If E is the total energy of a particle with zero potential energy, show that dE/dp=v, where p and v are the momentum and velocity of the particle, respectively.

United States electrical energy production (in trillions of kilowatt-hours) in year t (with 1900 corresponding to t = 0 ) is given by f(t), where f and its derivatives are graphed in the given figures.

(a) How much electrical energy was produced in 1950 ?

(b) How fast was energy production rising in 1950 ?

(c) When did energy production reach 3000 trillion kilowatthours?

(d) When was the level of energy production rising at the rate of 10 trillion kilowatt-hours per year?

(e) When was energy production growing at the greatest rate? What was the level of production at that time?

You have been asked to design a magnet system to steer a beam of 54-eV electrons. The goal is to be able to direct the electron beam to a specific target location with an accuracy of $\pm$ 1.0 mm. In your design, do you need to take the wave nature of electrons into account? Explain.

In the given figure, show that the rate at which energy is dissipated in $R$ as thermal energy is a maximum when R=r.

In general, how is the energy of a volcanic explosivity index number related to the energy of the next lower value?

Which statement correctly describes how thermal energy is transferred when Phoenix holds a piece of ice in her hand?

A) Thermal energy is transferred from her hand to the ice cube.

B) Thermal energy is transferred back and forth between her hand and the ice cube.

C) Thermal energy is transferred from the ice cube to her hand.

D) Thermal energy is not transferred between her hand and the ice cube.

Energy from passing high-energy electrons down the step of the electron transport chain is harnessed to move protons via active transport into the mitochondrial intermembrane space. How does this help mitochondria to produce energy?

In the earlier example the rotational kinetic energy of the professor and dumbbells increases. But since there are no external torques, no work is being done to change the rotational kinetic energy. Then, by Eq. , the kinetic energy must remain the same! Explain what is wrong with this reasoning, which leads to an apparent contradiction. Where does the extra kinetic energy come from?

The kinetic energy of the Ping-Pong ball is larger after its interaction with the bowling ball than before. From where does the extra energy come? Describe the event in terms of conservation of energy.

The circle graph shows the source of the United States' energy.

What is the biggest source of energy for the United States?

If the temperature in Problem (At $25^{\circ} \mathrm{C}$, what is the fraction of collisions with energy equal to or greater than an activation energy of $100 . \mathrm{kJ} / \mathrm{mol}$ ?) is increased to $50 .{ }^{\circ} \mathrm{C}$, by what factor does the fraction of collisions with energy equal to or greater than the activation energy change?

Where in the ATP molecule are the high-energy bonds that carry potential energy and are easily broken?

In the following exercise,

a. find the regression equation for the data points. Use the defining formulas to obtain $S_{x x}$ and $S_{x y}$.

b. graph the regression equation and the data points.

$$\begin{array}{l|lllll} \hline \boldsymbol{x} & 2 & 2 & 3 & 4 & 4 \\ \hline \boldsymbol{y} & 3 & 4 & 0 & 2 & 1 \\ \hline \end{array}$$

We provide independent simple random samples from several populations where, in each case, all the observations are distinct values. For this exercise, perform the following tasks.

a. Compute the Kruskal-Wallis test statistic, K, by using the defining formula. Use the defining formulas when obtaining SSTR and SST for the ranks.

b. Compute the Kruskal-Wallis test statistic, $K$, by using the computing formula, given in Equation (16.6) on page 730.

c. Compare your results in parts $(a)$ and $(b)$.

d. Explain the fact that parts $(a)-(c)$ are illustrating.

$$\begin{array}{c|c|c} \hline \text { Sample 1 } & \text { Sample 2 } & \text { Sample 3 } \\ \hline 31 & 49 & 97 \\ 7 & 17 & 71 \\ & 1 & \\ \hline \end{array}$$