Download Assignment 1 Chapter 8: Planar Forces

Chapter 8: Planar Forces
Assignment 1
Vectors and Net Forces (a)
1
The forces acting on a sailboat are 390 N north and 180 N
3
A dog pulls on a pillow with a force of 5 N at an angle of
0
east. If the boat (including crew) has a mass of 270 kg,
37 above the horizontal.
(a) Draw a free body diagram of the forces on the sailboat.
(a) Draw a free body diagram of the forces on the pillow
(b) What are the magnitude and direction of its
(b) Find the x and y components of this force.
acceleration?
ANSWERS
(c) What is the net force on the sailboat
(a) Drawing
(b) 4 N;
ANSWERS
3N
2
(b) 1.6 m/s
0
65 north of east
or
4
0
as shown in the figure below.
24 east of north
0
Two forces are applied to a car in an effort to accelerate it,
0
(c) 429 N 65 north of east or 24 east of North
(a) What is the net (resultant) force of these two forces?
(b) If the car has a mass of 3200 kg, what acceleration does
2
Four forces act on a hot air balloon, shown from the side in
it have? Disregard friction.
the figure below. Find the magnitude and direction of the
net (resultant) force on the balloon.
ANSWERS
(a) 780 N
0
8.1 to the right of forward
ANSWERS
2
(b) 0.24 m/s
0
8.1 to the right of forward
4305 N
0
15 above the 1520 N force
Chapter 8: Planar Forces
Assignment 2
Vectors and Net Forces (a)
5
A man is pulling on his 20 kg dog with a force of 70.0 N
0
7
A 3.00 kg ball is dropped from the roof of a building 176.4
directed at an angle of +30.0 above the horizontal.
m high. While the ball is falling to Earth, a horizontal wind
(a) Draw a free body diagram of the forces on the dog.
exerts a constant force of 12.0 N on it.
(b) Find the x component of this force.
(a) Draw the free body diagram.
(c) Find the y component of this force.
(b) How long does it take the ball to hit the ground?
(d) Find the normal force on the dog.
(c) How far from the building does the ball hit the ground?
(d) What is its speed and angle when it hits the ground?
(e) With what force and angle will the ball hit the ground?
ANSWERS
(a) Drawing
ANSWERS
(b) 60.6 N
Good review problem of projectile motion
(c) 35.0 N
(d) 161.2 N
(a)
(b) 72.0 m
6
A crate is pulled to the right with a force of 85 N, to the left
(c) 6.00 s
with a force of 115 N, upward with a force of 565 N, and
(d) 63.6 m/s 67.8
downward with a force of 236 N.
(e) 31.75 N 67.8
(a) Draw a free body diagram of the forces on the crate.
(b) Find the net external force in the x direction.
(c) Find the net external force in the y direction.
(d) Find the magnitude and direction of the net external
force on the crate.
ANSWERS
(a)
1
(b) -3.0 x 10 N left
(c) 329 N up
2
(d) 3.3 x 10 N
0
94.5 clockwise from the positive x-axis
0
0
Chapter 8: Planar Forces
Assignment
Pushing and Pulling (c)
8
Two men and a boy are pulling a boat along a canal. The
9
A gardener pushes a 10 kg lawn mower by applying a force
two men pull with forces F1 and F2 whose magnitudes and
of 150 N along the handle.
directions are indicated in the figure.
(a) Draw a free body diagram
(a) Find the magnitude and direction of the smallest force
(b) Find the horizontal component of this force when the
which the boy could exert to keep the boat in the middle of
lawn mower handle makes an angle of 30 .
the canal.
(c) Find the horizontal component of this force when the
(b) If the boa has a mass of 400 kg what is the net force on
lawn mower handle makes an angle of 45
the boat
(d) Find the horizontal component of this force when the
(c) What is the observed acceleration of the boat
lawn mower handle makes an angle of 60 with the
0
0
o
horizontal.
ANSWERS
(a)
(b) 130 N
(c) 106 N
(d) 75.0 N
ANSWERS
10
Two ropes are pulling on a log. Find the net (resultant)
0
force on the log if F1 is pulled with 12 N of force at 10 and
(Hard)
0
F2 is changed to 14.0 N at 310 .
