\begin{problem*}{2.5}
A position-time graph for a particle moving along the $x$ axis is
-shown in Figure P2.5. \Part{a} Find the average velocity in the time
+shown in Figure~P2.5. \Part{a} Find the average velocity in the time
interval $t=1.50\U{s}$ to $t=4.00\U{s}$. \Part{b} Determine the
instantaneous velocity at $t=2.00\U{s}$ by measuring the slope of the
tangent to the graph. \Part{c} At what value of $t$ is the velocity
it is $\vect{P}_0=7.60\E{3}\jhat\U{m}$. At $t=30.0\U{s}$, the
position vector leading from you to the airplane is
$\vect{P}_{30}=(8.04\E{3}\ihat+7.60\E{3}\jhat)\U{m}$ as suggested in
-Figure P3.43. Determine the magnitude and orientation of the
+Figure~P3.43. Determine the magnitude and orientation of the
airplane's position vector at $t=45.0\U{s}$.
\begin{center}
\begin{asy}
\begin{problem*}{5.25}
A bag of cement whose weight is $F_g$ hangs in equilibrium from three
-wires shown in Figure P5.24. Two of the wires make angles
+wires shown in Figure~P5.24. Two of the wires make angles
$\theta_1=60.0\dg$ and $\theta_2=40.0\dg$ with the horizontal.
Assuming the system is in equilibrium, show that the tension in the
left-hand wire is
An object of mass $m_1=5.00\U{kg}$ placed on a frictionless,
horizontal table is connected to a string that passes over a pulley
and then is fastened to a hanging object of mass $m_2=9.00\U{kg}$ as
-shown in Figure P5.28. \Part{a} Draw free-body diagrams of both
+shown in Figure~P5.28. \Part{a} Draw free-body diagrams of both
objects. Find \Part{b} the magnitude of that acceleration of the
objects and \Part{c} the tension in the string.
\begin{center}
\begin{problem*}{5.30}
Two objects are connected by a light string that passes over a
-frictionless pulley as shown in Figure P5.30. Assume the incline is
+frictionless pulley as shown in Figure~P5.30. Assume the incline is
frictionless and take $m_1=2.00\U{kg}$, $m_2=6.00\U{kg}$, and
$\theta=55.0\dg$. \Part{a} Draw free-body diagrams of both objects.
Find \Part{b} the magnitude of the acceleration of the
\begin{problem*}{5.63}
A crate of wieght $F_g$ is pushed by a force $\vect{P}$ on a
-horizontal floor as shown in Figure P5.63. The coefficient of static
+horizontal floor as shown in Figure~P5.63. The coefficient of static
friction is $\mu_s$, and $\vect{P}$ is directed at an angle $\theta$
below the horizontal. \Part{a} Show that the minimum value of $P$
that will move the crate is given by
\begin{problem*}{6.21}
An object of mass $m=0.500\U{kg}$ is suspended from the ceiling of an
-accelertating truck as shown in Figure P6.21. Taking
+accelertating truck as shown in Figure~P6.21. Taking
$a=3.00\U{m/s$^2$}$, find \Part{a} the angle $\theta$ that the string
makes with the vertical and \Part{b} the tension $T$ in the string.
