In the steel bars $BE$ and $AD$ each have a $6 \times 18-\mathrm{mm}$ cross section. Knowing that $E=200 \mathrm{~GPa}$, determine the deflections of points $A,B$, and $C$ of the rigid bar $ABC$., the $3.2-\mathrm{kN}$ force caused point $C$ to deflect to the right. Using $\alpha=11.7 \times 10^{-6} /{ }^{\circ} \mathrm{C}$, determine (a) the overall change in temperature that causes point $C$ to return to its original position, (b) the corresponding total deflection of points $A$ and $B$.

The sealed assembly is completely filled with water such that the pressures at $C$ and $D$ are zero. If the assembly is given an angular velocity of $\omega=15\ \mathrm{rad} / \mathrm{s}$, find the difference in pressure between points $A$ and $B$.

The tube is filled with oil to the level $h=0.4 \mathrm{~m}$. Find the angular velocity of the tube so that the pressure at $O$ becomes $-15 \mathrm{kPa}$. Assume $S_o=0.92$.

Water in the container is originally at a height of $h=3\ \mathrm{ft}$. If a block having a specific weight of $50\ \mathrm{lb} / \mathrm{ft}^3$ is placed in the water, find the new level $h$ of the water. The base of the block is $1\ \mathrm{ft}$ square, and the base of the container is $2\ \mathrm{ft}$ square.

The steel bars $BE$ and $AD$ each have a $6 \times 18-\mathrm{mm}$ cross section. Knowing that $E=200 \mathrm{~GPa}$, determine the deflections of points $A,B$, and $C$ of the rigid bar $ABC$.

The uniform rods $AB$ and $BC$ are made of steel and are loaded as shown. Knowing that $E=29 \times 10^{6} \mathrm{psi}$, determine the magnitude and direction of the deflection of point $B$ when $\theta=22^{\circ}$.

When loaded with gravel, the barge floats in water at the depth shown. If its center of gravity is located at $G$ find whether the barge will restore itself when a wave causes it to tip slightly.

The hot-air balloon contains air having a temperature of $180^{\circ} \mathrm{F}$, while the surrounding air has a temperature of $60^{\circ} \mathrm{F}$. Find the maximum weight of the load the balloon can lift if the volume of air it contains is $120\left(10^3\right) \mathrm{ft}^3$. The empty weight of the balloon is $200\ \mathrm{lb}$.

The hollow spherical float controls the level of water within the tank. If the water is at the level shown, find the horizontal and vertical components of the force acting on the supporting arm at the pin $A$, and the normal force on the smooth support $B$. Neglect the weight of the float.

The 6-ft-wide plate in the form of a quarter-circular arc is used as a sluice gate. Find the magnitude and direction of the resultant force of the water on the bearing $O$ of the gate. Find the moment of the force about the bearing.

Find the resultant force the water exerts on the quarter-circular wall $AB$ if it is $3\ \mathrm{ m}$ wide.

The length of the $2-\mathrm{mm}$-diameter steel wire $CD$ has been adjusted so that with no load applied, a gap of $1.5 \mathrm{~mm}$ exists between the end $B$ of the rigid beam $ACB$ and a contact point $E$. Knowing that $E=200 \mathrm{~GPa}$, determine where a $20-\mathrm{kg}$ block should be placed on the beam in order to cause contact between $B$ and $E$.

A gate is $1.5\ \mathrm{m}$ wide, is pinned at $A$, and rests on the smooth support at $B$. Find the reactions at these supports because of the water pressure.

The brass tube $AB\left(E=15 \times 10^{6} \mathrm{psi}\right)$ has a cross-sectional area of $0.22 \mathrm{~in}$ $^{2}$ and is fitted with a plug at $A$. The tube is attached at $B$ to a rigid plate that is itself attached at $C$ to the bottom of an aluminum cylinder $\left(E=10.4 \times 10^{6} \mathrm{psi}\right)$ with a cross-sectional area of $0.40 \mathrm{~in}^{2}$. The cylinder is then hung from a support at $D$. In order to close the cylinder, the plug must move down through $\frac{3}{64}$ $\mathrm{in}$. Determine the force $\mathbf{P}$ that must be applied to the cylinder.