Technical Measurements and Forces

Chapter 1: Technical Measurement and Vector
5. Newton’s law of universal gravitation is the positive x-axis. Find the magnitude and
represented by direction of the second displacement.
Mm
F =G 35. In Figure P1.35, find (a) the side opposite θ,
r2
(b) the side adjacent to φ, (c) cos θ, (d) sin φ,
where F is the gravitational force, M and m
and (e) tan φ.
are masses, and r is a length. Force has the SI
units kg ∙ m/s2. What are the SI units of the
proportionality constant G?

8. The speed of light is now defined to be 2.99
7924 58 × 108 m/s. Express the speed of light
to (a) three significant figures, (b) five
significant figures, and (c) seven significant
figures.
Figure P1.35
15. A rectangular building lot measures 100 ft by
9. A girl delivering newspapers covers her route
150 ft. Determine the area of this lot in square
by traveling 3.00 blocks west, 4.00 blocks
meters (m2).
north, and then 6.00 blocks east. (a) What is
her resultant displacement? (b) What is the
19. The speed of light is about 3.00 × 10 8 m/s.
total distance she travels?
Convert this figure to miles per hour.
14. The helicopter view in Figure P3.14 shows
22. (a) Find a conversion factor to convert from
two people pulling on a stubborn mule. Find
miles per hour to kilometers per hour. (b) For
(a) the single force that is equivalent to the
a while, federal law mandated that the
two forces shown and (b) the force that a
maximum highway speed would be 55 mi/h.
third person would have to exert on the mule
Use the conversion factor from part (a) to find
to make the net force equal to zero. The forces
the speed in kilometers per hour. (c) The
are measured in units of newtons (N).
maximum highway speed has been raised to
65 mi/h in some places. In kilometers per
hour, how much of an increase is this over the
55-mi/h limit?

5. A plane flies from base camp to lake A, a
distance of 280 km at a direction of 20.0°
north of east. After dropping off supplies, the
plane flies to lake B, which is 190 km and
30.0° west of north from lake A. Graphically
determine the distance and direction from
lake B to the base camp.

6. Vector A has a magnitude of 8.00 units and
makes an angle of 45.0° with the positive x-

axis. Vector B also has a magnitude of 8.00
units and is directed along the negative x-
axis. Using graphical methods, find (a) the
 
vector sum A + B and (b) the vector
  Figure P3.14
difference A – B .

15. A man pushing a mop across a floor causes
the mop to undergo two displacements. The
first has a magnitude of 150 cm and makes an
angle of 120° with the positive x-axis. The
resultant displacement has a magnitude of
140 cm and is directed at an angle of 35.0° to

1

Chapter 2: Translational Equilibrium and Friction

1. A 6.0-kg object undergoes an acceleration of with the horizontal? (b) What normal force
2.0 m/s2. (a) What is the magnitude of the does the ground exert on the suitcase?
resultant force acting on it? (b) If this same
force is applied to a 4.0-kg object, what
acceleration is produced?

13. A 150-N bird feeder is supported by three
cables as shown in Figure P4.13. Find the
tension in each cable.

Figure P4.34

35. The coefficient of static friction between the
3.00-kg crate and the 35.0° incline of Figure

P4.35 is 0.300. What minimum force F must
Figure P4.13
be applied to the crate perpendicular to the
incline to prevent the crate from sliding down
14. The leg and cast in Figure P4.14 weigh 220 N
the incline?
(w1). Determine the weight w2 and the angle α
needed so that no force is exerted on the hip
joint by the leg plus the cast.

Figure P4.35

29. A dockworker loading crates on a ship finds 42. A 2.00-kg block is held in equilibrium on an
that a 20-kg crate, initially at rest on a incline of angle θ = 60.0° by a horizontal force

horizontal surface, requires a 75-N horizontal F applied in the direction shown in Figure
force to set it in motion. However, after the P4.42. If the coefficient of static friction
crate is in motion, a horizontal force of 60 N is between block and incline is μs = 0.300,
required to keep it moving with a constant determine (a) the minimum value of and (b)
speed. Find the coefficients of static and the normal force exerted by the incline on the
kinetic friction between crate and floor. block.