(a) 186 N
0
90 from the bank on the 320 N side
ANSWERS
(b) 477 N
2
(c) 1.19 m/s
22.5 N
0
337.3
11
Three people are pulling on a tree. The first person pulls
0
0
with 15 N at 65.0 ; the second with 16 N at 135 ; the third
0
with 11 N at 195 . What is the magnitude and direction of
the net (resultant) force on the tree?
ANSWERS
27 N
0
125
Chapter 11: Planar Forces
Assignment
Pushing and Pulling (c)
12
Two men wish to pull down a tree by means of a rope
15
The rock shown below is acted on by one or more forces.
fastened near the top. If they use only one rope the tree will
Draw the free body diagram for the rock tied to a rope and
come down on top of them. To prevent this, they tie two
pulled so that the rock moves horizontally at constant
ropes 10 meters long to the same point and stand on the
velocity. Note: There must be air friction in this case.
ground 10.0 meters apart when they pull. If each pulls with
a force of 300 newtons, what is the net force exerted by the
ropes on the tree?
ANSWERS
520 newtons
13
ANSWERS
Three people attempt to haul a heavy sign to the roof of a
building by means of three ropes attached to the sign.
Person A stands directly above the sign and pulls straight
up on a rope. Person B and Person C stand on either side of
person A. Their ropes form 30 degree angles with Person
16
Dan applies a force of 92 N on a heavy box by using a rope
0
A's rope. A force of 10 newtons is applied on each rope.
held at an angle of 45 with the horizontal.
What is the net upward force acting on the sign?
(a) What are the vertical and horizontal components of the
2
92-N force?
(a) Draw the free body diagram
ANSWERS
(b) Calculate the upward force the ice exerts on the crate as
it is pulled.
278 Newtons
(c) Calculate the normal force on the crate.
(d) Calculate the net force on the box
14
The rock shown below is acted on by one or more forces.
Draw the free body diagram for the rock tied to a rope and
pulled so that the rock accelerates horizontally at 2g. No air
ANSWERS
friction
(a) Fh = 65 N;
Fv = 65 N
(b)
ANSWERS
Chapter 8: Planar Forces
Assignment
Pushing and Pulling (c)
17
Beth, a construction worker, attempts to pull a stake out of
19
Joe pushes on the handle of a 10-kg lawn spreader. The
0
the ground by pulling on a rope that is attached to the stake.
handle makes a 45 angle with the horizontal. Joe wishes to
0
The rope makes an angle of 60.0 with the horizontal. Beth
accelerate the spreader from rest to 1.39 m/s in 1.5 s.
exerts a force of 125 N on the rope.
(a) Draw a free body diagram.
(a) Draw a free body diagram of the forces on the stake
(b) What is the normal force on the spreader?
(b) What is the magnitude of the upward component of the
(c) What force must Joe apply to the handle? Neglect
force acting on the stake?
friction.
ANSWERS
ANSWERS
(class)
(a) Drawing
(b)108 N
(a)
(b) 107.2N
18
A 40-kg crate is pulled across the ice with a rope. A force
(c) 13 N
o
of 100 N is applied at an angle of 30 with the horizontal.
(a) Draw the free body diagram
20
A water skier is towed by a speedboat. The skier moves to
(b) Calculate the upward force the rope exerts on the ice
one side of the boat in such a way that the tow rope forms
block as it is pulled.
an angle of 55 with the direction of the boat. The tension
(c) Calculate the normal force on the crate.
on the rope is 350 N. What would be the tension on the rope
(d) Calculate the net force on the box
if the skier were directly behind the boat?
o
(e) What is the observed accleration of the ice block?
ANSWERS
ANSWERS
(class)
200 N
(a) picture
(b) 50 N
(c) 342 N, up
Refer to Problems and Solutions Manual for diagram
(d) 86.6 N
(e) 2.2 m/s
2
Chapter 11: Planar Forces
Assignment
Pushing and Pulling (c)
21
Wendy pushes a 15 kg lawn spreader across a lawn by
22
applying a force of 95 N along the handle that makes an
0
A student pulls a 125 kg box across a floor by means of a
0
rope making an angle of 60 with the horizontal. He applies
angle of 60.0 with the horizontal.
a 60 N force on the rope
(a) Draw a free body diagram.
(a) What is the component of the force in the horizontal
(b) What are the horizontal and vertical components of the
direction?
force?
