Download Unit III: Worksheet 1a

Unit II: Newton’s Laws
Subunit A: Balanced Forces
Equations
Variables, Units
NOTES:
Unit II-A Objectives
What you should know when all is said and done
1. State and use Newton’s first law to explain the motion of an object:
a. Describe the motion of a moving object on which balanced forces are acting.
b. Describe the motion of a stationary object on which balanced forces are acting.
c. Describe the balanced forces acting on a moving object commonly encountered.
2. Given a diagram or a written description of the forces acting on an object:
a. Draw a force diagram (using vectors) for the object.
b. Resolve forces into x and y components, then find the vector sum of the forces.
c. State whether the velocity of the object is constant or changing.
3. Given a diagram or description of an object in equilibrium, including the forces acting on the
object, determine the magnitude and direction of the unknown force required to keep the object
from accelerating.
4. State Newton’s third law and apply it to situations in which you are trying to determine all the
forces acting on an object.
5.
If a moose were chasing you through the woods, its enormous mass would be very threatening. But
if you zigzagged, then its great mass would be to your advantage. Explain why.
Unit II-A: Balanced Forces
Worksheet 1
6.
7.
1. Inertia can best be described as
Inertia
can
bestwhich
be described
as _____.
A) the
force
keeps moving
objects moving an stationary objects at rest.
a. the
force
which
keeps
moving
objects
moving
objects at rest.
B) the willingness of an object to eventually
lose an
its stationary
motion
b. C)
thethe
willingness
of causes
an object
eventually
force which
allto
objects
to stoplose its motion
c. the
force
which causes
all objects
to stop
D) the
tendency
of any object
to resist
change and keep doing whatever its doing
d. the tendency of any object to resist change and keep doing whatever its doing
Mass
and velocity
values
for afor
variety
of objects
are are
listed
below.
Rank
thethe
objects
from
smallest to
2. Mass
and velocity
values
a variety
of objects
listed
below.
Rank
objects
from
greatest
inertia.
_______
<
_______
<
_______
<
_______
smallest to greatest inertia. _______ < _______ < _______ < _______
3. Two bricks are resting on edge of the lab table. Shirley Sheshort stands on her toes and
spots the two bricks. She acquires an intense desire to know which of the two bricks are most
massive. Since Shirley is vertically challenged, she is unable to reach high enough and lift the
bricks; she can however reach high enough to give the bricks a push. Discuss how the process
of pushing the bricks will allow Shirley to determine which of the two bricks is most massive.
What difference will Shirley observe and how can this observation lead to the necessary
conclusion?
© The Physics Classroom, 2009
Page 1
4. Would Shirley Sheshort be able to conduct this same study if she was on a spaceship in a
location in space far from the influence of significant gravitational forces? _______ Explain your
answer.
5. If a moose were chasing you through the woods, its enormous mass would be very
threatening. But if you zigzagged, then its great mass would be to your advantage. Explain why.
6. Several forces act upon an object. The vector sum of these forces ends up being 0 Newtons.
The object is described as being
A) weightless
B) at equilibrium
C) stationary
D) disturbed
7. Which of the following is always true of an object that is at equilibrium?
A) The net force acting upon it is 0 Newtons.
B) The individual forces acting upon it are balanced.
C) The object is at rest.
D) The object has no acceleration.
E) The object has a constant (unchanging) velocity.
F) There are no forces acting on it.
8. The following statements were made about an Ewok. In which case could you conclude that
the Ewok is at equilibrium?
A) The Ewok is at rest.
B) The Ewok has a constant velocity.
C) The Ewok is moving.
D) The Ewok has a constant speed.
E) The Ewok is stationary.
F) The acceleration of the Ewok is 0 m/s2.
G) The individual forces acting on the Ewok are balanced.
H) There are no forces acting on the Ewok.
I) All the forces acting on the Ewok are equal in magnitude.
Newton's Laws
9. These graphs describe the motion of Carson Busses at various times during his trip to school.
5. Indicate
These graphs
describe
thevehicle
motion is
ofbeing
Carson
Busses
at various
times during
his trip
to aschool.
whether
Carson's
acted
upon
by an unbalanced
force.
Give
reason in
Indicate
whether
Carson's
vehicle
is
being
acted
upon
by
an
unbalanced
force.
