A $2.00 \mathrm{~kg}$ stone is tied to a thin, light wire wrapped around the outer edge of the uniform $10.0 \mathrm{~kg}$ cylindrical pulley. The inner diameter of the pulley is $60.0 \mathrm{~cm}$, while the outer diameter is $1.00 \mathrm{~m}$. The system is released from rest, and there is no friction at the axle of the pulley. Find
(a) the acceleration of the stone,
(b) the tension in the wire, and
(c) the angular acceleration of the pulley.

Vector $\overrightarrow{\mathbf{A}}$ points in the negative $x$ direction. Vector $\overrightarrow{\mathbf{B}}$ points at an angle of $30.0^{\circ}$ above the positive $x$ axis. Vector $\vec{C}$ has a magnitude of $15 \mathrm{~m}$ and points in a direction $40.0^{\circ}$ below the positive $x$ axis. Given that $\vec{A}+\vec{B}+\vec{C}=0$, find the magnitudes of $\overrightarrow{\mathbf{A}}$ and $\overrightarrow{\mathbf{B}}$.

A 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.00-kg weight by a thin, light wire that passes over a frictionless pulley. The pulley has the shape of a uniform solid disk of mass 2.00 kg and diameter 0.500 m. After the system is released, find the tension in the wire on both sides of the pulley,

Two large parallel metal plates are oriented horizontally and separated by a distance 3d. A grounded conducting wire joins them, and initially each plate carries no charge. Now a third identical plate carrying charge $Q$ is inserted between the two plates, parallel to them and located a distance $d$ from the upper plate, as in Figure P26.57. What potential difference appears between the middle plate and each of the other plates? Each plate has area $A$.

The electric field near the Earth is about $150 \mathrm{~N} / \mathrm{C}$. What is the energy density near the Earth?

When two capacitors are connected in parallel and then connected to a battery, the total stored energy is $5.0$ times greater than when they are connected in series and then connected to the same battery. What is the ratio of the two capacitances? (Before the battery is connected in each case, the capacitors are fully discharged.)

The electric field between the plates of a paperseparated $(K=3.75)$ capacitor is $8.24 \times 10^4 \mathrm{~V} / \mathrm{m}$. The plates are $1.95 \mathrm{~mm}$ apart, and the charge on each is $0.765 \mu \mathrm{C}$. Determine the capacitance of this capacitor and the area of each plate.

The electric field near the Earth is about $150 \mathrm{~N} / \mathrm{C}$. Approximately how much electric energy is stored in the Earth's electric field in the first $10 \mathrm{~m}$ above the Earth's surface?

A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley. The pulley is a uniform disk with mass 10.0 kg and radius 30.0 cm and turns on frictionless bearings. You measure that the stone travels 12.6 m in the first 3.00 s starting from rest. Find (a) the mass of the stone and (b) the tension in the wire.

How much charge can be placed on a capacitor with air between the plates before it breaks down if the area of each plate is $5.00 \textrm{cm}$ $^2$?

The electric field near the Earth is about $150 \mathrm{~N} / \mathrm{C}$. Approximately how much electric energy is stored in the Earth's electric field in the first $10 \mathrm{~m}$ above the Earth's surface? Compare (by a ratio) the answer with the daily output from a 2000-MW power station.

Two different dielectrics fill the space between the plates of a parallel-plate capacitor as shown in Fig. 24-31. Determine a formula for the capacitance in terms of $K_1, K_2$, the area $A$ of the plates, and the separation $d_1=d_2=d / 2$. [Hint: Can you consider this capacitor as two capacitors in series or in parallel?]

Two different dielectrics each fill half the space between the plates of a parallel-plate capacitor as shown in Fig. 24-30. Determine a formula for the capacitance in terms of $K_1, K_2$, the area $A$ of the plates, and the separation $d$. [Hint: Can you consider this capacitor as two capacitors in series or in parallel?]

The following sentence is not true: A magnetic field creates an electric field, and an electric field creates a magnetic field. Rewrite the sentence so that it is true.