(b) What is the component of the force in the vertical
(c) What is the normal force on the spreader?
direction?
0
(d) The handle is lowered so it makes an angle of 30.0
(c) What is the normal force on the box?
with the horizontal. Now what are the horizontal and
(d) If the angle of the rope is reduced to 30 and the same
vertical components of the force?
force applied, what will now be the magnitudes of the
(e) What is the new normal force on the spreader?
horizontal , vertical components and the normal force on
0
the box?
ANSWERS
ANSWERS
(a)
(b) horizontal = 48 N,
vertical = 82 N
(a) H= 30 N
(b) V= 52 N
(c)
(c) N
(d) horizontal = 82 N,
(d) Hcomp. 52 N
vertical = 48 N
(e)
Vcomp 30 N
Fnormal
Chapter 8: Planar Forces
Assignment
Pushing and Pulling with Friction (d)
23
A 3.5 kg block is pushed along a horizontal floor by a force
F = 15 N that makes an angle
25
= 40 degrees with the
A box of mass m rests on a horizontal table. The box is
pulled by a massless rope with a force F at an angle
as
horizontal, as shown in the figure below. The coefficient
shown in the figure below. The coefficient of static friction
of kinetic friction between the block and the floor is 0.25.
is 0.6. The minimum value of the force needed to move the
(a) Calculate the frictional force exerted on the block
box depends on the angle .
(b) Calculate the acceleration of the block.
(a) Discuss qualitatively how you would expect this force
to depend on .
(b) Compute the force for the angles
50, and 60 and make a plot of F versus
= 0, 10, 20, 30, 40,
for mg = 400 N.
From your plot, at what angle is it most efficient to apply
the force to move the box?
ANSWERS
(class0
ANSWERS
(a) 11.0 N
2
(a) The force initially decreases with 0 since the
(b) 0.14 m/s
upward component of F will decrease the normal
force exerted by the table, Fn. As q increases further,
24
A 5-kg block is held at rest against a vertical wall by a
however, the forward component of F decreases so
horizontal force of 100 N.
much that F must become larger again in order to
(a) What is the frictional force exerted by the wall on the
move the box.
block?
(b) What is the minimum horizontal force needed to
prevent the block from falling if the coefficient of friction
between the wall and the block is
s
= 0.40?
26
A student moves a box of books by attaching a rope to the
0
box and pulling with a force of 110.0 N at an angle of 30.0 .
The box of books has a mass of 20.0 kg and the coefficient
of kinetic friction between the bottom of the box and the
ANSWERS
sidewalk is 0.50. Find the acceleration of the box
(a) 49.05 N
(b) 123 N
ANSWERS
2
1.24 m/s
to the right
Chapter 11: Planar Forces
Assignment
Pushing and Pulling with Friction (d)
27
28
Two students are sliding a 225 kg sofa at a constant speed
30
A clerk moves a box of cans down an aisle by pulling on a
across the floor. The students carry the sofa, each exert a
rope attached to the box. The clerk pulls with a force of
force equal to half the weight of the sofa.
185.0 N at an angle of 25.0 with the horizontal. The box
(a) Which would be an improvement over sliding the sofa
has a mass of 35.0 kg, and the coefficient of kinetic friction
(b) What other changes could be made to make moving the
between box and floor is 0.450. Find the acceleration of the
sofa easier without lifting it off the floor?
box.
ANSWERS
ANSWERS
Change the angles or put the sofa on rollers
1.4 m/s
0
A box of books weighing 325 N moves with a constant
velocity across the floor when it is pushed with a force of
0
31
A 4.00 kg block is pushed along the ceiling with a constant
0
425 N exerted downward at an angle of 35.2 below the
applied force of 85.0 N that acts at an angle of 55.0 with
horizontal. Find
the horizontal, as in the figure below. The block accelerates
k
between the box and the floor.
to the right at 6.00 m/s. Determine the coefficient of kinetic
friction between the block and the ceiling.
ANSWERS
0.609
29
A student moves a box of books down the hall by pulling
on a rope attached to the box. The student pulls with a force
0
of 185 N at an angle of 25 above the horizontal. The box
ANSWERS
has a mass of 35 kg, and µk between box and floor is 0.27.
