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Principles of Physics

David Halliday , Robert Resnick , Jearl Walker

Chapter 6

Force and Motion-ll - all with Video Answers

Educators

Chapter Questions

03:14

Problem 1

Figure 6-12 shows a 6.0 kg block on a
60 ramp with a coefficient of static friction of 0.60. A force is applied up the
ramp. What magnitude of that force puts
the block on the verge of sliding down the
ramp?

Sandeep Kumar Dhania
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Numerade Educator
04:35

Problem 2

In a pickup game of dorm shuffleboard, students crazed by final exams use a
broom to propel a calculus book along the
dorm hallway. If the 3.5 kg book is pushed
from rest through a distance of 1.20 m by
the horizontal 25 N force from the broom
and then has a speed of 1.75 m/s, what is
the coefficient of kinetic friction between the book and floor?

Sandeep Kumar Dhania
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06:56

Problem 3

In Fig. 6-13, a 2.0 kg block is placed on top of a 3.0 kg block,
which lies on a frictionless surface. The coefficient of kinetic friction
between the two blocks is 0.30; they are connected via a pulley and a
string.A hanging block of mass 10 kg is connected to the 3.0 kg block
via another pulley and string. Both strings have negligible mass and
both pulleys are frictionless and have negligible mass. When the assembly is released, what are (a) the acceleration magnitude of the
blocks, (b) the tension in string 1, and (c) the tension in string 2?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
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08:21

Problem 4

Figure 6-14 shows a
block of mass m connected
to a block of mass M 2.00
kg, both on 45 inclined
planes where the coefficient
of static friction is 0.28. Find
the (a) minimum and (b)
maximum values of m for
which the system is at rest

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
05:14

Problem 5

A 2.5 kg block is initially
at rest on a horizontal surface. A horizontal force of magnitude 6.0 N and a vertical force are
then applied to the block (Fig. 6-15).
The coefficients of friction for the
block and surface are ms 0.40 and
mk 0.25. Determine the magnitude
of the frictional force acting on
the block if the magnitude of is (a) 8.0 N, (b) 10 N, and (c) 12 N.

Sandeep Kumar Dhania
Sandeep Kumar Dhania
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01:57

Problem 6

A baseball player with mass m 83 kg, sliding into second base,
is retarded by a frictional force of magnitude 485 N. What is the coefficient of kinetic friction mk between the player and the ground?

Sandeep Kumar Dhania
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03:29

Problem 7

A person pushes horizontally with a force of 260 N on a 55 kg
crate to move it across a level floor. The coefficient of kinetic friction is 0.30. What is the magnitude of (a) the frictional force and
(b) the crate’s acceleration?

Sandeep Kumar Dhania
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01:46

Problem 8

The mysterious sliding stones. Along the remote Racetrack
Playa in Death Valley, California, stones sometimes gouge out
prominent trails in the desert floor, as if the stones had been migrating (Fig. 6-16). For years curiosity mounted about why the
stones moved. One explanation was that strong winds during occasional rainstorms would drag the rough stones over ground softened by rain. When the desert dried out, the trails behind the
stones were hard-baked in place. According to measurements, the
coefficient of kinetic friction between the stones and the wet playa
ground is about 0.80. What horizontal force must act on a 20 kg
stone (a typical mass) to maintain the stone’s motion once a gust
has started it moving? (Story continues with Problem 37.)

Averell Hause
Averell Hause
Carnegie Mellon University
04:12

Problem 9

A 3.5 kg block is pushed along a
horizontal floor by a force of
magnitude 15 N at an angle 40
with the horizontal (Fig. 6-17). The
coefficient of kinetic friction between the block and the floor is
0.25. Calculate the magnitudes of
(a) the frictional force on the block
from the floor and (b) the block’s
acceleration.

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
04:02

Problem 10

In Fig. 6-18 a block of weight W
experiences two applied forces, each of
magnitude W/2. What coefficient of
static friction between the block and
the floor puts the block on the verge of
sliding?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
06:18

Problem 11

A 68 kg crate is dragged across a floor by pulling on a rope attached to the crate and inclined 15° above the horizontal. (a) If the
coefficient of static friction is 0.65, what minimum force magnitude
is required from the rope to start the crate moving? (b) If mk
0.35, what is the magnitude of the initial acceleration of the crate?

