Collar $A$ is free to slide with negligible friction on the circular guide mounted in the vertical frames. Determine the angle $\theta$ assumed by the collar if the frame is given a constant horizontal acceleration $a$ to the right.

The hemisphere $0<r<a, 0<\theta<\pi / 2,$ is composed of homogeneous conducting material of conductivity $\sigma.$ The flat side of the hemisphere rests on a perfectly conducting plane. Now, the material within the conical region $0<\theta<\alpha, 0<r<a$ is drilled out and replaced with material that is perfectly conducting. An air gap is maintained between the r = 0 tip of this new material and the plane. What resistance is measured between the two perfect conductors? Neglect fringing fields.

A Pelton wheel has a diameter of 2 m and develops 500 kW when rotating 180 rpm. What is the average force of the water against the blades? If the turbine is operating at maximum efficiency, determine the speed of the water jet from the nozzle and the mass flowrate.

Determine the vertical displacement of point E. Each member has a cross-sectional area of 4.5 ${in}^2$. $E=29\left(10^3\right) \mathrm{ksi}$. Use the method of virtual work.

Use the method of virtual work and determine the displacement of point C. E I is constant.

Use the method of virtual work and determine the displacement of point C of the beam made from steel. E=29$(10^3)$ ksi, I=245 ${in}^4$

The crate is at rest at point $A$ when it is nudged down the incline. If the coefficient of kinetic friction between the crate and the incline is $0.30$ from $A$ to $B$ and $0.22$ from $B$ to $C$, determine its speeds at points $B$ and $C$.

In a test to determine the crushing characteristics of polystyrene packing material, a steel cone of mass $m$ is dropped so that it falls a distance $h$ and then penetrates the material. The resistance $R$ of polystyrene to penetration depends on the cross-sectional area of the penetrating object and thus is proportional to the square of the cone penetration distance $x$, or $R=k x^2$. If the cone comes to rest at a distance $x=d$, determine the constant $k$ in terms of the test conditions and results.

In Fig. we saw earlier a conducting rod of length $L=30.0 \mathrm{~cm}$ moves in a magnetic field $\overrightarrow{\boldsymbol{B}}$ of magnitude $0.450 \mathrm{~T}$ directed into the plane of the figure. The rod moves with speed $v=5.00 \mathrm{~m} / \mathrm{s}$ in the direction shown.When the charges in the rod are in equilibrium, which point, $a$ or $b$, has an excess of positive charge?

In Fig. we saw earlier a conducting rod of length $L=30.0 \mathrm{~cm}$ moves in a magnetic field $\overrightarrow{\boldsymbol{B}}$ of magnitude $0.450 \mathrm{~T}$ directed into the plane of the figure. The rod moves with speed $v=5.00 \mathrm{~m} / \mathrm{s}$ in the direction shown.What is the potential difference across the rod if it moves (i) parallel to $a b$ and (ii) directly out of the page?

In Fig. we saw earlier a conducting rod of length $L=30.0 \mathrm{~cm}$ moves in a magnetic field $\overrightarrow{\boldsymbol{B}}$ of magnitude $0.450 \mathrm{~T}$ directed into the plane of the figure. The rod moves with speed $v=5.00 \mathrm{~m} / \mathrm{s}$ in the direction shown.What is the potential difference between the ends of the rod?

In Fig. we saw earlier a conducting rod of length $L=30.0 \mathrm{~cm}$ moves in a magnetic field $\overrightarrow{\boldsymbol{B}}$ of magnitude $0.450 \mathrm{~T}$ directed into the plane of the figure. The rod moves with speed $v=5.00 \mathrm{~m} / \mathrm{s}$ in the direction shown.Which point, $a$ or $b$, is at higher potential?

In Fig. we saw earlier a conducting rod of length $L=30.0 \mathrm{~cm}$ moves in a magnetic field $\overrightarrow{\boldsymbol{B}}$ of magnitude $0.450 \mathrm{~T}$ directed into the plane of the figure. The rod moves with speed $v=5.00 \mathrm{~m} / \mathrm{s}$ in the direction shown.When the charges in the rod are in equilibrium, what are the magnitude and direction of the electric field within the rod?

The uniform slender rod of mass m and length L is released from rest in the inverted vertical position. Neglect friction and the mass of the small end roller and find the initial acceleration of A. Evaluate your result for $\theta=30^{\circ}$.