(challenge)
Find the acceleration of the box.
0.816
ANSWERS
2
2.7 m/s
Chapter 11: Planar Forces
Assignment
Pushing and Pulling with Friction (d)
32
A brick layer applies a force of 100 N to each of two
34
Suppose you put a wooden block against a wall and push
handles of a wheelbarrow. Its mass is 20 kg and it is loaded
horizontally to keep it from falling. Draw a diagram
with 30 bricks, each of mass 1.5 kg. The handles of the
showing the forces on the block and the causes of those
0
wheelbarrow are 30 from the horizontal and the coefficient
forces. Pay special attention to the normal force and the
of friction is 0.20. What initial acceleration is given the
weight of the block. Are they in the same direction? Are
wheelbarrow?
they equal?
ANSWERS
ANSWERS
0.71 m/s
Weight down, friction up; force of your hand onto
wall; (normal) force of wallout. Normal force is
perpendicualr to the weight. Weight is equal (and
opposite to friction force, which is the coefficient of
33
Rachel pulls her 18-kg suitcase at a constant speed by
friction times the normal force.
pulling on a handle that makes an angle A with the
horizontal. The frictional force on the suitcase is 27 N and
Rachel exerts a 43-N force on the handle.
35
A giant crane in Washington, D. C., was tested by lifting a
6
(a) What angle does the handle make with the horizontal?
load with a mass of 2.232 x 10 kg.
(b) What is the normal force exerted on the suitcase?
(a) Find the force needed to lift the load with an observed
2
acceleration of 20.00 m/s .
(b) If the same force is applied to pull the load up a smooth
ANSWERS
(a) 51
0
0
slope that makes a 30.0 angle with the horizontal, what
would be the acceleration?
(b) 143 N, up
ANSWERS
7
2.19 x 10 N
2
4.90 m/s
Chapter 8: Planar Forces
Assignment 3
Frictionless Inclined Planes (e)
36
A box is held in position by a cable along a smooth incline
shown in the figure below. If
38
0
A horizontal force of 100 N pushes a 12-kg block up a
0
= 60 and m = 50 kg, find
frictionless incline that makes an angle of 25 with the
the tension in the cable and the normal force exerted by the
horizontal.
incline.
(a) What is the normal force that the incline exerts on the
block?
(b) What is the acceleration of the block?
ANSWERS
(Hard)
(a) 149 N
2
(b) 3.41 m/s
ANSWERS
39
A 65-kg girl weighs herself by standing on a scale mounted
on a skateboard that is rolling down an incline as shown in
T = 425N,
the picture. Assume there is no friction so that the force
Fn = 245N
exerted by the incline on the skateboard is perpendicular to
the incline. What is the reading on the scale if
37
A block is projected up a frictionless inclined plane with
0
initial speed 3.5 m/s. The angle of incline is 30 .
(a) How far up the plane does it go?
(b) How long does it take to get there?
(c) What is its speed when it gets back-to the bottom
ANSWERS
ANSWERS
(a) 1.25 m
(b) .714 sec
(c) 3.5 m/s since no friction
552 N
0
= 30 ?
Chapter 8: Planar Forces
Assignment 1
Frictionless Inclined Planes (e)
40
A 2.0 kg mass starts from rest at the top of an inclined plane
0
43
A 40.0 kg wagon is towed up a hill inclined at 18.5 with
85 cm long and slides down to the bottom in 0.50 s. What
respect to the horizontal. The tow rope is parallel to the
net force acts on the mass along the incline?
incline and exerts a force of 140 N on the wagon. Assume
that the wagon starts from rest at the bottom of the hill, and
disregard friction.
ANSWERS
(a) How fast is the wagon going after moving 30.0 m up
the hill?
13.6 N
(b) How fast is the wagon going after moving 80.0 m up
the hill?
41
A block with a mass of 5.0 kg is held in equilibrium on an
incline of angle
0
= 30.0 by the horizontal force, F, as
ANSWERS
shown in the figure.
(a) Find the magnitude of F.
(a) 4.9 m/s
(b) Find the normal force exerted by the incline on the
(b) 8.0 m/s
block.
2
44
Suppose a 3.00 x 10 N force is used to pull an
4
exceptionally large elephant with a mass of 1.22 x 10 kg up
a frictionless slope. What is the maximum angle that the
slope can make with the horizontal if the task is to be
completed?