Sandeep Kumar Dhania
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03:01

Problem 12

In about 1915, Henry Sincosky of
Philadelphia suspended himself from a rafter by
gripping the rafter with the thumb of each hand on
one side and the fingers on the opposite side (Fig.
6-19). Sincosky’s mass was 79 kg. If the coefficient
of static friction between hand and rafter was 0.70,
what was the least magnitude of the normal force
on the rafter from each thumb or opposite fingers?
(After suspending himself, Sincosky chinned himself on the rafter and then moved hand-over-hand
along the rafter. If you do not think Sincosky’s grip
was remarkable, try to repeat his stunt.)

Sandeep Kumar Dhania
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07:13

Problem 13

A worker pushes horizontally on a 35 kg crate
with a force of magnitude 110 N.The coefficient of
static friction between the crate and the floor is
0.37. (a) What is the value of fs,max under the circumstances? (b) Does the crate move? (c) What is
the frictional force on the crate from the floor?
(d) Suppose, next, that a second worker pulls directly upward on the crate to help out. What is the
least vertical pull that will allow the first worker’s 110 N push to
move the crate? (e) If, instead, the second worker pulls horizontally
to help out, what is the least pull that will get the crate moving?

Sandeep Kumar Dhania
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04:59

Problem 14

Figure 6-20 shows the cross
section of a road cut into the side of
a mountain.The solid line AA represents a weak bedding plane along
which sliding is possible. Block B
directly above the highway is separated from uphill rock by a large
crack (called a joint), so that only
friction between the block and the
bedding plane prevents sliding. The
mass of the block is 1.5  107 kg, the dip angle u of the bedding plane
is 24°, and the coefficient of static friction between block and plane is
0.63. (a) Show that the block will not slide under these circumstances.
(b) Next, water seeps into the joint and expands upon freezing, exerting on the block a force parallel to AA . What minim

Sandeep Kumar Dhania
Sandeep Kumar Dhania
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02:44

Problem 15

In Fig. 6-21, a block of mass
m 5.0 kg is at rest on a ramp.The coefficient of static friction between the
block and ramp is not known. Find the
magnitude of the net force exerted
by the ramp on the block.

Sandeep Kumar Dhania
Sandeep Kumar Dhania
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13:46

Problem 16

In Fig. 6-22, a small block of
mass m is sent sliding with velocity v
along a slab of mass 10m, starting at
a distance of l from the far end of
the slab. The coefficient of kinetic
friction between the slab and the
floor is m1; that between the block
and the slab is m2, with m2  11m1. (a)
Find the minimum value of v such that the block reaches the far
end of the slab. (b) For that value of v, how long does the block
take to reach the far end?

Cyra Jelle Calleja
Cyra Jelle Calleja
Numerade Educator
04:17

Problem 17

7 In Fig. 6-23, a force acts on a block weighing 45 N.The block
is initially at rest on a plane inclined at angle u 15 to the horizontal. The positive direction of the x axis is up the plane. Between
block and plane, the coefficient of static friction is ms 0.50 and
the coefficient of kinetic friction
is mk 0.34. In unit-vector notation, what is the frictional force
on the block from the plane when
is (a) (5.0 N) , (b) (8.0 N) ,
and (c) (15 N) ?

Narayan Hari
Narayan Hari
Numerade Educator
06:20

Problem 18

8 You testify as an expert witness in a case involving an accident
in which car A slid into the rear of car B, which was stopped at a red
light along a road headed down a hill (Fig. 6-24). You find that the
slope of the hill is u 12.0°, that the cars were separated by distance d 30.0 m when the driver of car A put the car into a slide (it
lacked any automatic anti-brake-lock system), and that the speed of
car A at the onset of braking was v0 18.0 m/s.With what speed did
car A hit car B if the coefficient of kinetic friction was (a) 0.60 (dry
road surface) and (b) 0.10 (road surface covered with wet leaves)?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
03:09

Problem 19

9 A 12 N horizontal force
pushes a block weighing 5.0 N
against a vertical wall (Fig. 6-25).
The coefficient of static friction between the wall and the block is 0.60,
and the coefficient of kinetic friction
is 0.40. Assume that the block is not
moving initially. (a) Will the block move? (b) In unit-vector notation, what is the force on the block from the wall?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
04:27