Give
a reason
in
terms of a description of what the car is doing (speeding up, slowing down, or constant
velocity).
terms of a description of what the car is doing (speeding up, slowing down, or constant velocity).
6.
Unbalanced Force?
Yes or No?
Unbalanced Force?
Yes or No?
Unbalanced Force?
Yes or No?
Reason/Description:
Reason/Description:
Reason/Description:
A free-body diagrams show all the individual forces acting upon an object. The net force is the
vector sum of all these forces (! F). Determine the net force and state if there is an acceleration.
a.
! F=
Accel'n?
7.
b.
! F=
Yes or No
Accel'n?
c.
! F=
Yes or No
Accel'n?
Yes or No
During an in-class discussion, Anna Litical suggests to her lab partner that the dot diagram for the
motion of the object in # 6b could be
UNIT II-A: Balanced Forces
Reading: Force Diagrams
Forces can intuitively be thought of as pushes and pulls. For example, you exert a force (a push
or a pull) on a door to open it. Gravity exerts a force on you (a pull) which holds you to the
surface of the earth. Friction with the surface of a hill exerts a force on your car that keeps it
from sliding when parked. Note that in every situation, forces are an interaction between two
objects--you can't touch without being touched. In order to analyze the reason behind the
behavior of an object (or the dynamics), we will refer to the object under consideration as the
system, and everything else in the environment that might in any significant way affect the
system as the surroundings. This analysis process can often times be greatly simplified by
using a technique of constructing force diagrams (sometimes called free-body diagrams or
FBDs) to assist you in selecting the relevant forces and appropriately representing these forces
with vector notations.
To make a force diagram for problem analysis, all forces will be categorized as either contact or
long-range forces. Contact forces are all forces acting on the system under analysis that
result from the contact between the system and its surroundings at the systems boundaries.
These forces include applied forces, forces of static and kinetic friction, tension forces and
normal forces. Long-range forces result from the systems interaction with a force field of some
kind, such as magnetic, electric, or gravitational fields.
Here are some of the ones we will use in class:

Contact Forces: When two surfaces touch each other, forces perpendicular to the
surfaces are called Normal forces (here "normal" is a mathematical term meaning
perpendicular) and forces parallel to the surfaces in contact are Frictional. The Friction
force that allows us to step forward or keeps car wheels from spinning can be called
traction. When we touch things a combination of both normal and frictional forces are
present. For simplicity, we can call a combination force a push or a pull. A push or pull
force can be labeled simply as an Applied force.

Extended or linked materials such as a string or chain exert Tension forces on an
object.

When an object interacts with a fluid, such as water or air, propelling forces are called
thrust, resistive forces are called drag, floating forces are called buoyant, and steering
(or Bernoulli's) forces are called lift.

When two objects interact without touching, they exert forces through a force field. Earth,
for example, exerts a gravitational force on the Moon even though the Earth and Moon
do not touch. Other non-contact forces include electric and magnetic forces.
When we label forces, we want to indicate the type of interaction between the objects, what
object the force is acting on and what object the force is by. Therefore, we will use the following
notation:
Fkind
Such as the Force due to gravity, Fg, the force of Tension, FT, or the Normal Force, FN.
Consider the analysis of forces acting on a log as a tractor pulls it at a constant speed. (Figure 2
below) The analysis proceeds as follows:
1. Shrink the system to a point at the center of coordinate axes with one axis parallel to
the direction of motion.
2. Represent all relevant forces (across the system boundary) by a vector labeled with
an appropriate symbol.
As an illustration of this process, consider the forces acting on a log being pulled by a tractor
follows:
Step 1
Since the shape of the object is unimportant, shrink it to a
point. Place it at the intersection of a set of coordinate axes
with one of the axes parallel to the direction of motion as
shown in figure 4.
Step 2
Proceed around the system boundary line and identify all points
at which there is contact between the system (log) and its
surroundings. Construct qualitative vectors (indicate directions
and relative magnitudes) to represent these forces. The contact
forces would be kinetic friction, Fk (parallel to the supporting
surface), the normal force, FN (the component of force that is
perpendicular to the supporting surface), and the tension force of
the rope, FT. The long-range force(s), in this case would be only
the force of gravity, Fg. See Figure 4 at left.
Step 3
Indicate which forces (if any) are equal in magnitude to other forces. The problem states that the
tractor pulls the log at constant velocity, so we know that the net force has to be zero. In other
words, the forces up must equal the forces down, and the forces left must equal the forces right.