ANSWERS
(challenge)
ANSWERS
(a) 28 N
(b) 56 N
42
0.144 degrees
A laundry basket has a mass of 5.5 kg, find the magnitude
0
of the normal force at rest on a ramp inclined 12 above the
horizontal
ANSWERS
53 N
Chapter 8: Planar Forces
Assignment 3
Frictionless Inclined Planes (e)
45
0
The largest squash ever grown had a mass of 409 kg.
47
Suppose you want to push a squash with this mass up a
A 3.00 kg block starts from rest at the top of a 30.0 incline
and slides 2.00 m down the incline in 1.50 s.
0
smooth ramp that is 6.00 m long and that makes a 30.0
(a) Find the acceleration of the block.
angle with the horizontal. You push the squash with a force
(b) Find the coefficient of kinetic friction between the
of 2080 N.
block and the incline.
(a) Calculate the net force exerted on the squash
(c) Find the frictional force acting on the block.
(b) Calculate the observed acceleration of the squash
(d) Find the speed of the block after it has slid a distance of
(c) Calculate the time it will it take to reach the top of the
2.00 m.
ramp
ANSWERS
ANSWERS
2
(a) 1.78 m/s
(a) 76 N
(b) 0.37
2
46
(b) .19 m/s
(c) 9.4 N
(c) 8.2 s
(d) 2.67 m/s
The rock shown below is acted on by one or more forces.
48
The coefficient of static friction between the 3.00 kg crate
0
Draw the free body diagram for the rock. Sliding without
and the 35.0 incline of the figure shown below is 0.300.
friction.
What is the minimum force, FN that must be applied to the
crate perpendicular to the incline to prevent the crate from
sliding down the incline?
ANSWERS
ANSWERS
(challenge)
32.1 N
Chapter 8: Planar Forces
Assignment 2
Friction and Inclined Planes (f)
49
The most massive car ever built was the official car of the
3
51
In 1994, a 3.00 x 10 kg pancake was cooked, and flipped,
General Secretary of the Communist Party in the former
in Manchester, England.
Soviet Union. The car had a mass of 3,335 kg. Suppose
(a) If the pancake is placed on a surface that is inclined
0
0
this car is moving down a 10.0 slope when the driver
31.0 with respect to the horizontal, what must the
applies the brakes. The wheels stop rotating, and the car
coefficient of kinetic friction be in order for the pancake to
2
slides, decelerating at a rate of 6.00 m/s .
slide down the surface with a constant velocity?
(a) Calculate the force of kinetic friction acting on the car
(b) What would be the frictional force acting on the
as it decelerates.
pancake?
(b) Determine the coefficient of kinetic friction.
ANSWERS
ANSWERS
0.601
4
1.52 x 10 N
25,682 N
0.798
50
Walter Arfeuille of Belgium lifted a 281.5 kg load off the
ground using his teeth. Suppose Arfeuille can hold three
0
times that mass on a 30.0 slope using the same force. What
is the coefficient of static friction between the load and the
slope?
ANSWERS
0.2
Chapter 8: Planar Forces
Assignment
Friction and Inclined Planes (f)
52
A 5.0 kg block on an inclined plane is acted upon by a
0
53
You slide a 325-N trunk up a 20.0 inclined plane with a
horizontal force of 50 N shown in the figure below. The
constant velocity by exerting a force of 211 N parallel to
coefficient of friction between block and plane is 0.30 .
the inclined plane.
(a) What is the acceleration of the block if it is moved up
(a) What is the component of the trunk's weight parallel to
the plane?
the plane?
(b) How far up the plane will the block go if it has an
(b) What is the sum of your applied force, friction, and the
initial upward speed of 4.0 m/s?
parallel component of the trunk's weight? Why?
(c) What happens to the block after it reaches the highest
(c) What is the size and direction of the friction force?
point?
(d) What is the coefficient of friction?
ANSWERS
(a) 111 N;
(b) zero, constant velocity;
(c) 100 N, down plane;
(d) 0.327
54
A 91 kg refrigerator is placed on a ramp. The refrigerator
0
ANSWERS
begins to slide when the ramp is raised to an angle of 34 .
(class Problem)
What is the coefficient of static friction?
