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.

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?

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.What is the potential difference across the rod if it moves (i) parallel to $a b$ and (ii) directly out of the page?

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 $\theta=30^{\circ}$.

The uniform slender rod of length l is released from rest in the dashed vertical position. With what speed $v_A$ does end A strike the 30$^\circ$ incline? Neglect the small mass and friction of the end rollers.

The A992 steel bars are pin connected at C and D. If they each have the same rectangular cross section, with a height of $200 \mathrm{~mm}$ and a width of $100 \mathrm{~mm}$, determine the vertical displacement at $B$. Neglect the axial load in the bars.

The A992 steel bars are pin connected at B and C. If they each have a diameter of 30 mm, determine the slope at $E$.

The slender rod has a mass of $10 \mathrm{~kg}$ and is released from rest when it is in the vertical position. Determine its angular velocity at the instant it becomes horizontal. The attached block at $D$ has a mass of $4 \mathrm{~kg}$. The mass of the cable and pulley at $C$ can be neglected.

Solve the following problem using Castigliano's theorem.

The A992 steel beam has a moment of inertia of $I=125\left(10^6\right) \mathrm{mm}^4$. Determine the slope at $A$.

Determine the slope at B of the beam made from A992 steel and having a moment of inertia of $I=22.3\left(10^6\right) \mathrm{mm}^4$

Determine the slope at B of the beam made from A992 steel and having a moment of inertia of $I=53.8 \mathrm{in}^4$.

Using Castigliano's theorem. use the method of virtual work and determine the vertical displacement of joint B of the truss. Each steel member has a cross-sectional area of 300 ${~mm}^2$. E=200 GPa.