By what factor would your weight change if Earth’s diameter were doubled and its mass were also doubled?

What would be the difference in your weight if you were five times farther from the center of Earth than you are right now? Ten times?

The weight of an apple near the surface of Earth is 1 N. What is the weight of Earth in the gravitational field of the apple?

How would the gravitational field at Earth’s surface be affected if Earth shrank in size without any change in mass? What would be its relative strength at the new surface if Earth shrank to half size? To one-tenth size?

Solve for x on the domain $0 \leqslant x \leqslant 2 \pi$: $3 \cos \left(\frac{x}{2}\right)+1=0$

Infrared light of wavelength $2.5 \mu \mathrm{m}$ illuminates a 0.20-mm-diameter hole. What is the angle of the first dark fringe in radians? In degrees?

A 0.14-kg baseball moves toward home plate with a velocity $\overrightarrow{\mathbf{v}}_{\mathrm{i}}=(-36 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{x}}$. After striking the bat, the ball moves vertically upward with a velocity $\overrightarrow{\mathbf{v}}_f=(18 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{y}}$. Find the direction and magnitude of the impulse delivered to the ball by the bat. Assume that the ball and bat are in contact for $1.5 \mathrm{~ms}$.

You took a running leap off a high diving platform. You were running at 2.8 m/s and hit the water 2.6 s later. How high was the platform, and how far from the edge of the platform did you hit the water? Ignore air resistance.

The planet Jupiter is about 300 times as massive as Earth, but an object on its surface would weigh only 2.5 times as much as it would on Earth. Can you come up with an explanation?

Show that for a pn junction in which the p side ismuchmore heavily doped than the n side $\left( i. e., N_{A} \gg N_{D}\right),$ referred to as a $p^{+} n$ diode, Eqs. (3.26), (3.27), (3.28), (3.29), and (3.30) can be simplified as follows:

$$\begin{array}{l} W \simeq \sqrt{\frac{2 \epsilon_{s}}{q N_{D}} V_{0}} \quad \left(3.26^{\prime}\right) \\ x_{n} \simeq W \quad \left(3.27^{\prime}\right) \\ x_{p} \simeq W /\left(N_{A} / N_{D}\right) \quad \left(3.28^{\prime}\right) \\ Q_{J} \simeq A q N_{D} W \quad \left(3.29^{\prime}\right) \\ Q_{J} \simeq A \sqrt{2 \epsilon_{s} q N_{D} V_{0}} \quad \left(3.30^{\prime}\right) \end{array}$$

Earth and the moon are gravitationally attracted to each other. Does the more massive Earth attract the moon with a greater force, the same force, or less force than the moon attracts Earth?

During heavy rains, earthworms often emerge from their burrows. What might happen to an earthworm if it did not return to its burrow when the ground dried out?

In what way is gravity reduced with distance from Earth?

The formula for the growth rate of a population in the presence of a quantity $x$ of food was given as $f(x)=\frac{K x}{A+x}$ This was referred to as Michaelis-Menten kinetics. a. Find the rate of change of the growth rate with respect to the amount of food. b. The quantity $A$ in the formula for $f(x)$ represents the quantity of food for which the growth rate is half of its maximum. Using your answer from part a, find the rate of change of the growth rate when $x=A$ .