Problem 20

0 In Fig. 6-26, a box of Cheerios
(mass mC 1.0 kg) and a box of
Wheaties (mass mW 3.0 kg) are
accelerated across a horizontal surface by a horizontal force applied
to the Cheerios box. The magnitude
of the frictional force on the Cheerios box is 2.0 N, and the magnitude of the frictional force on the Wheaties box is 3.5 N. If the magnitude of is 12 N, what is the magnitude of the force on the
Wheaties box from the Cheerios box?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
05:09

Problem 21

In Fig. 6-27, a 15 kg sled is attached to a 2.0 kg sand box by a
string of negligible mass, wrapped over a pulley of negligible mass
and friction.The coefficient of kinetic friction between the sled andtable top is 0.040. Find (a) the acceleration of the sled and (b) the
tension of the string.

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
06:04

Problem 22

2 In Fig. 6-28a, a sled is held on an inclined plane by a cord
pulling directly up the plane. The sled is to be on the verge
of moving up the plane. In Fig. 6-28b, the magnitude F required
of the cord’s force on the sled is plotted versus a range of values
for the coefficient of static friction ms between sled and plane:
F1 2.0 N, F2 5.0 N, and m2 0.25. At what angle u is the
plane inclined?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
05:46

Problem 23

When the three blocks in
Fig. 6-29 are released from rest, they
accelerate with a magnitude of 0.500
m/s2
. Block 1 has mass M, block 2
has 2M, and block 3 has 2M. What is
the coefficient of kinetic friction between block 2 and the table?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
05:04

Problem 24

A 4.10 kg block is pushed
along a floor by a constant applied
force that is horizontal and has a
magnitude of 50.0 N. Figure 6-30
gives the block’s speed v versus
time t as the block moves along an x
axis on the floor. The scale of the
figure’s vertical axis is set by vs
5.0 m/s. What is the coefficient of
kinetic friction between the block
and the floor?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
05:25

Problem 25

Block B in Fig. 6-31 weighs 750
N. The coefficient of static friction
between block and table is 0.25; angle u is 30°; assume that the cord between B and the knot is horizontal.
Find the maximum weight of block
A for which the system will be stationary

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
07:24

Problem 26

Figure 6-32 shows three crates
being pushed over a concrete floor
by a horizontal force of magnitude 425 N. The masses of the
crates are m1 30.0 kg, m2 10.0
kg, and m3 20.0 kg. The coefficient of kinetic friction between the
floor and each of the crates is 0.700.
(a) What is the magnitude F32 of the
force on crate 3 from crate 2? (b) If
the crates then slide onto a polished
floor, where the coefficient of kinetic friction is less than 0.700, is magnitude F32 more than, less than, or the same as it was when the
coefficient was 0.700?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
04:23

Problem 27

In Fig. 6-33, a 2.0 kg block lies on a 20 kg trolley that can roll
across a floor on frictionless bearings. Between the block and the
trolley, the coefficient of kinetic friction is 0.20 and the coefficient
of static friction is 0.25. When a horizontal 2.0 N force is applied to
the block, what are the magnitudes of (a) the frictional force
between the block and the trolley and (b) the acceleration of the
trolley?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
05:46

Problem 28

In Fig. 6-34, two blocks are
connected over a pulley. The mass
of block A is 15 kg, and the coefficient of kinetic friction between A
and the incline is 0.20. Angle u of
the incline is 30°. Block A slides
down the incline at constant speed.
What is the mass of block B?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
07:09

Problem 29

In Fig. 6-35, block A of mass
2.0 kg, block B of 3.0 kg, and block
C of 6.0 kg are connected by strings
of negligible mass that run over pulleys of negligible mass and friction.
The coefficient of kinetic friction between block B and the table top is
0.40. When the system is released,
the blocks move. What is the magnitude of their acceleration?

Sandeep Kumar Dhania
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Numerade Educator
07:40

Problem 30

A toy chest and its contents
have a combined weight of 200 N. The coefficient of static friction
between toy chest and floor is 0.47. The child in Fig. 6-36 attempts
to move the chest across the floor by pulling on an attached rope.
(a) If u is 42°, what is the magnitude of the force that the child
must exert on the rope to put the chest on the verge of moving? (b)
Write an expression for the magnitude F required to put the chest
on the verge of moving as a function of the angle u. Determine (c)
the value of u for which F is a minimum and (d) that minimum
magnitude.