34. A woman at an airport is towing her 20.0-kg
suitcase at constant speed by pulling on a
strap at an angle θ above the horizontal (Fig.
P4.34). She pulls on the strap with a 35.0-N
force, and the friction force on the suitcase is
20.0 N. Draw a free-body diagram of the
suitcase. (a) What angle does the strap make
Figure P4.42

45. (a) What is the resultant force exerted by the
two cables supporting the traffic light in
Figure P4.45? (b) What is the weight of the
light?

Chapter 3: Torque and Rotational Equilibrium

1. If the torque required to loosen a nut that is
holding a flat tire in place on a car has a
magnitude of 40.0 N ∙ m, what minimum force
must be exerted by the mechanic at the end of
a 30.0-cm lug wrench to accomplish the task?

3. Calculate the net torque (magnitude and
direction) on the beam in Figure P8.3 about
(a) an axis through O perpendicular to the
page and (b) an axis through C perpendicular
to the page.

17. A 500-N uniform rectangular sign 4.00 m
wide and 3.00 m high is suspended from a
horizontal, 6.00-m-long, uniform, 100-N rod
as indicated in Figure P8.17. The left end of
the rod is supported by a hinge, and the right
end is supported by a thin cable making a
30.0° angle with the vertical. (a) Find the
tension T in the cable. (b) Find the horizontal
and vertical components of force exerted on
the left end of the rod by the hinge.
4. Write the necessary equations of equilibrium
of the object shown in Figure P8.4. Take the
origin of the torque equation about an axis
perpendicular to the page through the point
O.

20. A 20.0-kg floodlight in a park is supported at
the end of a horizontal beam of negligible
mass that is hinged to a pole, as shown in
Figure P8.20. A cable at an angle of 30.0° with
9. A cook holds a 2.00-kg carton of milk at arm’s the beam helps to support the light. Find (a)
 the tension in the cable and (b) the horizontal
length (Fig. P8.9). What force FB must be
and vertical forces exerted on the beam by the
exerted by the biceps muscle? (Ignore the pole.
weight of the forearm.)

21. A uniform plank of length 2.00 m and mass
30.0 kg is supported by three ropes, as
indicated by the blue vectors in Figure P8.21.
Find the tension in each rope when a 700-N
person is 0.500 m from the left end.

26. One end of a uniform 4.0-m-long rod of
weight w is supported by a cable. The other
end rests against a wall, where it is held by
friction. (See Fig. P8.26.) The coefficient of
static friction between the wall and the rod is
μs = 0.50. Determine the minimum distance x
from point A at which an additional weight w
(the same as the weight of the rod) can be
hung without causing the rod to slip at point
A.

Chapter 4: Uniform Acceleration and Circular Motion

5. A motorist drives north for 35.0 minutes at acceleration does the aircraft require if it is to
85.0 km/h and then stops for 15.0 minutes. be airborne after a takeoff run of 240 m? (b)
He then continues north, traveling 130 km in How long does it take the aircraft to become
2.00 h. (a) What is his total displacement? (b) airborne?
What is his average velocity?
34. It is possible to shoot an arrow at a speed as
6. A graph of position versus time for a certain high as 100 m/s. (a) If friction is neglected,
particle moving along the x-axis is shown in how high would an arrow launched at this
Figure P2.6. Find the average velocity in the speed rise if shot straight up? (b) How long
time intervals from (a) 0 to 2.00 s, (b) 0 to 4.00 would the arrow be in the air?
s, (c) 2.00 s to 4.00 s, (d) 4.00 s to 7.00 s, and (e)
0 to 8.00 s. 37. A small mailbag is released from a helicopter
that is descending steadily at 1.50 m/s. After
2.00 s, (a) what is the speed of the mailbag,
and (b) how far is it below the helicopter? (c)
What are your answers to parts (a) and (b) if
the helicopter is rising steadily at 1.50 m/s?

39. A student throws a set of keys vertically
upward to his fraternity brother, who is in a
window 4.00 m above. The brother’s
outstretched hand catches the keys 1.50 s
later. (a) With what initial velocity were the
keys thrown? (b) What was the velocity of the
keys just before they were caught?

