A long, straight telephone cable contains six wires, each carrying a current of $0.300 \mathrm{~A}$. The distances between wires can be neglected.
(a) If the currents in all six wires are in the same direction, what is the magnitude of the magnetic field $2.50$ r from the cable?
(b) If four wires carry currents in one direction and the other two carry currents in the opposite direction, what is the magnitude of the field $2.50 \mathrm{~m}$ from the cable?

A playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.500 rev/s. What is its angular velocity after a 22.0-kg child gets onto it by grabbing its outer edge? The child is initially at rest.

A string vibrates at its third-harmonic frequency. The amplitude at a point 30 cm from one end is half the maximum amplitude. How long is the string?

A proton is bent into a circular path of radius $2 \mathrm{~m}$ by a magnetic field of $0.5 \mathrm{~T}$. (a) What is the momentum of the proton? (b) What is its kinetic energy?

A pendulum is formed by taking a $2 \mathrm{~kg}$ mass and hanging it from the ceiling using a steel wire with a diameter of $1.1 \mathrm{~mm}$. It is observed that the wire stretches by $0.05 \mathrm{~mm}$ under the weight of the mass. What is the period of oscillation of the pendulum?

A cheetah spots a Thomson's gazelle, its preferred prey. and leaps into action, quickly accelerating to its top speed of $30 \mathrm{~m} / \mathrm{s}$, the highest of any land animal. However, a cheetah can maintain this extreme speed for only $15 \mathrm{~s}$ before having to let up. The cheetah is $170 \mathrm{~m}$ from the gazelle as it reaches top speed, and the gazelle sees the cheetah at just this instant. With negligible reaction time, the gazelle heads directly away from the cheetah, accelerating at $4.6 \mathrm{~m} / \mathrm{s}^2$ for $5.0 \mathrm{~s}$, then running at constant speed. Does the gazelle escape? If so, by what distance is the gazelle in front when the cheetah gives up?

(a) For a parallel plate capacitor with a fixed plate separation distance, a larger plate area results in (1) a larger capacitance value, (2) an unchanged capacitance value, (3) a smaller capacitance value. (b) A 2.50-nF parallel plate capacitor has a plate area of $0.514\ \mathrm{m}^{2}.$ If the plate area is doubled, what is the new capacitance value?

Silver has a density of $10.5 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$ and a resistivity of $1.60 \times 10^{-8} \Omega \cdot \mathrm{m}$ at room temperature. (a) On the basis of the classical free electron gas model, and assuming that each silver atom contributes one electron to the electron gas, calculate the average time between collisions of the electrons. (b) Calculate the mean free path from $\tau$ and the electron’s thermal velocity. (c) How does the mean free path compare to the lattice spacing?

A train whistle is heard at 300 Hz as the train approaches town. The train cuts its speed in half as it nears the station, and the sound of the whistle is then 290 Hz. What is the speed of the train before and after slowing down?

A 2.0-kg object moving to the right at $6.0 \mathrm{~m} / \mathrm{s}$ collides head-on with a $4.0-\mathrm{kg}$ object that is initially at rest. After the collision, the $2.0-\mathrm{kg}$ object is moving to the left at $1.0 \mathrm{~m} / \mathrm{s}$.

$(a)$ Find the velocity of the $4.0-\mathrm{kg}$ object after the collision.

How long does it take the Sun to melt a block of ice at $0^{\circ} \mathrm{C}$ with a flat horizontal area $1.0 \mathrm{~m}^2$ and thickness $1.0 \mathrm{~cm}$ ? Assume that the Sun's rays make an angle of $35^{\circ}$ with the vertical and that the emissivity of ice is $0.050$.

How long does it take the Sun to melt a block of ice at $0^{\circ} \mathrm{C}$ with a flat horizontal area $1.0 \mathrm{~m}^2$ and thickness $1.0 \mathrm{~cm}$ ? Assume that the Sun's rays make an angle of $35^{\circ}$ with the vertical and that the emissivity of ice is $0.050$.

A hunter aims directly at a target (on the same level) 68.0 m away. At what angle should the gun be aimed so the target will be hit?

Consider a thin film of soap in air under illumination by yellow light with $\lambda=0.6 \mu \mathrm{m}$ in vacuum. If the film is treated as a planar dielectric slab with $\epsilon_{\mathrm{r}}=1.72$, surrounded on both sides by air, what film thickness would produce strong reflection of the yellow light at normal incidence?