A flow calorimeter is a device used to measure the specific heat of a liquid. Energy is added as heat at a known rate to a stream of the liquid as it passes through the calorimeter at a known rate. Measurement of the resulting temperature difference between the inflow and the outflow points of the liquid stream enables us to compute the specific heat of the liquid. Suppose a liquid of density $0.85 \mathrm{~g} / \mathrm{cm}^3$ flows through a calorimeter at the rate of $8.0 \mathrm{~cm}^3 / \mathrm{s}$. When energy is added at the rate of $250 \mathrm{~W}$ by means of an electric heating coil, a temperature difference of $15 \mathrm{C}^{\circ}$ is established in steady-state conditions between the inflow and the outflow points. What is the specific heat of the liquid?

Suppose that the force is applied perpendicular to the torque arm. Given: $\tau=35.7\ \mathrm{lb}\ \mathrm{ft}$ $r=0.0240 \mathrm{ft}$

$$F= ?$$

The Stanford linear accelerator can accelerate electrons to kinetic energies of $50 \mathrm{GeV}$. What's the de Broglie wavelength of these electrons? Compare with the diameter of a proton, about $2 \mathrm{fm}$.

A soccer player $20.0 \mathrm{~m}$ from the goal stands ready to score. In the way stands a goalkeeper, $1.70 \mathrm{~m}$ tall and $5.00 \mathrm{~m}$ out from the goal, whose crossbar is at $2.44 \mathrm{~m}$ high. The striker kicks the ball toward the goal at $18 \mathrm{~m} / \mathrm{s}$. Determine whether the ball makes it over the goalkeeper and/or over the goal for each of the following launch angles (above the horizontal): (c) $30^{\circ}$.

A cylindrical pressure vessel having a radius $r=14\ \text{in.}$ and wall thickness $t=0.5\ \text{in.}$ is subjected to internal pressure $p=375\ \text{psi}$. In addition, a torque $T=90\ \mathrm{kip}- \mathrm{ft}$ acts at each end of the cylinder. (a) Determine the maximum tensile stress $\sigma_{\max }$ and the maximum in-plane shear stress $\tau_{\operatorname{mix}}$ in the wall of the cylinder. (b) If the allowable in-plane shear stress is $4.5\ \mathrm{ksi}$, what is the maximum allowable torque $T$ ? (c) If $T=150\ \mathrm{kip-ft}$ and allowable in-plane shear and allowable normal stresses are $4.5\ \mathrm{ksi}$ and $11.5\ \mathrm{ksi}$, respectively, what is the minimum required wall thickness?

The table lists the measurements of a lot bounded by a stream and two straight roads that meet at right angles, where x and y are measured in feet.

Use the model in part (a) to estimate the area of the lot.

Will two limp pieces of paper held a few inches apart come closer together or move farther apart if you blow between them? Explain.\s* Q31. A gust of wind blows sideways across an open outward-swinging door. Will the door slam shut or swing open as a result of this? Explain.

The viscosity of a fluid is to be measured by a viscometer constructed of two 5-ft-long concentric cylinders. The inner diameter of the outer cylinder is 6 in, and the gap between the two cylinders is 0.035 in. The outer cylinder is rotated at 250 rpm, and the torque is measured to be $1.2 lbf \cdot ft.$ Determine the viscosity of the fluid.

Graph the region bounded by the graphs of the equations. Then find the area of the region analytically. y = 1/10xe^3x, y = 0, x = 0, x = 2

Knowing that d = 1.2 in., determine the torque T that causes a maximum shearing stress of $7.5\ \text{ksi}$ in the hollow shaft shown.

Getting into a car involves these steps. Open the car door. Sit down. Close the door. Buckle the seat belt. Describe the steps you take in getting out of a car. How are they related to the steps involved in getting into a car?

When the growth of a spherical cell depends on the flow of nutrients through the surface, it is reasonable to assume that the growth rate, $d V / d t$, is proportional to the surface area, S. Assume that for a particular cell $d V / d t=\dfrac{1}{3} \cdot S$. At what rate is its radius $r$ increasing?

"Suppose the snark population on Citsigol Island is currently 3,400 and growing at a rate of 18% per year.

a. Write a recursive definition for the sequence $P$ of snark populations $n$ years from now (assuming an unlimited growth model).

b. Write an explicit formula for the population $P$ of snarks $n$ years from now (assuming an unlimited growth model).

c. If the snark population is modeled with the limited growth model difference equation $P_{n+1}=P_n+0.18 P_n\left(1-\frac{P_n}{17000}\right)$, what is the end behavior of the sequence $P$ ? What does the end behavior mean in this situation?"

If the competitor leans slightly farther back (increasing the angle between his body and the vertical) but remains stationary in this new position, which statement is true? Assume that the rope remains horizontal.
A. The difference between $T_1$ and $T_2$ increases, balancing the increased torque about his feet that his weight produces when he leans farther back.
B. The difference between $T_1$ and $T_2$ decreases, balancing the increased torque about his feet that his weight produces when he leans farther back.
C. Neither $T_1$ nor $T_2$ changes because no other forces are changing.
D. Both $T_1$ and $T_2$ change, but the difference between them remains the same.