21. A brick is thrown upward from the top of a
12. A race car moves such that its position fits the building at an angle of 25° to the horizontal
relationship and with an initial speed of 15 m/s. If the
x = (5.0 m/s)t + (0.75 m/s3)t3 brick is in flight for 3.0 s, how tall is the
building?
where x is measured in meters and t in
seconds. (a) Plot a graph of the car’s position
24. A fireman 50.0 m away from a burning
versus time. (b) Determine the instantaneous building directs a stream of water from a
velocity of the car at t = 4.0 s, using time
ground-level fire hose at an angle of 30.0°
intervals of 0.40 s, 0.20 s, and 0.10 s. (c) above the horizontal. If the speed of the
Compare the average velocity during the first
stream as it leaves the hose is 40.0 m/s, at
4.0 s with the results of (b). what height will the stream of water strike
the building?
13. Find the instantaneous velocities of the tennis
player of Figure P2.13 at (a) 0.50 s, (b) 2.0 s, (c)
25. A projectile is launched with an initial speed
3.0 s, and (d) 4.5 s. of 60.0 m/s at an angle of 30.0° above the
horizontal. The projectile lands on a hillside
4.00 s later. Neglect air friction. (a) What is the
projectile’s velocity at the highest point of its
trajectory? (b) What is the straight-line
distance from where the projectile was
launched to where it hits its target?

25. A Cessna aircraft has a lift-off speed of 120
km/h. (a) What minimum constant

Chapter 5: Work, Energy and Power

1. A weight lifter lifts a 350-N set of weights 26. A 0.400-kg bead slides on a curved wire,
from ground level to a position over his head, starting from rest at point in Figure P5.26.
a vertical distance of 2.00 m. How much work If the wire is frictionless, find the speed of the
does the weight lifter do, assuming he moves bead (a) at and (b) at .
the weights at constant speed?

5. A sledge loaded with bricks has a total mass
of 18.0 kg and is pulled at constant speed by a
rope inclined at 20.0° above the horizontal.
The sledge moves a distance of 20.0 m on a
horizontal surface. The coefficient of kinetic
friction between the sledge and surface is
0.500. (a) What is the tension in the rope? (b)
How much work is done by the rope on the
sledge? (c) What is the mechanical energy lost
due to friction?
40. A skier of mass 70 kg is pulled up a slope by a
7. A mechanic pushes a 2.50 × 103-kg car from motor-driven cable. (a) How much work is
rest to a speed of v, doing 5 000 J of work in required to pull him 60 m up a 30° slope
the process. During this time, the car moves (assumed frictionless) at a constant speed of
25.0 m. Neglecting friction between car and 2.0 m/s? (b) What power must a motor have
road, find (a) v and (b) the horizontal force to perform this task?
exerted on the car.
43. The electric motor of a model train accelerates
14. A 0.60-kg particle has a speed of 2.0 m/s at the train from rest to 0.620 m/s in 21.0 ms.
point A and a kinetic energy of 7.5 J at point The total mass of the train is 875 g. Find the
B. What is (a) its kinetic energy at A? (b) its average power delivered to the train during
speed at point B? (c) the total work done on its acceleration.
the particle as it moves from A to B?
46. A 650-kg elevator starts from rest and moves
15. A 2 000-kg car moves down a level highway upwards for 3.00 s with constant acceleration
under the actions of two forces: a 1 000-N until it reaches its cruising speed, 1.75 m/s.
forward force exerted on the drive wheels by (a) What is the average power of the elevator
the road and a 950-N resistive force. Use the motor during this period? (b) How does this
work–energy theorem to find the speed of the amount of power compare with its power
car after it has moved a distance of 20 m, during an upward trip with constant speed?
assuming that it starts from rest.

21. A daredevil on a motorcycle leaves the end of
a ramp with a speed of 35.0 m/s as in Figure
P5.21. If his speed is 33.0 m/s when he
reaches the peak of the path, what is the
maximum height that he reaches? Ignore
friction and air resistance.

Chapter 6: Impulse and Momentum

1. A ball of mass 0.150 kg is dropped from rest
from a height of 1.25 m. It rebounds from the
floor to reach a height of 0.960 m. What
impulse was given to the ball by the floor?