In the diagram below these equalities have been marked with hashes like those used to indicate
congruences in geometry.
Now, it should be easy to determine the net force on the object. To do this, consider the force in
each direction (x or y) separately. That is,
x-axis
FT and Fk
y-axis
Fg and FN
In this case, the two forces in the x-direction are equal, but opposite, so they sum to zero. Also
note that the two forces in the y-direction sum to zero. Therefore, you can conclude that this
object will not accelerate in either direction. That leaves two possibilities: it is either motionless,
or it is moving at constant velocity.
For a more complicated problem, consider the block at rest on a ramp.
As before, we use a point to represent the object. Note
that we have rotated the coordinate axes as shown
above so that the x-axis is parallel to the surface of the
ramp (the likely direction of motion).
Next, break any force vector that is not parallel to the
coordinate axes (in this case, the force of gravity, Fg)
into its x and y components. See the diagram at right.
Note that the x-component and y-component form the
sides of a right triangle with the original force vector, Fg
as the hypotenuse.
In this case, the y-component balances out the normal
force, so the object does not accelerate up or down. The
x-component of Fg is opposed by the force of static
friction. If these forces have the same magnitude, the
object will stay put.
To determine the magnitudes of Fx and Fy, you need to
use some simple trigonometry.
There are just a few points to keep in mind.
1. The angle θ should be drawn so that it is included in
the triangle formed by the three vectors.
2. The side opposite the angle has magnitude equal to
the original vector times the sine of the angle.
3. The side adjacent to the angle has magnitude equal
to the original vector times the cosine of the angle.
Remember Newton’s 1st Law:
If ΣF = 0, then v = 0, and
If v = 0, then ΣF = 0
The S.I. unit for force is named after Sir Isaac Newton himself. All forces are measure in
Newtons.
Symbol
Name of Force
FA
FG
FN
FT
1.
Ff
2.
Agent/Interaction
Unit II-A: Balanced Forces
Worksheet 2
For each situation below, write a list of relevant objects in the system and draw the system
behavior diagram. On separate paper, write a sentence justifying why you choose to include
each of the objects in your list.
Situation
1. The object lies motionless
2. The object slides at a constant
speed without friction.
3. The object slows due to kinetic
friction.
4. The object slides without
friction.
5. Static friction prevents sliding.
6. The object is suspended from
the ceiling by a single rope.
List of Objects
Force Diagram
7. The object is suspended from
the ceiling by the two ropes.
8. The object is held motionless
by the two ropes.
9. The object is motionless.
10. The object is motionless.
11. The object is being pulled at
a constant velocity by a string
attached as shown.
12. The object is being pulled
(constant velocity) by a string
attached as shown.
13. The object is being pushed
by a person as shown and is
moving at a constant velocity.
14. The object falls at a constant
speed because of a parachute.
15. The object falls. (No air
resistance)
16. The object rises after being
thrown into the air.
17. The object is at the top of its
path after it was thrown into the
air.
Unit II-A: Balanced Forces
Worksheet 3
1. Free-body diagrams for four situations are shown below. For each situation, determine the
net force acting upon the object.
Situation A
Situation B
FN = 3
Fk = 5
N
FN = 3
N
Fg = 3
FA = 5
Fk = 5
N
N
N
Fg = 3
N
N
Situation D
Situation C
Fair = 30
FN = 10 N
N
Fg = 15
Fg = 10
N force is known for each
2. Free-body diagrams
for four situations are shown below. The net
NN
situation. However, the magnitudes of a few of the individual forces are not known. Analyze
each situation individually and determine the magnitude of the unknown forces.
Free Particle Model Worksheet 1a:
Force Diagrams
In each of the following situations, represent the object with a particle. Sketch all the forces acting
upon the object, making the length of each vector represent the magnitude of the force. Also use
Create
a marks
forceto diagram
theare
object
all caps!
congruency
indicate whichon
vectors
equal inin
magnitude.
3. A CAT is at rest
4. A student sitting
1. Draw a force diagram for the motionless cat on a rug. Label the forces and use equality marks
on aonrug.
a CHAIR.
the force vectors.
5. BOBO the Panda is hanging from a
branch.
6. Sammy the snail sitting
on TIM THE TURTLE standing
on top of a table.