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
05:40

Problem 31

1 In Fig. 6-37, two blocks, in contact, slide down an inclined plane
AC of inclination 30°. The coefficient of kinetic friction between the
2.0 kg block and the incline is
m1 0.20 and that between the 4.0
kg block and the incline is m2 0.30.
Find the magnitude of the
acceleration.

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
07:04

Problem 32

celeration.
32 A block is pushed across a floor by a constant force that is
applied at downward angle u (Fig. 6-17). Figure 6-38 gives the
acceleration magnitude a versus a range of values for the coefficient of kinetic friction mk between block and floor: a1 3.0 m/s2
,
mk2 0.20, and mk3 0.40.What is the value of u?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
03:39

Problem 33

A 1000 kg boat is traveling at 100 km/h when its engine is shut
off. The magnitude of the frictional force between boat and water is proportional to the speed v of the boat:fk 70v, where v is in
meters per second and fk is in newtons. Find the time required for
the boat to slow to 45 km/h.

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
06:07

Problem 34

4 In Fig. 6-39, a slab of mass
m1 40 kg rests on a frictionless
floor, and a block of mass m2 12 kg
rests on top of the slab. Between
block and slab, the coefficient of
static friction is 0.60, and the coefficient of kinetic friction is 0.40. A horizontal force of magnitude
120 N begins to pull directly on the block, as shown. In unit-vector
notation, what are the resulting accelerations of (a) the block and
(b) the slab?

Averell Hause
Averell Hause
Carnegie Mellon University
02:44

Problem 35

The two blocks (m 16 kg and
M 88 kg) in Fig. 6-40 are not attached to each other. The coefficient
of static friction between the blocks
is ms 0.33, but the surface beneath
the larger block is frictionless. What
is the minimum magnitude of the
horizontal force required to keep
the smaller block from slipping down the larger block?

Averell Hause
Averell Hause
Carnegie Mellon University
01:43

Problem 36

A water droplet 4.0 mm in diameter is falling with a speed of
10 km/h at an altitude of 20 km. Another droplet 6.0 mm in diameter is falling at 25% of that speed and at 25% of that altitude. The
density of air at 20 km is 0.20 kg/m3 and that at 5.0 km is 0.70 kg/m3
.
Assume that the drag coefficient C is the same for the two drops.
Find the ratio of the drag force on the higher drop to that on the
lower drop.

Akshaya Rs
Akshaya Rs
Numerade Educator
02:56

Problem 37

Continuation of Problem 8. Now assume that Eq. 6-14 gives
the magnitude of the air drag force on the typical 20 kg stone,
which presents to the wind a vertical cross-sectional area of 0.040
m2 and has a drag coefficient C of 0.80. Take the air density to be1.21 kg/m3
, and the coefficient of kinetic friction to be 0.80. (a) In
kilometers per hour, what wind speed V along the ground is
needed to maintain the stone’s motion once it has started moving? Because winds along the ground are retarded by the ground,
the wind speeds reported for storms are often measured at a
height of 10 m. Assume wind speeds are 2.00 times those along
the ground. (b) For your answer to (a), what wind speed would be
reported for the storm? (c) Is that value reasonable for a highspeed wind in a storm?

Averell Hause
Averell Hause
Carnegie Mellon University
03:15

Problem 38

8 Assume Eq. 6-14 gives the drag force on a pilot plus ejection
seat just after they are ejected from a plane traveling horizontally
at 1300 km/h. Assume also that the mass of the seat is equal to the
mass of the pilot and that the drag coefficient is that of a sky diver.
Making a reasonable guess of the pilot’s mass and using the
appropriate vt value from Table 6-1, estimate the magnitudes of (a)
the drag force on the pilot  seat and (b) their horizontal deceleration (in terms of g), both just after ejection. (The result of (a)
should indicate an engineering requirement:The seat must include
a protective barrier to deflect the initial wind blast away from the
pilot’s head.)

Keshav Singh
Keshav Singh
Numerade Educator
03:44

Problem 39

Calculate the ratio of the drag force on a jet flying at 1200
km/h at an altitude of 15 km to the drag force on a prop-driven
transport flying at half that speed and altitude. The density of air is
0.38 kg/m3 at 10 km and 0.67 kg/m3 at 5.0 km. Assume that the airplanes have the same effective cross-sectional area and drag coefficient C.