3. Calculate the magnitude of the linear
momentum for the following cases: (a) a
proton with mass 1.67 × 10 –27 kg, moving with
a speed of 5.00 × 10 6 m/s; (b) a 15.0-g bullet
moving with a speed of 300 m/s; (c) a 75.0-kg
sprinter running with a speed of 10.0 m/s; (d)
the Earth (mass = 5.98 × 1024 kg) moving with 20. A rifle with a weight of 30 N fires a 5.0-g
an orbital speed equal to 2.98 × 104 m/s. bullet with a speed of 300 m/s. (a) Find the
recoil speed of the rifle. (b) If a 700-N man
10. A 0.500-kg football is thrown toward the east holds the rifle firmly against his shoulder,
with a speed of 15.0 m/s. A stationary find the recoil speed of the man and rifle.
receiver catches the ball and brings it to rest
in 0.020 0 s. (a) What is the impulse delivered 32. (a) Three carts of masses 4.0 kg, 10 kg, and 3.0
to the ball as it’s caught? (b) What is the kg move on a frictionless horizontal track
average force exerted on the receiver? with speeds of 5.0 m/s, 3.0 m/s, and 4.0 m/s,
as shown in Figure P6.32. The carts stick
11. The force shown in the force vs. time diagram together after colliding. Find the final velocity
in Figure P6.11 acts on a 1.5-kg object. Find of the three carts. (b) Does your answer
(a) the impulse of the force, (b) the final require that all carts collide and stick together
velocity of the object if it is initially at rest, at the same time?
and (c) the final velocity of the object if it is
initially moving along the x-axis with a
velocity of –2.0 m/s.

35. A 25.0-g object moving to the right at 20.0
cm/s overtakes and collides elastically with a
10.0-g object moving in the same direction at
15.0 cm/s. Find the velocity of each object
after the collision

13. The forces shown in the force vs. time
diagram in Figure P6.13 act on a 1.5-kg
particle. Find (a) the impulse for the interval
from t = 0 to t = 3.0 s and (b) the impulse for
the interval from t = 0 to t = 5.0 s. (c) If the
forces act on a 1.5-kg particle that is initially
at rest, find the particle’s speed at t = 3.0 s and
at t = 5.0 s.

Chapter 7: Rotation of Rigid Bodies

1. The tires on a new compact car have a
diameter of 2.0 ft and are warranted for 60
000 miles. (a) Determine the angle (in radians)
through which one of these tires will rotate
during the warranty period. (b) How many
revolutions of the tire are equivalent to your
answer in (a)?

2. A wheel has a radius of 4.1 m. How far (path
length) does a point on the circumference
travel if the wheel is rotated through angles
of 30°, 30 rad, and 30 rev, respectively?

3. Find the angular speed of Earth about the Sun
in radians per second and degrees per day.

4. A potter’s wheel moves from rest to an
angular speed of 0.20 rev/s in 30 s. Find its
angular acceleration in radians per second
per second.

5. A dentist’s drill starts from rest. After 3.20 s
of constant angular acceleration, it turns at a
rate of 2.51 × 104 rev/min. (a) Find the drill’s
angular acceleration. (b) Determine the angle
(in radians) through which the drill rotates
during this period.

6. A centrifuge in a medical laboratory rotates at
an angular speed of 3 600 rev/min. When
switched off, it rotates through 50.0
revolutions before coming to rest. Find the
constant angular acceleration of the
centrifuge.

7. A machine part rotates at an angular speed of
0.60 rad/s; its speed is then increased to 2.2
rad/s at an angular acceleration of 0.70
rad/s2. Find the angle through which the part
rotates before reaching this final speed.

12. A coin with a diameter of 2.40 cm is dropped
on edge onto a horizontal surface. The coin
starts out with an initial angular speed of 18.0
rad/s and rolls in a straight line without
slipping. If the rotation slows with an angular
acceleration of magnitude 1.90 rad/s 2, how
far does the coin roll before coming to rest?

13. A rotating wheel requires 3.00 s to rotate 37.0
revolutions. Its angular velocity at the end of
the 3.00-s interval is 98.0 rad/s. What is the
constant angular acceleration of the wheel?

Chapter 8: The Electric Force

1. A charge of 4.5 × 10−9 C is located 3.2 m from
a charge of −2.8 × 10−9 C. Find the electrostatic
force exerted by one charge on the other.

3. An alpha particle (charge = +2.0e) is sent at
high speed toward a gold nucleus (charge =
+79e). What is the electrical force acting on
the alpha particle when it is 2.0 × 10 −14 m from
the gold nucleus?