2. Draw a force diagram for the skater, moving at constant speed across frictionless ice. Label the
forces and use equality marks on the force vectors.
Newton's Laws
5.
These graphs describe the motion
of Carson
Newton's
Laws Busses at various times during his trip to school.
Name:
Indicate whether Carson's vehicle is being acted upon by an unbalanced force. Give a reason in
terms of a description of what the car is doing (speeding up, slowing down, or constant velocity).
7. An EGG is free-falling
from a nest in a tree.
Neglect air resistance.
8. SLICK STEVE slidingRecognizing Forces
down a slide at a constant
Read from Lesson
2 of the Newton's Laws chapter at The Physics Classroom:
speed.
http://www.physicsclassroom.com/Class/newtlaws/u2l2a.html
http://www.physicsclassroom.com/Class/newtlaws/u2l2b.html
MOP Connection:
Newton's Laws: sublevel 4
Unbalanced Force? There are several
Unbalanced
Force?
Force? fill in the list provide
described
For each situation,
9. Calvin pulling
10.situations
A horse
pulling below.Unbalanced
Yes or No?
Yes
or No?
Yes of
or the
No?situation you used to determ
which
forces
are
present
and
stating
which
features
Hobbes on a SLED
a WAGON up a hill
or absence of
the
To facilitate
utilize the Net Force Help Sheet. Up
Reason/Description:
Reason/Description:
(flat surface)Reason/Description:
at a
atforce.
a constant
speed.this exercise,
this assignment, check your answers using the available Web page.
constant speed.
http://www.physicsclassroom.com/morehelp/recforce/recforce.htm
6.
A free-body diagrams show all the individual forces acting upon an object. The net force is the
vector sum of all these forces (! F). Determine the net force and state if there is an acceleration.
Description of b.
Situation
Force Present
c. (P)
11. A rightward force a.
12. A rightward force
or Absent (A)?
applied
a TABLE
applied
to Label
a BOOK
4.is Draw
a forceto
diagram
for a chandelier that is suspended from the is
ceiling
by a chain.
the
andto
usemove
equalityitmarks on the force vectors.
Gravity
in forces
order
in order to move it across
across the floor with
a rightward acceleration.
Consider frictional forces.
! F=
a desk at constant velocity.
Consider frictional forces.
Spring:
! F=
Tension
! F=
P or A?
P or A?
P or A?
13. A SKYDIVER is
14. A CAR driving
or A?
Accel'n?
Yes or No
Accel'n?
Yes or
No Normal:
Accel'n? P Yes
or No
descending with
a
at a constant
velocity.
1.
A
block
hangs
at
rest
constant velocity.
7. During an in-class discussion, Anna Litical
to her
fromsuggests
the ceiling
bylab
a partner that the dot diagram for the
Consider
air resistance.
Friction
P or A?
motion
of the object in # 6b could be
piece of rope. Consider
the forces acting on the
block.
Air Res.:
P or A?
Anna's partner objects, arguing that the object in # 6b could not have any horizontal motion if there
are only vertical forces
acting
upon well
it. Who16.
is right?
____________
Explain.
A BUCKET
raised
from
A well
BLOCK
hangs from
a spring
5.15.
Draw
a force diagramisforbeing
the bucket
of water
that isabeing
raised from the
at constant
Gravity
P or A?
speed.
Label
the
forces
and
use
equality
marks
on
the
force
vectors.
at a constant speed.
from the ceiling.
8.
P ortoA?
During an in-class discussion, Aaron Agin asserts that the object in #Spring:
6a must be moving
the left
since the only horizontal force acting upon it is a "left-ward" force. Is he right? ______ Explain.
Tension
P or A?
Normal:
P acting
or
A? an
diagramsbelow
belowdepict
depict the
the magnitude
and
direction
of the
individual
forces
acting
upon
17.9.TheThe
diagrams
magnitude
and
direction
of
individual
forces
upon
2. A block
hangs
from
thethe
object.
Whichall
objects
could be moving ceiling
to the right?
Circle all that apply.
by a spring.
an object.
Choose
that apply.
Consider the forces
acting on the block when
it is at rest (at its
equilibrium position).
Friction
P or A?
Air Res.:
P or A?
6. Draw a force diagram for a skydiver who has just left the plane and is still speeding up. Label
the forces and use equality marks on the force vectors.
A) Which objects could be moving to the right?
