A thin rod of length 0.75 meters and mass 0.42 kilogram is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular speed $4.0 \text{~rad/s}$. Neglecting friction and air resistance, find the rod’s kinetic energy at its lowest position.

To find the height of a lamppost, you stand a 6 ft pole 20 ft from the lamp and measure the length a of its shadow, finding it to be 15 ft, give or take an inch. Calculate the height of the lamppost using the value a = 15 and estimate the possible error in the result.

A wheel has a constant angular acceleration of 5.0 rad/s². Starting from rest, it turns through 300 rad. (a) What is its final angular velocity? (b) How much time elapses while it turns through the 300 radians?

Let Y be a random variable with some distribution. Suppose that you have available as many pseudo-random variables as you want with the same distribution as $Y$. Describe a simulation method for estimating the skewness of the distribution of Y.

Whether an object is dropped, thrown horizontally, or thrown at some angle of elevation or depression, acceleration of the object during its flight will be due to gravity. Nolan can throw a ball with a velocity of 150 ft/s. If he throws the ball horizontally and his release point is 6 feet above the ground, what is the horizontal distance the ball travels before hitting the ground? (Assume level ground and no air resistance.)

Graph each equation. y=-4

What do the y-coordinates on the least-squares regression line represent?

Determine the phase or phases in a system consisting of $H_{2}O$ at the following conditions and sketch $p-\upsilon$ and $T-\upsilon$ diagrams showing the location of each state.

$$\begin{array}{l l } \text{(a) $p=10$ bar, $T=179.9^{\circ} \mathrm{C}$}\\ \text{(b) $p=10$ bar, $T=150^{\circ} \mathrm{C}$}\\ \text{(c) $T=100^{\circ} \mathrm{C}, p=0.5 \mathrm{bar}$}\\ \text{(d) $T=20^{\circ} \mathrm{C}, p=50 \mathrm{bar}$}\\ \text{(e) $p=1$ bar, $T=-6^{\circ} \mathrm{C}$}\\ \end{array}$$

(a) Find the velocity, acceleration, and speed of a particle traveling along the curve traced out by the vector function $\mathbf{r}=\mathbf{r}(t)$. (b) Find the tangential and normal components of the acceleration. $\mathbf{r}(t)=(1-3 t) \mathbf{i}+2 t \mathbf{j}-(5+t) \mathbf{k}$

How does the U.S. Constitution reflect the principle of "republicanism"?

A concentric tube arrangement, for which the inner and outer diameters are 80 mm and 100 mm, respectively, is used to remove heat from a biochemical reaction occurring in a 1-m-long settling tank. Heat is generated uniformly within the tank at a rate of $10^{5} \mathrm{W} / \mathrm{m}^{3}$, and water is supplied to the annular region at a rate of 0.2 kg/s. (a) Determine the inlet temperature of the supply water that will maintain an average tank surface temperature of $37^{\circ} \mathrm{C}$. Assume fully developed flow and thermal conditions. Is this assumption reasonable? (b) It is desired to have a slight, axial temperature gradient on the tank surface, since the rate of the biochemical reaction is highly temperature dependent. Sketch the axial variation of the water and surface temperatures along the flow direction for the following two cases: (i) the fully developed conditions of part (a), and (ii) conditions for which entrance effects are important. Comment on features of the temperature distributions. What change to the system or operating conditions would you make to reduce the surface temperature gradient?

A wooden access ramp is being built to reach a platform that sits 30 inches above the floor. The ramp drops 2 inches for every 25-inch run. Write a linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform.

The angular velocity of a rotating rigid body increases from 500 to 1500 rev/min in 120 s. (a) What is the angular acceleration of the body? (b) Through what angle does it turn in this 120 s?

Metabolizing 1.0 kg of fat results in about $3.7 \times 10^{7} \mathrm{J}$ of internal energy in the body. How long would it take to burn 1.0-kg of fat this way assuming there is no food intake?