5. The nucleus of 8Be, which consists of 4
protons and 4 neutrons, is very unstable and
spontaneously breaks into two alpha particles
(helium nuclei, each consisting of 2 protons
and 2 neutrons). (a) What is the force between Figure P15.12
the two alpha particles when they are 5.00 ×
10−15 m apart, and (b) what will be the 13. Two small metallic spheres, each of mass 0.20
magnitude of the acceleration of the alpha g, are suspended as pendulums by light
particles due to this force? Note that the mass strings from a common point as shown in
of an alpha particle is 4.0026 u. Figure P15.13. The spheres are given the same
electric charge, and it is found that they come
8. An electron is released a short distance above to equilibrium when each string is at an angle
the surface of the Earth. A second electron of 5.0° with the vertical. If each string is 30.0
directly below it exerts an electrostatic force cm long, what is the magnitude of the charge
on the first electron just great enough to on each sphere?
cancel the gravitational force on it. How far
below the first electron is the second?

9. Two identical conducting spheres are placed
with their centers 0.30 m apart. One is given a
charge of 12 × 10−9 C, the other a charge of
−18 × 10−9 C. (a) Find the electrostatic force
exerted on one sphere by the other. (b) The
spheres are connected by a conducting wire.
Find the electrostatic force between the two
after equilibrium is reached.

10. Calculate the magnitude and direction of the
Coulomb force on each of the three charges Figure P15.13
shown in Figure P15.10.

Figure P15.10 (Problems 10 and 18)

12. Three charges are arranged as shown in
Figure P15.12. Find the magnitude and
direction of the electrostatic force on the 6.00-
nC charge.

Chapter 9: The Electric Field

15. An object with a net charge of 24 μC is placed magnitude E = 6.2 × 105 N/C. Determine the
in a uniform electric field of 610 N/C, electric flux through this area (a) when the
directed vertically. What is the mass of the electric field is perpendicular to the surface
object if it “floats” in the electric field? and (b) when the electric field is parallel to
the surface.
17. An airplane is flying through a thundercloud
at a height of 2 000 m. (This is a very 29. An electric field of intensity 3.50 kN/C is
dangerous thing to do because of updrafts, applied along the x-axis. Calculate the electric
turbulence, and the possibility of electric flux through a rectangular plane 0.350 m
discharge.) If there are charge concentrations wide and 0.700 m long if (a) the plane is
of +40.0 C at a height of 3 000 m within the parallel to the yz-plane; (b) the plane is
cloud and −40.0 C at a height of 1000 m, what parallel to the xy-plane; and (c) the plane

is the electric field E at the aircraft? contains the y-axis, and its normal makes an
angle of 40.0° with the x-axis.
21. A proton accelerates from rest in a uniform
electric field of 640 N/C. At some later time, 31. A 40-cm-diameter loop is rotated in a uniform
its speed is 1.20 × 10 6 m/s. (a) Find the electric field until the position of maximum
magnitude of the acceleration of the proton. electric flux is found. The flux in that position
(b) How long does it take the proton to reach is measured to be 5.2 × 10 5 N·m2/C. Calculate
this speed? (c) How far has it moved in that the electric field strength in this region.
interval? (d) What is its kinetic energy at the
later time? 32. A point charge of +5.00 μC is located at the
center of a sphere with a radius of 12.0 cm.
22. Three charges are at the corners of an Determine the electric flux through the
equilateral triangle, as shown in Figure surface of the sphere.
P15.22. Calculate the electric field at a point
midway between the two charges on the x- 33. A point charge q is located at the center of a
axis. spherical shell of radius a that has a charge −q
uniformly distributed on its surface. Find the
electric field (a) for all points outside the
spherical shell and (b) for a point inside the
shell a distance r from the center.

Figure P15.22

23. In Figure P15.23, determine the point (other
than infinity) at which the total electric field is
zero.

Figure P15.23

28. A flat surface having an area of 3.2 m2 is
rotated in a uniform electric field of

Chapter 10: Electric Potential

1. A proton moves 2.00 cm parallel to a uniform
electric field of E = 200 N/C. (a) How much
work is done by the field on the proton? (b)
What change occurs in the potential energy of
the proton? (c) What potential difference did
the proton move through?