2
(a) -2.06 m/s
ANSWERS
(b) 3.83 m
(c) stops
0.67
0
55
Two forces act on an object. A 36-N force acts at 225 . A
0-
48-N force acts at 315 . What would be the magnitude and
direction of their equilibrant?
ANSWERS
0
60 N 99
Chapter 8: Planar Forces
Assignment
Hanging Signs (h)
56
A weight of 50.0 newtons is hung from the center of a
60
A street lamp weighs 150 N. It is supported equally by two
0
stretched horizontal wire 10.0 m long. It causes the wire to
wires that form an angle of 120 with each other.
sag 1.0 meter at its center. What is the force exerted by
(a) What is the tension of each of these wires?
each half of the wire supporting the weight? (Hint: make a
(b) If the angle is changed to 90 , What is the new tension
scale diagram of the wire with the weight hung from it.)
on the string?
ANSWERS
ANSWERS
125 N
(a) 150 newtons in each wire
0
(b) 106 newtons in each wire
57
A person weighs 612 N. If the person sits in the middle of a
hammock that is 3.0 m long and sags 1.0 m below the
points of support, what force would be exerted by each of
the two hammock ropes?
-4
61
A sphere of mass 3.0 x 10 kg is suspended from a cord. A
steady horizontal breeze pushes the sphere so that the cord
makes an angle of 37 degrees with the vertical when at rest.
(a) Draw a free body diagram.
ANSWERS
(b) Find the magnitude of the push.
(c) Find the tension in the cord.
460 N on each side
58
A bell ringer decides to use a bowling ball to ring the bell.
ANSWERS
He hangs the 7.3-kg ball from the end of a 2.0 m long rope.
He attaches another rope to the ball to pull the ball back,
(a)
and pulls it horizontally until the ball has moved 0.60 m
(b) 2.22 x 10 N
away from the vertical. How much force must he apply?
(c) 3.69 x 10 N
ANSWERS
22 N
59
An electric sign weighing 200 newtons is supported by two
slanting cables. Each cable is attached to the same point of
0
the sign and makes a 45 angle with the horizontal. What is
the force exerted by the sign along each of its cables?
ANSWERS
141 N.
-3
-3
Chapter 8: Planar Forces
Assignment 5
Hanging Signs (h)
62
The largest toad ever caught had a mass of 2.65 kg.
64
Joe wishes to hang a sign weighing 750 N so that cable A
0
Suppose a toad with this mass is placed on a metal plate
attached to the store makes a 30.0 angle as shown in the
that is attached to two cables, as shown in the figure below.
figure below. Cable B is attached to an adjoining building.
If the plate is pulled upward so that it has an observed
Calculate the necessary tension in cable B.
2
acceleration of 2.55 m/s , what is the tension in the cables?
ANSWERS
433 N , right
ANSWERS
65
Two students are sliding a 225 kg sofa at a constant speed
across the floor. One student pulls with a force of 225 N at
23 N
0
an angle of 13 above the horizontal. The other student
-23 N
pushes with a force of 250 N at an angle of 230 below the
horizontal. What is the coefficient of kinetic friction
between the sofa and the floor?
0
63
A traffic light is supported by two cables that are 140 apart.
Each cable exerts a force of 150 newtons on the light.
(a) Draw a free body diagram
ANSWERS
(b) How much does the light weigh? (Think of the weight
of the light, the downward force, as the eqilibriant.)
0.20
ANSWERS
66
A block of mass 8.0 kg, starting from rest, is pulled along a
horizontal tabletop by a constant force of 2.0 Newtons at an
(a)
0
0
(b) net (resultant) 102 newtons 70
equilibriant 102 newtons down
angle of 35 from the horizontal.
(a) Draw a picture of the situation.
(b) What is the net force on the watermelon?
(c) What is the acceleration of the body?
ANSWER
Chapter 5: Linear Forces
Assignment
Pushing and Pulling (c)
67
A 5.5 kg watermelon is pushed across a table at an angle of
0
71
0
47 from the horizontal. The acceleration of the watermelon
push 55 kg crate across a level floor. If the coefficient of
2
is 4.2 m/s to the right.
kinetic friction is 0.35.
(a) Draw a free body diagram of the situation.
(a) Draw a picture of the horizontal
(b) Find the net external force exerted on the watermelon.