B) Which objects could be speeding up?
The Physics
2009
C) ©Which
objectsClassroom,
could be stationary?
© The Physics Classroom, 2009
Page 4
Explan
Unit II-A: Balanced Forces
Worksheet 4
1. The standard metric unit for mass is _____ and the standard metric unit for weight is _____.
2. An object's mass refers to ______ and an object's weight refers to _______.
A) the amount of space it takes up
B) the force of gravitational attraction to Earth
C) how dense an object is
D) the amount of stuff present in the object
3. When an astronaut lands on the moon, which of the following are more than, less, than, or
the same as on Earth:
A) The astronaut’s mass
B) The astronaut's weight
C) The astronaut’s inertia
4. Which weighs more, a pound of feathers or a pound of bricks? Which has more mass?
5. The value of g in the British system is 32 ft/sec2. The unit of force is pounds. The unit of
mass is the slug. Use your weight in pounds to calculate your mass in units of slugs.
6. You might be wondering about your metric weight. Using conversion factors, convert your
weight in pounds to units of N. (Use 1 N = 0.22 pounds, and okay, you can lie…)
7. When an elevator is ascending at a constant velocity, there are two forces acting on it, gravity
and the cable pulling on it. Which of these is greater? Why do you say so?
8. When you go roller-blading (if you don’t then try to imagine that you do), you must keep
pushing with your feet in order to maintain a constant speed. Explain why this is, talk about the
forces acting on you in your explanation.
9. Do chickens weigh more here on earth or on the moon? Do they have more mass here or
there?
10. A shopping cart sits in a parking lot. Sophie Shopper walks up to it and begins pushing it
towards the door at a constant speed. Because of the way the handle is attached, Sophie must
push downward at an angle on the cart. Describe what happens to the normal (or support) force
acting on the cart before and after Sophie begins pushing.
11. An armadillo weighs has a mass of 15 kg. Find its weight.
12. Wile E. Coyote has a new plan to catch the Roadrunner involving a 100 kg box of TNT. In
preparation he starts pushing it at a constant velocity to the edge of a cliff. Friction has a force
of 200 N.
A) With how much force should Wile E. Coyote be pushing?
B) What is the support force of the ground on the box?
13. A car’s engine pushes with 45N to the right. If it is at equilibrium, how much air friction is
there and what is the car’s acceleration?
14. Spaceman Spiff weighs 350 N on Earth when decked out in full astronaut gear. How much
would he weigh on planet Zorg, where the gravitational field strength is 20 N/kg?
15. Find the normal force from a level table on a 2-kg pineapple.
16. A wagon rolls at a constant speed of 2 m/s on level ground. Marvin Mole (mass = 3.5 kg)
rides in the 10 kg wagon.
A) What is the combined weight (force of gravity) of Marvin and the wagon?
B) What is the normal force (support force) that acts on Marvin (only) in the wagon?
C) What normal force (support) acts on the wagon carrying Marvin?
ction of the two components by circling two
h component (or effect) is greatest in magnitude.
Components: E W N S Components: E
Greatest magnitude? ______
W
N
Greatest magnitude? ______
Force and Vector Applications
S Components: E
W
N
S
Greatest magnitude? ______
Name:
Each diagram displays
a vector.
Thehave
anglecombined
between the
vector of
and
the nearest
17. Burl
and Paul
weights
1300
N. The coordinate
tensions inaxes
theissupporting ropes that
marked as theta (! ). If ! is gradually increased to 90 degrees, the magnitudes of the components
support the scaffold they stand on
add to 1700
N. Find the weight
of the scaffold.
would change. Which component would increase
horizontal
(E/ W) or vertical
(N/ S)? Equilibrium Situations
Using- Vector
Components
to Analyze
Read from Lesson 3 of the Vectors and Motion in Two-Dimensions chapter at The Physics Classroom:
http://www.physicsclassroom.com/Class/vectors/u3l3b.html
http://www.physicsclassroom.com/Class/vectors/u3l3c.html
!
E
W
N
S Components:
E Connection:
W N S
MOP
Forces in Two Dimensions: sublevels 3 and 4
!
nitude? ______
Greatest magnitude? ______
Many physical situations involve forces exerted at angles to the coordinate axes. A proper analysis of
18. Harry gives
his
little sister
a !piggyback
Harry
has a mass
of 40 kg and
his lie
little
sister
these
situations
demands
that theride.
forces
be resolved
into components
which
along
the horizontal and
ween the vector and
the
nearest
coordinate
axes
is
vertical
axes.