2. A uniform electric field of magnitude 250
V/m is directed in the positive x-direction. A
12-μC charge moves from the origin to the
point (x, y) = (20 cm, 50 cm). (a) What was the Figure P16.11 (Problems 11 and 12)
change in the potential energy of this charge?
12. Three charges are situated at corners of a
(b) Through what potential difference did the
rectangle as in Figure P16.11. How much
charge move?
energy would be expended in moving the
5. The potential difference between the 8.00-μC charge to infinity?
accelerating plates of a TV set is about 25 kV.
14. A point charge of 9.00 × 10−9 C is located at
If the distance between the plates is 1.5 cm,
the origin. How much work is required to
find the magnitude of the uniform electric
bring a positive charge of 3.00 × 10 −9 C from
field in the region between the plates.
infinity to the location x = 30.0 cm?
6. To recharge a 12-V battery, a battery charger
17. In Rutherford’s famous scattering
must move 3.6 × 105 C of charge from the
experiments that led to the planetary model
negative terminal to the positive terminal.
of the atom, alpha particles (having charges
How much work is done by the charger?
of +2e and masses of 6.64 × 10 −27 kg) were
Express your answer in joules.
fired toward a gold nucleus with charge +79e.
An alpha particle, initially very far from the
7. Oppositely charged parallel plates are
gold nucleus, is fired at 2.00 × 10 7 m/s
separated by 5.33 mm. A potential difference
directly toward the nucleus, as in Figure
of 600 V exists between the plates. (a) What is
P16.17. How close does the alpha particle get
the magnitude of the electric field between
to the gold nucleus before turning around?
the plates? (b) What is the magnitude of the
Assume the gold nucleus remains stationary.
force on an electron between the plates? (c)
How much work must be done on the
electron to move it to the negative plate if it is
initially positioned 2.90 mm from the positive
plate?

9. (a) Find the electric potential 1.00 cm from a
proton. (b) What is the electric potential
difference between two points that are 1.00
cm and 2.00 cm from a proton?
Figure P16.17
11. (a) Find the electric potential, taking zero at
infinity, at the upper right corner (the corner
without a charge) of the rectangle in Figure
P16.11. (b) Repeat if the 2.00-μC charge is
replaced with a charge of −2.00 μC.

Chapter 11: Capacitance

20. (a) How much charge is on each plate of a 29. (a) Find the equivalent capacitance of the
4.00-μF capacitor when it is connected to a group of capacitors in Figure P16.29. (b) Find
12.0-V battery? (b) If this same capacitor is the charge on each capacitor and the potential
connected to a 1.50-V battery, what charge is difference across it.
stored?

22. The potential difference between a pair of
oppositely charged parallel plates is 400 V. (a)
If the spacing between the plates is doubled
without altering the charge on the plates,
what is the new potential difference between
the plates? (b) If the plate spacing is doubled
while the potential difference between the
plates is kept constant, what is the ratio of the
final charge on one of the plates to the
original charge?

23. An air-filled capacitor consists of two parallel
Figure P16.29
plates, each with an area of 7.60 cm2 and
separated by a distance of 1.80 mm. If a 20.0-
31. Four capacitors are connected as shown in
V potential difference is applied to these
Figure P16.31. (a) Find the equivalent
plates, calculate (a) the electric field between
capacitance between points a and b. (b)
the plates, (b) the capacitance, and (c) the
Calculate the charge on each capacitor if a
charge on each plate.
15.0-V battery is connected across points a
and b.
24. A 1-megabit computer memory chip contains
many 60.0 × 10−15-F capacitors. Each capacitor
has a plate area of 21.0 × 10−12 m2. Determine
the plate separation of such a capacitor.
(Assume a parallel-plate configuration). The
diameter of an atom is on the order of 10 −10 m
= 1 Å. Express the plate separation in
angstroms.

25. A parallel-plate capacitor has an area of 5.00
cm2, and the plates are separated by 1.00 mm
with air between them. The capacitor stores a
charge of 400 pC. (a) What is the potential
Figure P16.31
difference across the plates of the capacitor?
(b) What is the magnitude of the uniform
electric field in the region between the plates?

27. A series circuit consists of a 0.050-μF
capacitor, a 0.100-μF capacitor, and a 400-V
battery. Find the charge (a) on each of the
capacitors and (b) on each of the capacitors if
they are reconnected in parallel across the
battery.

28. Three capacitors, C1 = 5.00 μF, C2 = 4.00 μF,
and C3 = 9.00 μF, are connected together. Find
the effective capacitance of the group (a) if
they are all in parallel, and (b) if they are all
in series.