\begin{center}
\begin{problem*}{6.39}
A string under a tension of $50.0\U{N}$ is used to whirl a rock in a
horizontal circle of radius $2.50\U{m}$ at a speed of $20.4\U{m/s}$ on
-a frictionless surface as shown in Figure P.39. As the string is
+a frictionless surface as shown in Figure~P.39. As the string is
pulled in, the speed of the rock increases. When the string is
$1.00\U{m/s}$ long and the speed of the rock is $51.0\U{m/s}$, the
string breaks. What is the breaking strength, in newtons, of the
\begin{problem*}{8.8}
Two objects are connected by a light string passing over a light,
-frictionless pulley as shown in Figure P8.7. The object of mass $m_1$
+frictionless pulley as shown in Figure~P8.7. The object of mass $m_1$
is released from rest at a height $h$ above the table. Using the
isolated system model, \Part{a} determine the speed of $m_2$ just as
$m_1$ hits the table and \Part{b} find the maximum height above the
\begin{problem*}{8.11}
-The system shown in Figure P8.11 consists of a light, inextensible
+The system shown in Figure~P8.11 consists of a light, inextensible
cord, light, frictionless pulleys, and blocks of equal mass. Notice
that block $B$ is attached to one of the pulleys. The system is
initially held at rest so that the blocks are at the same height above
\begin{problem*}{8.15}
A block of mass $m=2.00\U{kg}$ is attached to a spring of force
-constant $k=500\U{N/m}$ as shown in Figure P8.15. The block is pulled
+constant $k=500\U{N/m}$ as shown in Figure~P8.15. The block is pulled
to a position $x_i=5.00\U{cm}$ to the right of equilibrium and
released from rest. Find the speed the block has as it passes through
equilibrium if \Part{a} the horizontal surface is frictionless
\begin{problem*}{8.22}
The coefficient of friction between the block of mass $m_1=3.00\U{kg}$
-and the surface in Figure P8.22 is $\mu_s=0.400$. The system starts
+and the surface in Figure~P8.22 is $\mu_s=0.400$. The system starts
from rest. What is the speed of the bal of mass $m_2=5.00\U{kg}$ when
it has fallen a distance $h=1.50\U{m}$?
% m1-block-on-table -- pulley -- hanging m2
\begin{problem*}{9.56}
-Figure P9.56 shows three points in the operation of the ballistic
+Figure~P9.56 shows three points in the operation of the ballistic
pendulum discussed in Example 9.6 (and shown in Fig.~9.9b). The
-projectile approaches the pendulum in Figure P9.56a. Figure P9.56b
+projectile approaches the pendulum in Figure~P9.56a. Figure~P9.56b
shows the situation just after the projectile is captured in the
-pendulum. In Figure P9.56c, the pendulum arm has swung upward and
+pendulum. In Figure~P9.56c, the pendulum arm has swung upward and
come to rest at a height $h$ above its initial position. \Part{a}
Prove that the ratio of kinetic energy of the projectile-pendulum
system immediately after the collision to the kenetic energy
\begin{problem*}{10.35}
-Find the net torque on the wheel in Figure P10.35 about the axle
+Find the net torque on the wheel in Figure~P10.35 about the axle
through $O$, taking $a=10.0\U{cm}$ and $b=25.0\U{cm}$.
% 10.0N at a point b N of O, pulling E
% 9.00N at a point b E of O, pulling S
\begin{problem*}{10.44}
-Consider the system shown in Figure P10.44 with $m_1=20.0\U{kg}$,
+Consider the system shown in Figure~P10.44 with $m_1=20.0\U{kg}$,
$m_2=12.5\U{kg}$, $R=0.200\U{m}$, and the mass of the pulley
$M=5.00\U{kg}$. Object $m_2$ is resting on the floor, and object
$m_1$ is $4.00\U{m}$ above the floor when it is released from rest.
light string wrapped around a reel of radius $R=0.250\U{m}$ and mass
$M=3.00\U{kg}$. The reel is a solid disk, free to rotate in a
vertical plane about the horiizontal axis passing through its center
-as shown in Figure P10.51. The suspended object is released from rest
+as shown in Figure~P10.51. The suspended object is released from rest
$6.00\U{m}$ above the floor. Determine \Part{a} the tension in the
string, \Part{b} the acceleration of the object, and \Part{c} the
speed with which the object hits the floor. \Part{d} Verify your
\begin{problem*}{23.17}
A point charge $+2Q$ is at the origin and a point charge $-Q$ is
-located along the $x$ axis at $x=d$ as in Figure P23.17. Find a
+located along the $x$ axis at $x=d$ as in Figure~P23.17. Find a
symbolic expression for the net force on a third point charge $+Q$
located along the $y$ axis at $y=d$.
\begin{center}
\begin{problem*}{23.50}
A small sphere of charge $q_1=0.800\U{$\mu$C}$ hangs from the end of a
-spring as in Figure P23.50a. When another small sphere of charge
+spring as in Figure~P23.50a. When another small sphere of charge
$q_2=-0.600\U{$\mu$C}$ is held beneath the first sphere as in Figure
P23.50b, the spring stretches by $d=3.50\U{cm}$ from its original
length and reaches a new equilibrium position with a separation
\begin{problem*}{23.59}
A charged cork ball of mass $1.00\U{g}$ is suspended on a light string
-in the presence of a uniform electric field as shown in Figure P23.59.