This
involves
the useforce
of trigonometric
has a mass of 20 kg. Calculate the support
supplied byfunctions.
the floor.
d to 90 degrees, the magnitudes of the components
1. For the following situations, draw and label the force components as the projection onto the axes.
ase - horizontal (E/ W) or vertical (N/ S)?
Then use trigonometric functions to determine the magnitude of each component. Label the
Increasing component?
Increasing
component?
Increasing
component?
magnitudes
of the
component on the diagram.
PSYW
E
E Mauer
W pulls
N up with
S a force of E
N Yuss
S yanks on Spot's dog chain with
Lon
75 N atW b. Jean
an angle of 45° to the horizontal on the
a force of 12 N at an angle of 60° to the
handle
his manual
lawn mower.
horizontal.
For the following situations, draw and label
theofforce
components
of the given vector. Then
use
trigonometric functions
to
determine
the
magnitude
of
each
component.
Label
the
magnitudes
of given vector. Then
19. For the following situations,
draw
and
label
the
force
components
of
the
!
the component on
the
diagram.
PSYW
use trigonometric functions to determine the magnitude of each component. Label the
a.!
W
S
a.
magnitudes
of thea component
A 5.0 N force
is exerted upon
dog chain on
b. the
A diagram.
baseball is hit by a bat with a force of
N force
is exerted upon a dog
chain
at an angle
of 65° above the horizontal.
at an angleA)
of A
65°5.0
above
the horizontal.
325 N
at a direction
of 105°.
ng component?
W
N
N
S
Increasing component?
E
W
N
S
force components of the givenUse
vector.
Then use
your noodle
(that's your brain) to logically think through the following two questions.
tude of each component. Label the magnitudes of
2. Which of the following statements is ALWAYS 3. The following statements were made about an
true of an object at equilibrium?
object. In which case could you conclude that
a. a force
The object
is at rest.
the object is at equilibrium?
b. A baseball is hit by a bat with
of
a. The object is at rest.
325 N at a direction of 105°. b. The object is maintaining its state of
motion.
The object has a constant velocity.
B) A baseball is hit by
a bat with a force of 325 N at a direction of b.
105°.
c. The object's velocity is not changing.
c. The object is moving.
d. The net force on the object is 0 Newtons.
d. The object has a constant speed.
e. The object is NOT accelerating.
e. The object is stationary.
f. The individual forces acting on the object
f. The acceleration of the object is 0 m/ s/ s.
are balanced.
g. The individual forces acting on the object
he Physics Classroom, 2009
Page 4
g. All individual forces acting on the object
are balanced.
are equal in magnitude.
4.
Three forces - F1, F2 , and F3 - are acting upon an object.
and direction
areobject.
shownTheir
at the
20. Three forces Their
- F1, relative
F2, andmagnitude
F3 - are acting
upon an
right.
The
xand
y-components
are
also
shown.
relative magnitude and direction are shown at the right. The x- and ythe Complete
following mathematical
by
components are Complete
also shown.
the followingstatements
mathematical
placing > , < , and = symbols in the blanks.
statements by placing >, <, and = symbols in the blanks.
F1x ____ F2x
F1y ____ F3
F1x ____ F2x
F2y
Page 4
____ F3
F1y ____ F3
F2y ____ F3
F1y + F2y ____ F3
F1y + F2y ____ F3
© The Physics Classroom, 2009
Page 5
Unit II-A: Balanced Forces
3. The figure below is a snapshot looking down on a bowling ball moving at constant velocity from
Worksheet
5is given a short, sharp hit in a
left to right on a smooth, level floor. At the position
shown, the ball
direction perpendicular to the ball's initial motion.
3. The
figure
below
a snapshot
looking
down
a bowling
moving
at constant
velocity from
1. The
figure
below
is aissnapshot
looking
down
on on
a bowling
ballball
moving
at constant
velocity
left
to
right
on
a
smooth,
level
floor.
At
the
position
shown,
the
ball
is
given
a
short,
sharp
hit in a
from left to right on a smooth, level floor. At the position shown, the ball is given a short, sharp
direction
perpendicular
to
the
ball's
initial
motion.
hit in a direction perpendicular to the ball's initial motion.