(b) What is the magnitude of the frictional force?
(c) What is the applied force on the watermelon?
(c) What is the acceleration of the crate?
ANSWER
ANSWER
0
68
A person applies a 220 N force at 25 to the horizontal to
A tow rope at a 50 angle with the ground is used to pull a
72
2
In 1988, a 3,500 kg telephone constructed by a Dutch
1,750-kg car, giving it an acceleration of 1.35 m/s .
telecommunications company was demonstrated in the
(a) Draw a free body diagram of the situation.
Netherlands. Suppose this phone is towed horizontally by a
(b) What is the net force on the car?
force equal to 8,800 N and pulled at a 15 angle. Given that
(c) What is the force applied to the rope?
the coefficient of kinetic friction is 0.12; calculate the
0
magnitude of the net acceleration of the telephone.
ANSWER
ANSWER
2,362.5 N
in the direction of the acceleration
0
69
70
You give to a 24.3 kg box a push at an angle of 20 with the
5
73
A blue whale with a mass of 1.90 x 10 kg was caught in
horizontal and a force of 85.5 N.
1947. What minimum force pulled at an angle 10 would be
(a) Draw a free body diagram of the motion.
needed to pull the whale at a constant velocity along a
(b) What is the net force on the car?
horizontal ramp if the coefficient of kinetic friction between
(b) What is the acceleration of the car?
the ramp's surface and the whale were 0.160?
ANSWER
ANSWER
A 5-kg object is pulled along a frictionless horizontal
0
0
74
Cleopatra's Needle, an obelisk given by the Egyptian
surface by a force of 10 N at 15 from the horizontal.
government to Great Britain in the late nineteenth century,
(a) Draw a free body diagram of the situation.
is more than 20 m tall and has a mass of roughly 1.89 x 10
(b) What is the net force on the block?
kg. Suppose the monument is lowered onto its side and
(c) What is the observed acceleration of the block?
dragged horizontally to a new location. Given that the
(d) If the object is at rest at t = 0, how fast is it moving
magnitude of the acceleration of the monument is 0.120
after 3 s?
m/s and the coefficient of kinetic friction is 0.100,
(e) How far does it travel from t = 0 to t = 3 s?
calculate the magnitude of the force applied at 10 that must
ANSWER
5
2
0
be applied to the monument in order to move it.
ANSWER
Chapter 5: Linear Forces
Assignment
Pushing and Pulling with Friction (d)
75
Isaac Newton developed the laws of mechanics. Brian
79
In order to drag a 100-kg log along the ground at constant
Newton put those laws into application when he ran a
velocity, you have to pull on it with a force of 400 N at an
marathon in about 8.5 h while carrying a bag containing 51
angle of 35 from the horizontal.
kg of coal. (By doing this, he set a strange but impressive
(a) Draw a free body diagram of the situation.
world record in 1983.) Suppose Brian Newton wants to
(b) What is the resistive force exerted by the ground?
remove the bag from the finish line. He drags the bag with a
(c) What force must you exert if you want to give the log
0
0
2
an acceleration of 2 m/s ?
force of 280 N at 45 . If the coefficient of kinetic friction
between the bag and the pavement is 0.16, what is the
magnitude of the net acceleration of the bag?
ANSWER
ANSWER
80
found in Malaysia. A single flower is almost a meter across
0
76
The largest flowers in the world are the Rafflesia Arnoldii,
If you use a force of 30.0 N pulled at 12 to the horizontal
and has a mass up to 11.0 kg. Suppose you cut off a single
to slide a 12.0-kg wooden crate across a floor at a constant
flower and drag it along with a force of 42.0 N and at an
velocity, what is the coefficient of sliding friction between
0
angle of 15 . If the flower's velocity is constant, what is the
crate and floor?
coefficient of kinetic friction between the flower and the
ground?
ANSWER
ANSWER
77
A 200-kg crate is pushed with a force of 800 N downward
0
at 15 . If the coefficient of friction is 0.20, calculate the
81
acceleration of the crate.
Use trig to solve the following problems.
(a) Find q if tan q = 9.5143.
(b) Find q if sin q = .4540.
ANSWER
(c) Find q if cos q = . 8192.
(d) Find q if tan q = .1405.
