Estimate the net force on a 2.0-C charge at the origin of an $x y$-coordinate system if there is a $+5.0$-C charge at $(3 \mathrm{~m}, 0)$ and a $-3.0$-C charge at $(0,4 \mathrm{~m})$.

Four point charges are placed at the following $x y$ coordinates:

$$\begin{aligned} &Q_1=-1 \mathrm{mC} \text {, at }(-3 \mathrm{~cm}, 0 \mathrm{~cm}) \\ &Q_2=-1 \mathrm{mC}_2 \text { at }(+3 \mathrm{~cm}, 0 \mathrm{~cm}) \\ &Q_3=+1.024 \mathrm{mC} \text {, at }(0 \mathrm{~cm}, 0 \mathrm{~cm}) \\ &Q_4=+2 \mathrm{mC}_2 \text {, at }(0 \mathrm{~cm},-4 \mathrm{~cm}) \end{aligned}$$

Calculate the net force on charge $Q_4$ due to charges $Q_1, Q_2$, and $Q_3$.

Two protons placed near one another with no other objects close by would a) accelerate away from each other. b) remain motionless. c) accelerate toward each other. d) be pulled together at constant speed. e) move away from each other at constant speed.

An airplane traveling at half the speed of sound emits a sound of frequency 5.00 kHz. At what frequency does a stationary listener hear the sound as the plane approaches?

(a) How fast would a motorist have to be traveling for a yellow $(\lambda=590 \mathrm{nm})$ traffic light to appear green $(\lambda=550 \mathrm{nm})$ because of the Doppler shift? (b) Should the motorist be traveling toward or away from the traffic light to see this effect? Explain.

A 10.0-g mass is suspended $5.00 \mathrm{~cm}$ above a nonconducting flat plate, directly above an embedded charge of $q$ (in coulombs). If the mass has the same charge, $q$, how much must $q$ be so that the mass levitates (just floats, neither rising nor falling)? If the charge $q$ is produced by adding electrons to the mass, by how much will the mass be changed?

Your sister wants to participate in the yearly science fair at her high school and asks you to suggest some exciting project. You suggest that she experiment with your recently created electron extractor to suspend her cat in the air. You tell her to buy a copper plate and bolt it to the ceiling in her room and then use your electron extractor to transfer electrons from the plate to the cat. If the cat weighs $7.00 \mathrm{~kg}$ and is suspended $2.00 \mathrm{~m}$ below the ceiling, how many electrons have to be extracted from the cat? Assume that the cat and the metal plate are point charges.

From collisions with cosmic rays and from the solar wind, the Earth has a net electric charge of approximately $-6.8 \cdot 10^5 \mathrm{C}$. Find the charge that must be given to a $1.0 \mathrm{~g}$ object for it to be electrostatically levitated close to the Earth's surface.

Three point charges are positioned on the $x$-axis: $+64.0 \mu \mathrm{C}$ at $x=0.00 \mathrm{~cm},+80.0 \mu \mathrm{C}$ at $x=25.0 \mathrm{~cm}$, and $-160.0 \mu \mathrm{C}$ at $x=50.0 \mathrm{~cm}$. What is the magnitude of the electrostatic force acting on the $+64.0-\mu \mathrm{C}$ charge? 21.67 From collisions with cosmic rays and from the solar wind, the Earth has a net electric charge of approximately $-6.8 \cdot 10^5 \mathrm{C}$. Find the charge that must be given to a $1.0 \mathrm{~g}$ object for it to be electrostatically levitated close to the Earth's surface.

Tell whether the following statements are always, sometimes, or never true. If a statement is not always true, explain. The product of a non-zero rational number and an irrational number is irrational.

A particle (charge $=+19.0 \mu \mathrm{C}$ ) is located on the $x$-axis at $x=-10.0 \mathrm{~cm}$, and a second particle (charge $=-57.0 \mu \mathrm{C}$ ) is placed on the $x$-axis at $x=+20.0 \mathrm{~cm}$. What is the magnitude of the total electrostatic force on a third particle (charge = $-3.80 \mu \mathrm{C})$ placed at the origin $(x=0)$ ?

Two charged objects experience a mutual repulsive force of $0.10 \mathrm{~N}$. If the charge of one of the objects is reduced by half and the distance separating the objects is doubled, what is the new force?

The nucleus of a carbon- 14 atom (mass = 14 amu) has diameter of $3.01 \mathrm{fm}$. It has 6 protons and a charge of $+6 e$. a) What is the force on a proton located at $3 \mathrm{fm}$ from the surface of this nucleus? Assume that the nucleus is a point charge. b) What is the proton's acceleration?

A helium-neon laser produces light of wavelength $\lambda_{\text {vac }}=632.8 \mathrm{~nm}$ in vacuum. If this light passes into water, with index of refraction $n=1.333$, what then will be its a) speed? b) frequency? c) wavelength? d) color?