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
05:32

Problem 40

0 In downhill speed skiing a skier is retarded by both the air
drag force on the body and the kinetic frictional force on the skis.
(a) Suppose the slope angle is u 40.0°, the snow is dry snow with a
coefficient of kinetic friction mk 0.0380, the mass of the skier and
equipment is m 85.0 kg, the cross-sectional area of the (tucked)
skier is A 1.30 m2, the drag coefficient is C 0.150, and the air
density is 1.20 kg/m3
. (a) What is the terminal speed? (b) If a skier
can vary C by a slight amount dC by adjusting, say, the hand positions, what is the corresponding variation in the terminal speed?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
04:07

Problem 41

A cat dozes on a stationary merry-go-round, at a radius of 6.0
m from the center of the ride. Then the operator turns on the ride
and brings it up to its proper turning rate of one complete rotation
every 6.0 s. What is the least coefficient of static friction between
the cat and the merry-go-round that will allow the cat to stay in
place, without sliding?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
03:43

Problem 42

Suppose the coefficient of static friction between the road and
the tires on a car is 0.60 and the car has no negative lift.What speed
will put the car on the verge of sliding as it rounds a level curve of
32.0 m radius?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
03:18

Problem 43

What is the smallest radius of an unbanked (flat) track around
which a bicyclist can travel if her speed is 35 km/h and the ms between tires and track is 0.40?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
01:11

Problem 44

During an Olympic bobsled run, the Jamaican team makes a
turn of radius 7.6 m at a speed of 96.6 km/h. What is their acceleration in terms of g?

Averell Hause
Averell Hause
Carnegie Mellon University
05:07

Problem 45

5 A student of weight 667 N rides a steadily rotating Ferris
wheel (the student sits upright). At the highest point, the magnitude of the normal force on the student from the seat is 556 N.
(a) Does the student feel “light” or “heavy” there? (b) What is the
magnitude of at the lowest point? If the wheel’s speed is doubled, what is the magnitude FN at the (c) highest and (d) lowest
point?

Averell Hause
Averell Hause
Carnegie Mellon University
05:10

Problem 46

A police officer in hot pursuit drives her car through a circular
turn of radius 300 m with a constant speed of 75.0 km/h. Her mass is
55.0 kg.What are (a) the magnitude and (b) the angle (relative to vertical) of the net force of the officer on the car seat? (Hint: Consider
both horizontal and vertical forces.)

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
03:33

Problem 47

A circular-motion addict of mass 80 kg rides a Ferris wheel
around in a vertical circle of radius 12 m at a constant speed of 5.5
m/s. (a) What is the period of the motion? What is the magnitude of
the normal force on the addict from the seat when both go through
(b) the highest point of the circular path and (c) the lowest point?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
05:30

Problem 48

A roller-coaster car has a mass of 1300 kg when fully loaded
with passengers. As the car passes over the top of a circular hill of
radius 20 m, its speed is not changing. At the top of the hill, what
are the (a) magnitude FN and (b) direction (up or down) of the
normal force on the car from the track if the car’s speed is v 11
m/s? What are (c) FN and (d) the direction if v 14 m/s?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
01:45

Problem 49

In Fig. 6-41, a car is driven at constant speed over a circular
hill and then into a circular valley with the same radius. At the top
of the hill, the normal force on the driver from the car seat is 0.The
driver’s mass is 80.0 kg. What is the magnitude of the normal force
on the driver from the seat when the car passes through the bottom
of the valley?

Averell Hause
Averell Hause
Carnegie Mellon University
03:55

Problem 50

An 85.0 kg passenger is made to move along a circular path of
radius r 3.50 m in uniform circular motion. (a) Figure 6-42a is a
plot of the required magnitude F of the net centripetal force for a
range of possible values of the passenger’s speed v. What is the
plot’s slope at v 8.30 m/s? (b) Figure 6-42b is a plot of F for a
range of possible values of T, the period of the motion. What is the
plot’s slope at T 2.50 s?