A)On
Onthe
thediagram,
diagram,draw
draw
a path
might
follow
after
Explain
your reasoning for
a.
a path
thatthat
thethe
ballball
might
follow
after
thethe
hit.hit.
Explain
your
reasoning
for drew.
the path you drew.
the path you
a. On the diagram, draw a path that the ball might follow after the hit. Explain your
reasoning for the path you drew.
b.
of of
thethe
ball
bebe
equal
to, greater
than,than,
or smaller
B)Immediately
Immediatelyafter
afterthe
thehit,
hit,will
willthe
thespeed
speed
ball
equal
to, greater
or smaller than
than
the
ball's
velocity
before
the
hit?
Explain
your
reasoning.
the ball's velocity before the hit? Explain your reasoning.
b. Immediately after the hit, will the speed of the ball be equal to, greater than, or smaller
than the ball's velocity before the hit? Explain your reasoning.
c.
How will the velocity of the ball behave as time goes by after the blow? That is, will either
C) How will the velocity of the ball behave as time goes by after the blow? That is, will either the
the magnitude or the direction of the velocity change? If so, how?
magnitude or the direction of the velocity change? If so, how?
c. How will the velocity of the ball behave as time goes by after the blow? That is, will either
the magnitude or the direction of the velocity change? If so, how?
4. You push a grocery cart along a level floor in the presence of friction effects
a 10-kg
between2.
theYou
cartpush
and the
floor.shopping cart at a constant velocity of 0.5 m/s as you leisurely
stroll HEB looking for toilet paper. Finding a screaming deal, you pick up 4
4. You
push
a grocery
aalevel
floor
in
the2presence
of
friction
effects
packages
thatdiagrams
you
estimate
toalong
have
mass
of about
kg each
(you
like the
extra
a.
Draw
force
forcart
you,
the cart,
and
the
floor/earth.
Fully
label
between
the
cart
and
the
floor.
thick
kind).
all vectors.
A) Write the equation for the forces acting in the vertical direction and calculate the
a. Draw force diagrams for you, the cart, and the floor/earth. Fully label
normal force the floor is providing.
all vectors.
you
cart
B) Write the equation for the forces acting in the horizontal direction. If friction is resisting you
cart
with 10 N of force, you
how hard must you push?
floor/Earth
floor/Earth
3. Determine the tension in each cable in case A and case B if the ball has a mass of 5 kg.
Case A
Case B
Free Particle Model Works
Quantitative Force Analysis & Ve
1. Determine the tension in each cable below. Draw a force diag
the problem.
Case A - ball suspended on one cable Case B - ball suspen
4. Determine tension in each cable. (Hint: There is more than one way to define the system.)
2. Determine tension in each cable.
7kg
4kg
3. Find the horizontal and vertical components of the tension i
5. Find the horizontal and vertical components of the Tension
in the fishing line if the tension is 100 N.
5
5̊
6. A 2000 kg elephant stands on a ramp. Draw a force diagram to determine the components of
the elephant’s weight parallel and perpendicular to the ramp.
©2009 Modeling Instruction Program
1
Physics Tip: When a sign is hung at equilibrium, the downward pull of gravity must be balanced by the
upward pull of the wires (cables, strings, etc.). In most cases, the wires are oriented diagonally such that
the tension force has both a horizontal and vertical component. If the sign is hung symmetrically, then
each wire pulls with the same amount of force and at the same angle. The vertical component of the
tension will be the same in each wire. And if there are two wires, each wire must supply sufficient up
pull to balance one-half the weight of the sign.
7. The three identical signs below are supported by wires at three different angle orientations.
Since
each
sign
has asigns
weight
of 10.0
N, each wire
mustatexert
verticalangle
component
of force
of
5. The
three
identical
below
are supported
by wires
three adifferent
orientations.
Since
5.0 N.
Use
a
trigonometric
function
to
determine
the
tension
in
each
wire.
A
diagram
of
each
each sign has a weight of 10.0 N, each wire must exert a vertical component of force of 5.0 N. Use a
situation
is shown.function to determine the tension in each wire. A diagram of each situation is shown.
trigonometric
If hanging the above sign with a given wire, which one of the above angles would provide for the
safest arrangement? _____________ Explain.
If hanging the above sign with a given wire, which one of the above angles would provide for the
6. Suppose
that a student
pulls with two large forces (F1 and F2) in order to lift a 1-kg book by two
safest
arrangement?
