A 3.0-cm-thick plate has heat generated uniformly at the rate of $5 \times 10^5 \mathrm{~W} / \mathrm{m}^3$. One side of the plate is maintained at $200^{\circ} \mathrm{C}$ and the other side at $45^{\circ} \mathrm{C}$. Calculate the temperature at the center of the plate for $k=16 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$.

The ball is released from position A and drops 0.75 m to the incline. If the coefficient of restitution in the impact is e = 0.85, determine the slant range R.

An 8-ft-long tank open to the atmosphere initially contains 3-ft-high water. It is being towed by a truck on a level road. The truck driver applies the brakes and the water level at the front rises 0.5 ft above the initial level. Determine the deceleration of the truck.

The wood block has a specific weight of $45 \mathrm{lb} / \mathrm{ft}^3$. Determine the depth h at which it floats in the oil-water system. The block is $1 \mathrm{ft}$ wide. Take $\rho_o=1.75 \mathrm{slug} / \mathrm{ft}^3$.

The wheel rolls without slipping with an angular velocity of $\omega=10 \mathrm{rad} / \mathrm{s}$. Determine the magnitude of the velocity of point $B$ at the instant shown.

A spring–mass system is driven from rest harmonically such that the displacement response exhibits a beat of period of $0.2\pi s.$ The period of oscillation is measured to be $0.02\pi s.$ Calculate the natural frequency and the driving frequency of the system.

A velocity field is given by u = V cosθ, v = V sinθ, and w = 0, where V and θ are constants. Derive a formula for the streamlines of this flow.

Two 5.0-cm-diameter aluminum bars, $2 \mathrm{~cm}$ long, have ground surfaces and are joined in compression with a $0.025-\mathrm{mm}$ brass shim at a pressure exceeding $20 \mathrm{~atm}$. The combination is subjected to an overall temperature difference of $200^{\circ} \mathrm{C}$. Calculate the temperature drop across the contact join.

Steady flow devices that result in a drop in working fluid pressure from inlet to exit are

$$\begin{array}{l l } \text{(a) Nozzle, pump, throttling device}\\ \text{(b) Diffuser, turbine, throttling device}\\ \text{(c) Nozzle, turbine, throttling device}\\ \text{(d) Diffuser, pump, throttling device}\\ \end{array}$$

The freight cars $A$ and $B$ have a mass of $20 \mathrm{Mg}$ and $15 \mathrm{Mg}$ respectively. Car A is moving with a velocity of $3\text{ m/s}$ towards $B$ (right to car $A$) and car $B$ is moving with a velocity of $1.5 \text{ m/s}$ towards car $A$. Determine the velocity of $A$ after collision if the cars collide and rebound, such that $B$ moves to the right with a speed of $2 \mathrm{~m} / \mathrm{s}$. If $A$ and $B$ are in contact for $0.5 \mathrm{~s}$, find the average impulsive force which acts between them.

Determine the velocity of point A on the rim of the gear at the instant shown.

A steel spur pinion has a pitch of 6 teeth/in, 22 full-depth teeth, and a $20^{\circ}$ pressure angle. The pinion runs at a speed of 1200 rev/min and transmits 15 hp to a 60-tooth gear. If the face width is 2 in, estimate the bending stress.

Argon gas expands in an adiabatic turbine from 3 MPa and $750^{\circ} \mathrm{C}$ to 0.2 MPa at a rate of 5 kg/s. The maximum power output of the turbine is (a) 1.06 MW (b) 1.29 MW (c) 1.43 MW (d) 1.76 MW (e) 2.08 MW

For the state of stress shown, determine two values of $\sigma_y$ for which the maximum shearing stress is $64 \mathrm{MPa}$.