Heat is generated uniformly in a stainless steel plate having $k=20 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$. The thickness of the plate is $1.0 \mathrm{~cm}$ and the heat-generation rate is $500 \mathrm{MW} / \mathrm{m}^3$. If the two sides of the plate are maintained at 100 and $200^{\circ} \mathrm{C}$, respectively, calculate the temperature at the center of the plate.

As air flows as shown in Fig. over a flat plate, the velocity is reduced to zero at the wall. If $u(y)=10\left(20 y-100 y^2\right)~\mathrm{m} / \mathrm{s}$, find the mass flux $\dot{m}$ through a surface parallel to the plate and $0.2 \mathrm{~m}$ above the plate. The plate is $2 \mathrm{~m}$ wide and $\rho=1.23 \mathrm{~kg} / \mathrm{m}^3$.

A rectangular plate is located with vertices at points $(0, 0), (2, 0), (2, 3)$ and $(0, 3)$ in the $xy$-plane. The density of the plate at point $(x, y)$ is $\delta(y) = 2+y^{2}\ \text{gm/cm}^{2}$ and $x$ and $y$ are in cm. Find the total mass of the plate.

You want to increase the maximum potential difference of a parallel-plate capacitor. Describe how you can do this for a fixed plate separation.

A parallel-plate capacitor is made using two circular plates of radius a, with the bottom plate on the xy plane, centered at the origin. The top plate is located at z = d, with its center on the z axis. Charge Q is on the top plate; -Q is on the bottom plate. Dielectric having z -dependent permittivity fills the region between plates. The permittivity is given by $\epsilon(z)=\epsilon_{0}(1+ \left.z^{2} / d^{2}\right).$ Find $(a) \mathbf{D} ;(b) \mathbf{E} ;(c) V_{0} ;(d) C$

An aluminum plate of 25 mm thick $(k = 235 W/m \cdot K)$ is attached on a copper plate with thickness of 10 mm. The copper plate is heated electrically to dissipate a uniform heat flux of $5300 W/m^2.$ The upper surface of the aluminum plate is exposed to convection heat transfer in a condition such that the convection heat transfer coefficient is $67 W/m^2 \cdot K$ and the surrounding roora temperature is $20^\circ C.$ Other surfaces of the two attached plates are insulated such that heat only dissipates through the upper surface of the aluminum plate. If the surface 0f the copper plate that is attached to the aluminum plate has a temperature of $100^\circ C,$ determine the thermal contact conductance of the aluminum/copper interface.

A $5.00-\mathrm{kg}$ steel ball is dropped onto a copper plate from a height of $10.0 \mathrm{~m}$. If the ball leaves a dent $3.20 \mathrm{~mm}$ deep in the plate, what is the average force exerted by the plate on the ball during the impact?

A square metal plate of edge length 8.0 cm and negligible thickness has a total charge of $6.0 \times 10^{-6} C$. Estimate E at a distance of 30 m (large relative to the plate size) by assuming that the plate is a charged particle.

Consider a flat metal plate to be placed vertically underwater with its top 2 m below the surface of the water. Determine a shape for the plate so that if the plate is divided into any number of horizontal strips of equal height, the force on each strip is the same.

A mass $q$ of sand is discharged per unit time from a conveyor belt moving with a velocity $\mathbf{v}_0$. The sand is deflected by a plate at $A$ so that it falls in a vertical stream. After falling a distance $h$ the sand is again deflected by a curved plate at $B$. Neglecting the friction between the sand and the plates, determine the force required to hold in the position shown (a) plate $A,(b)$ plate $B$.

A 10.0-V battery is connected to two parallel metal plates placed in a vacuum. An electron is accelerated from rest from the negative plate toward the positive plate. a) What kinetic energy does the electron have just as it reaches the positive plate?

Two slots have been cut in plate $D E F$, and the plate has been placed so that the slots fit two fixed, frictionless pins $A$ and $B$. Knowing that $P=15\ \mathrm{lb}$, determine (a) the force each pin exerts on the plate, (b) the reaction at $F$.

Capacitance increases with a. larger plate area and greater distance between the plates. b. smaller plate area and greater distance between the plates. c. larger plate area and less distance between the plates. d. higher values of applied voltage.

(a) Three capacitors are connected in parallel. Each has plate area $A$ and plate spacing $d$. What must be the spacing of a single capacitor of plate area $A$ if its capacitance equals that of the parallel combination? (b) What must be the spacing if the three capacitors are connected in series?