Chapter 12: Current and Resistance

13. Calculate the diameter of a 2.0-cm length of
tungsten filament in a small lightbulb if its 8. (a) Find the equivalent resistance of the
resistance is 0.050 Ω. circuit in Figure P18.8. (b) If the total power
supplied to the circuit is 4.00 W, find the emf
15. A potential difference of 12 V is found to of the battery.
produce a current of 0.40 A in a 3.2-m length
of wire with a uniform radius of 0.40 cm.
What is (a) the resistance of the wire? (b) the
resistivity of the wire?

17. A wire 50.0 m long and 2.00 mm in diameter
is connected to a source with a potential
difference of 9.11 V, and the current is found
to be 36.0 A. Assume a temperature of 20°C,
and, using Table 17.1, identify the metal out
of which the wire is made.

28. If electrical energy costs 12 cents, or $0.12, per
kilowatt-hour, how much does it cost to (a)
burn a 100-W lightbulb for 24 h? (b) operate
an electric oven for 5.0 h if it carries a current
Figure P18.8
of 20.0 A at 220 V?
9. Consider the circuit shown in Figure P18.9.
35. A copper cable is designed to carry a current
Find (a) the current in the 20.0-Ω resistor and
of 300 A with a power loss of 2.00 W/m.
(b) the potential difference between points a
What is the required radius of this cable?
and b.
1. A battery having an emf of 9.00 V delivers 117
mA when connected to a 72.0-Ω load.
Determine the internal resistance of the
battery.

2. A 4.0-Ω resistor, an 8.0-Ω resistor, and a 12-Ω
resistor are connected in series with a 24-V
battery. What are (a) the equivalent resistance
and (b) the current in each resistor? (c) Repeat
for the case in which all three resistors are
connected in parallel across the battery.
Figure P18.9
5. (a) Find the equivalent resistance between
points a and b in Figure P18.5. (b) Calculate
the current in each resistor if a potential
difference of 34.0 V is applied between points
a and b.

Figure P18.5

Chapter 13: Magnetism and the Magnetic Field

1. An electron gun fires electrons into a
magnetic field directed straight downward.
Find the direction of the force exerted by the
field on an electron for each of the following
directions of the electron’s velocity: (a)
horizontal and due north; (b) horizontal and
30° west of north; (c) due north, but at 30°
below the horizontal; (d) straight upward.
(Remember that an electron has a negative Figure P19.3 (Problems 3 and 13) For Problem 13,
charge.) replace the velocity vector with a current in that
direction.
2. (a) Find the direction of the force on a proton
(a positively charged particle) moving 5. At the equator, near the surface of Earth, the
through the magnetic fields in Figure P19.2, magnetic field is approximately 50.0 μT
as shown. (b) Repeat part (a), assuming the northward, and the electric field is about 100
moving particle is an electron. N/C downward in fair weather. Find the
gravitational, electric, and magnetic forces on
an electron with an instantaneous velocity of
6.00 × 106 m/s directed to the east in this
environment.

6. The magnetic field of the Earth at a certain
location is directed vertically downward and
has a magnitude of 50.0 μT. A proton is
moving horizontally toward the west in this
field with a speed of 6.20 × 106 m/s. What are
the direction and magnitude of the magnetic
force the field exerts on the proton?

7. What velocity would a proton need to circle
Earth 1 000 km above the magnetic equator,
where Earth’s magnetic field is directed
horizontally north and has a magnitude of
4.00 × 10−8 T?

8. An electron is accelerated through 2 400 V
from rest and then enters a region where
there is a uniform 1.70-T magnetic field. What
are (a) the maximum and (b) the minimum
magnitudes of the magnetic force acting on
Figure P19.2 (Problems 2 and 12) For Problem 12, this electron?
replace the velocity vector with a current in that
direction. 9. A proton moves perpendicularly to a uniform

3. Find the direction of the magnetic field acting magnetic field B at 1.0 × 107 m/s and
on the positively charged particle moving in exhibits an acceleration of 2.0 × 1013 m/s2 in
the various situations shown in Figure P19.3 the +x-direction when its velocity is in the +z-
if the direction of the magnetic force acting on direction. Determine the magnitude and
it is as indicated. direction of the field.

Technical Measurements and Forces

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Technical Measurements and Forces

Similar to Technical Measurements and Forces (11)

Technical Measurements and Forces