<9,0,-5>$ (on the ground) with initial velocity role="math" localid="1656668041027" $\mathbf{<}\mathbf{-}\mathbf{10}\mathbf{,}\mathbf{13}\mathbf{,}\mathbf{-}\mathbf{5}\mathbf{>}\mathbf{m}\mathbf{/}\mathbf{s}$ . Neglecting air resistance: (a) What is the velocity of the ball 0.6 s after being kicked? (b) What is the location of the ball 0.6 s after being kicked? (c) What is the maximum height reached by the ball?

A simplified model of a hydrogen atom is that the electron cloud is a sphere of radius $\mathit{R}$with uniform charge density and total charge$\mathbf{鈥�}\mathit{e}$. (The actual charge density in the ground state is nonuniform.) See Figure 15.74.

a) For the uniform-density model, calculate the polarizability $\mathit{伪}$of atomic hydrogen in terms of $\mathit{R}$. Consider the case where the magnitude $\mathit{E}$of the applied electric field is much smaller than the electric field required to ionize the atom. Suggestions for your analysis: Imagine that the hydrogen atom is inside a capacitor whose uniform field polarizes but does not accelerate the atom. Consider forces on the proton in the equilibrium situation, where the proton is displaced a distance from the center of the electron cloud ( $\mathit{s}\mathbf{<}\mathbf{<}\mathit{R}$in the diagram). (b) For a hydrogen atom, $\mathit{R}$can be taken as roughly $\mathbf{1}\mathbf{脳}{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{}\mathbf{m}$(the Bohr model of the H atom gives $\mathit{R}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{5}\mathbf{脳}{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{}\mathbf{m}$). Calculate a numerical value for the polarizability $\mathit{伪}$of atomic hydrogen. For comparison, the measured polarizability of a hydrogen atom is $\mathbf{伪}\mathbf{=}\mathbf{7}\mathbf{.}\mathbf{4}\mathbf{脳}{\mathbf{10}}^{\mathbf{-}\mathbf{41}}\mathbf{}\mathbf{C}\mathbf{脳}\mathbf{m}\mathbf{(}\mathbf{N}\mathbf{/}\mathbf{m}\mathbf{)}$; see the note below. (c) If the magnitude $\mathit{E}$of the applied electric field is $\mathbf{1}\mathbf{脳}{\mathbf{10}}^{\mathbf{6}}\mathbf{}\mathbf{N}\mathbf{/}\mathbf{m}$,use the measured value of $\mathit{伪}$to calculate the shift shown in Figure 15.74. (d) For some purposes it is useful to model an atom as though the nucleus and electron cloud were connected by a spring. Use the measured value of $\mathit{伪}$to calculate the effective spring stiffness ${\mathit{k}}_{\mathbf{s}}$for atomic hydrogen. For comparison, measurements of Young鈥檚 modulus show that the effective spring stiffness of the interatomic force in solid aluminum is about $\mathbf{16}\mathbf{}\mathbf{N}\mathbf{/}\mathbf{m}$. (e) If 伪 were twice as large, what would ${\mathit{k}}_{\mathbf{s}}$be?

Note: Quantum-mechanical calculations agree with the experimental measurement of 伪 reported in T. M. Miller and B. Bederson, 鈥淎tomic and molecular polarizabilities: a review of recent advances,鈥� Advances in Atomic and Molecular Physics 13, 1鈥�55, 1977. They use cgs units, so their value is 1/(4蟺蔚0 ) greater than the value given here.

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?

In the Figure, location A is at 鉄� 0.5, 0, 0鉄� m, location C is 鉄�1.3, 0, 0鉄� m, and location B is 鉄�1.7, 0, 0鉄� m. ${\stackrel{\mathbf{鈫�}}{\mathbf{E}}}_{\mathbf{1}}$= 鉄� 650, 0, 0鉄� N/C and ${\stackrel{\mathbf{鈫�}}{\mathbf{E}}}_{\mathbf{2}}$=鉄�-350, 0, 0鉄� N/C. Calculate the following quantities: (a)螖V along a path going from A to B.

(1)You push on a spring whose stiffness is 11 N/m, compressing it until it is 2.5 cm shorter than its relaxed length. What is the magnitude of the force the spring now exerts on your hand?

(2) A different spring is 0.17 m long when it is relaxed.

(a) When a force of magnitude 250 N is applied, the spring becomes 0.24 m long. What is the stiffness of this spring?

(b) This spring is compressed so that length is 0.15 m. What magnitude of the force is required to do this?