78
A force of 30 N accelerates a 9.0-kg wagon at 2.0 m/s
(e) Find q if sin q = .7547.
2
0
along the sidewalk when it is applied to the handle at 25 .
(a) How large is the frictional force?
(f) Find q if cos q = .9781.
Answer
(b) What is the coefficient of friction?
0
ANSWER
(a) q = 84.00
0
(b) q = 27.00
0
(c) q = 35.00
0
(d) q = 7.998
0
(e) q = 49.00
0
(f) q = 12.01
Chapter 6: Vectors
Assignment
Trig Review (a)
82
Use trig to solve the following problems.
84
0
(a) Find the tan 28 .
Solve for all sides and all angles for the following right
triangles.
0
(b) Find the sin 86 .
0
(c) Find the cos 20 .
0
(d) Find the tan 58
0
(e) Find the sin 40
0
(f) Find the cos 71
Answer
Answer
(a) 0.53
opp 9.4
(b) 1.00
adj 7.61
(c) 1.00
angle 51
0
(d) 1.6
(c) 0.64
85
(f) 0.33
83
Solve for all sides and all angles for the following right
triangles.
Solve for all sides and all angles for the following right
triangles.
Answer
Answer
hyp 9.65
adj 5.1
hypothesis 4.7
opp 2.5
0
angle 32
0
angle 58.1
opp 5.1
0
angle 31.9
Chapter 6: Vectors
Assignment
Trig Review (a)
86
Solve for all sides and all angles for the following right
89
Find the vertical and horizontal components of a force of 50
0
triangles.
N that is directed 50 above the horizontal.
Answer
38.3 N vert
32.2 N. horiz
Answer
90
A 110-N force and a 55-N force both act on an object point
0
0
P. The 110-N force acts at 90 . The 55-N force act at 0 .
Missing side 9.62
What is the magnitude and direction of the resultant force?
adj 7.0 side
Answer
0
angle 54
0
opp 7.0 side 36
122 N
0
87
63
A right triangle has two sides A and B.
(a) If tan q = A/B which side of the triangle is longer if the
91
tangent is greater than one?
(b) If tan q = A/B which side of the triangle is longer if the
A 40-N and a 70-N force act concurrently.
(a) Find the magnitude of the resultant force when the
0
angle between them is 0.0 .
tangent is less than one?
(c) If tan q = A/B what does it mean if the tangent equals
(b) Find the magnitude of the resultant force when the
0
angle between them is 30.0 .
one?
(c) Find the magnitude of the resultant force when the
Answer
angle between them is 60.0
0
(d) Find the magnitude of the resultant force when the
0
(a) side A;
angle between them is 90.0 .
(b) side B;
(e) Find the magnitude of the resultant force when the
(c) Side A = side B
angle between them is 180.0 .
0
they have the same length.
Answer
88
A heavy box is pulled across a wooden floor with a rope.
The rope makes an angle of 60 with the floor. A force of
(a) 110 N
75 N is exerted on the rope. What is the component of the
(b) 107 N
force parallel to the floor?
(c) 96 N
0
(d) 81 N
Answer
(e) 30 N
Chapter 6: Vectors
Assignment
Analytically Adding Vectors (b)
92
Two 15-N forces act concurrently on point P.
(a) Find the magnitude of their resultant when the angle
0
between them is 0.0
(b) Find the magnitude of their resultant when the angle
0
between them is 30.0 .
(c) Find the magnitude of their resultant when the angle
0
between them is 90.0 .
(d) Find the magnitude of their resultant when the angle
0
between them is 120.0 .
(e) Find the magnitude of their resultant when the angle
0
between them is 180.0 .
Answer
(a) 30 N
(b) 29 N
(c) 21 N
(d) 15 N
(e) 0 N
93
Joanne pulls on a trunk with a 12-N force. Bev pulls at right
angles to Joanne. How hard must Bev pull to make the
resultant force on the trunk 13 N?
Answer
5N
94
Find the magnitude and direction of the resultant of a 60 N
0
force that acts at an angle of 45 clockwise from the +Y
0
axis , a 20 N force that acts at an angle of 90 from the +Y
0
axis , and a 40 N force that acts at an angle of 300
clockwise from the +Y axis.
Answer
68 N at
0
24
clockwise from the +Y axis