Keshav Singh
Keshav Singh
Numerade Educator
01:52

Problem 51

An airplane is flying in a horizontal circle at a speed of 600
km/h (Fig. 6-43). If its wings are tilted at angle 40° to the horizontal, what is the radius of the circle in which the plane is flying?
Assume that the required force is provided entirely by an “aerodynamic lift” that is perpendicular to the wing surface.

Averell Hause
Averell Hause
Carnegie Mellon University
03:34

Problem 52

An amusement park ride consists of a car moving in a vertical
circle on the end of a rigid boom of negligible mass. The combined
weight of the car and riders is 6.0 kN, and the circle’s radius is 10 m.
At the top of the circle, what are the (a) magnitude FB and (b) direction (up or down) of the force on the car from the boom if the
car’s speed is v 5.0 m/s? What are (c) FB and (d) the direction if
v 12 m/s?

Alex Garger
Alex Garger
Numerade Educator
03:42

Problem 53

An old streetcar rounds a flat corner of radius 10.5 m, at 16
km/h. What angle with the vertical will be made by the loosely
hanging hand straps?

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
03:03

Problem 54

In designing circular rides for amusement parks, mechanical
engineers must consider how small variations in certain parameters can alter the net force on a passenger. Consider a passenger of
mass m riding around a horizontal circle of radius r at speed v.
What is the variation dF in the net force magnitude for (a) a variation dr in the radius with v held constant, (b) a variation dv in the
speed with r held constant, and (c) a variation dT in the period
with r held constant?

Averell Hause
Averell Hause
Carnegie Mellon University
01:18

Problem 55

A bolt is threaded onto one
end of a thin horizontal rod, and
the rod is then rotated horizontally
about its other end. An engineer
monitors the motion by flashing a
strobe lamp onto the rod and bolt,
adjusting the strobe rate until the
bolt appears to be in the same eight
places during each full rotation of
the rod (Fig. 6-44).The strobe rate is
2000 flashes per second; the bolt has
mass 33 g and is at radius 4.0 cm.What is the magnitude of the force
on the bolt from the rod?

Averell Hause
Averell Hause
Carnegie Mellon University
06:08

Problem 56

A banked circular highway curve is designed for traffic moving at 65 km/h. The radius of the curve is 200 m. Traffic is moving
along the highway at 40 km/h on a rainy day.What is the minimum
coefficient of friction between tires
and road that will allow cars to take
the turn without sliding off the
road? (Assume the cars do not have
negative lift.)

Sandeep Kumar Dhania
Sandeep Kumar Dhania
Numerade Educator
01:13

Problem 57

A puck of mass m 1.50 kg
slides in a circle of radius r 25.0
cm on a frictionless table while attached to a hanging cylinder of mass
M 2.50 kg by means of a cord that
extends through a hole in the table
(Fig. 6-45). What speed keeps the
cylinder at rest?

Averell Hause
Averell Hause
Carnegie Mellon University
04:44

Problem 58

Brake or turn? Figure 6-46 depicts an overhead view of a car’s
path as the car travels toward a wall.
Assume that the driver begins to
brake the car when the distance to
the wall is d 107 m, and take the
car’s mass as m 1400 kg, its initial
speed as v0 35 m/s, and the coefficient of static friction as ms 0.50.
Assume that the car’s weight is distributed evenly on the four wheels,
even during braking. (a) What magnitude of static friction is needed (between tires and road) to stop
the car just as it reaches the wall? (b) What is the maximum possible static friction fs,max? (c) If the coefficient of kinetic friction between the (sliding) tires and the road is mk 0.40, at what speed
will the car hit the wall? To avoid the crash, a driver could elect to
turn the car so that it just barely misses the wall, as shown in the figure. (d) What magnitude of frictional force would be required to
keep the car in a circular path of radius d and at the given speed v0,
so that the car moves in a quarter circle and then parallel to the
wall? (e) Is the required force less than fs,max so that a circular path
is possible?

Averell Hause
Averell Hause
Carnegie Mellon University
05:14

Problem 59

In Fig. 6-47, a 1.34 kg ball is connected by means of two massless strings,
each of length L 1.70 m, to a vertical,
rotating rod. The strings are tied to the
rod with separation d 1.70 m and are
taut. The tension in the upper string is
35 N.What are the (a) tension in the lower
string, (b) magnitude of the net force
on the ball, and (c) speed of the ball? (d)
What is the direction of ?

Keshav Singh
Keshav Singh
Numerade Educator