+in the presence of a uniform electric field as shown in Figure~P23.59.
When $\vect{E}=(3.00\ihat+5.00\jhat)\E{5}\U{N/C}$, the ball is in
equilibrium at $\theta=37.0\dg$. Find \Part{a} the charge on the ball
and \Part{b} the tension in the string.
\begin{problem*}{23.62}
Four identical charged particles ($q=+10.0\U{$\mu$C}$) are located on
-the corners of a rectangle as shown in Figure P23.62. The dimensions
+the corners of a rectangle as shown in Figure~P23.62. The dimensions
of the rectangle are $L=60.0\U{cm}$ and $W=15.0\U{cm}$.
Calculate \Part{a} the magnitude and \Part{b} the direction of the
total electric force exerted on the charge at the lower left corner by
\begin{problem*}{24.11}
Four closed surfaces, $S_1$ through $S_4$, together with the charges
-$-2Q$, $Q$, and $-Q$ are sketched in Figure P24.11. (The colored
+$-2Q$, $Q$, and $-Q$ are sketched in Figure~P24.11. (The colored
lines are the intersections of the surfaces with the page.) Find the
electric flux through each surface.
% -2Q
\begin{problem*}{24.21}
-Figure P24.21 represents the top view of a cubic gaussian surface in a
+Figure~P24.21 represents the top view of a cubic gaussian surface in a
uniform electric field \vect{E} oriented parallel to the top and
bottom faces of the cube. The field makes an angle $\theta$ with side
$a$, and the area of each face is $A$. In sumbolic form, find the
positive charge of $Q=3.00\U{$\mu$C}$ uniformly distributed throughout
its volume. Concentric with this sphere is a conducting spherical
shell with inner radius $b=10.0\U{cm}$ and outer radius $c=15.0\U{cm}$
-as shown in Figure P24.51, having net charge $q=-1.00\U{$\mu$C}$.
+as shown in Figure~P24.51, having net charge $q=-1.00\U{$\mu$C}$.
Prepare a graph of the magnitude of the electric field due to this
configuration versus $r$ for $0<r<25.0\U{cm}$.
\end{problem*}
\begin{problem*}{25.36}
An electric field in a region of space is parallel to the $x$ axis.
-The electric potential varies with position as shown in Figure P25.36.
+The electric potential varies with position as shown in Figure~P25.36.
Graph the $x$ component of the electric field versus position in this
region of space.
\begin{center}
\begin{problem*}{29.40}
-Consider the system pictured in Figure P29.40. A $15.0\U{cm}$
+Consider the system pictured in Figure~P29.40. A $15.0\U{cm}$
horizontal wire of mass $15.0\U{g}$ is placed between two thin,
vertical conductors, and a uniform magnetic field acts perpendicular
to the page. The wire is free to move vertically without friction on
\begin{problem*}{30.61}
Two long, straight wires cross each other perpendicularly as shown in
-Figure P30.61. The wires do not touch. Find \Part{a} the magnitude
+Figure~P30.61. The wires do not touch. Find \Part{a} the magnitude
and \Part{b} the direction of the magnetic field at point $P$, which
is in the same plane as the two wires. \Part{c} Find the magnetic
field at a point $30.0\U{cm}$ above the point of intersection of the
\begin{problem*}{30.64}
Two coplanar and concentric circular loops of wire carry currents of
$I_1=5.00\U{A}$ and $I_2=3.00\U{A}$ in opposite directions as in
-Figure P30.64. If $r_1=12.0\U{cm}$ and $r_2=9.00\U{cm}$, what
+Figure~P30.64. If $r_1=12.0\U{cm}$ and $r_2=9.00\U{cm}$, what
are \Part{a} the magnitude and \Part{b} the direction of the magnetic
field at the center of the two loops? \Part{c} Let $r_1$ remain fixed
at $12.0\U{cm}$ and let $r_2$ be variable. Determine the value of
projects / course.git / commitdiff