Explain.
cables. If the cables make a 1-degree angle with the horizontal, then what is the tension in the cable?
8. A normal force is a force which is always directed
A) upwards
B) sideways
C) perpendicular to the surface the object is contacting
9. An object is upon a surface. The normal force is equal to the force of gravity
A) in all situations
B) only when the object is at rest
C) only when the object is accelerating
D) only when there is no vertical acceleration
E) only when there is no vertical acceleration AND FN and Fg are the only vertical forces
© The Physics Classroom, 2009
Page 6
Unit II-A: Balanced Forces
Worksheet 6
For each of the problems below, carefully draw a force diagram of the system before attempting
to solve the problem.
1. A person pulls on a 50 kg desk with a 200-N force acting at a 30º angle above the
horizontal. The desk does not move.
A) Draw a force diagram for the desk.
B) Write the equation that describes the forces that act in the x
direction.
C) Write the equation that describes the forces that act in the y
direction.
D) Determine the x and y components of the force of tension.
E) Determine the value of the frictional force. Do the same for the normal force.
2. Suppose that the person in the previous problem were pushing down at a 30º angle with
200 N of force. The desk still does not move.
A) Draw a force diagram for the desk.
B) Write the equation that describes the forces that act in the x
direction.
C) Write the equation that describes the forces that act in the y
direction.
D) Determine the value of the frictional force. Do the same for the normal force.
3.
a. Draw a force diagram for the block held at rest.
25
T1
b. Write the equation that describes the forces that act in the x
direction.
T2
c. Write the equation that describes the forces that act in the
y direction.
d. Suppose that the magnitude of T1 is 50 N. Determine the magnitude of T2.
e. Determine the weight of the box. What is its mass?
4. Draw the force diagram for the box, which rests motionless on the ramp.
20

a. Write the equation that describes the forces that act in the x direction.
b. Write the equation which describes the forces which act in the y direction.
c. If the mass of the box is 8.0 kg, determine the value of the normal force.
Unit II-A: Balanced Forces
Worksheet 7
1. A) Draw a force diagram for each block held at rest.
B) Write the equation for the forces acting in the x-direction for the larger block.
C) Write the equation for the forces acting in the y-direction for each block.
D) How does the tension on the smaller block compare to the tension on the larger block?
E) Calculate the amount of friction required to hold the system at rest.
2. The sign shown hangs outside the physics classroom, advertising the
most important truth to be found inside. The sign (mass = 50 kg) is
supported by a diagonal cable and a rigid horizontal bar.
A) Draw a force diagram for the sign.
B) Write the equation describing the forces acting horizontally on the
sign.
C) Write the equation describing the forces acting vertically on the sign.
D) Calculate the Tension in the cable.
E) Calculate the amount of force the bar applies to the sign.
3. You were so excited about your Thanksgiving ski trip that you over-packed your duffle bag.
The bag (and all your stuff) has a mass of 80 kg. You drag the heavy bag at a constant velocity
by exerting a force of 400 N at an angle of 45 degrees to the floor.
A) Draw a force diagram for your duffle bag.
B) Write the equation describing the forces acting horizontally on the duffle bag.
C) Write the equation describing the forces acting vertically on the duffle bag.
D) Calculate the frictional force acting against your duffle bag.
E) Calculate the normal force acting on your duffle bag.
4. Your little brother is pushing his Thomas the Tank Engine along the train track. He pushes
downward at an angle of 20 degrees to the floor with a force of 5 N in order to make the train go
at a constant velocity. The train has a mass of 0.2 kg.
A) Draw a force diagram for the train.
B) Write the equation describing the forces acting in the horizontal direction.
C) Write the equation describing the forces acting in the vertical direction.
D) Calculate the friction acting on the train.
E) Calculate the normal force supporting the train.
5. A box of Girl Scout cookies is being unloaded from a truck using
an inclined plane that forms a 37-degree angle with the ground as
shown in the diagram. The box has a mass of 10 kg. It is allowed to
slide down the ramp at a constant speed.
A) Draw a force diagram for the box.
B) Write the equation describing the forces acting parallel to the ramp (in the horizontal
direction).
C) Write the equation describing the forces acting perpendicular to the ramp (in the vertical
direction).
D) Calculate the amount of friction resisting your next snack.
E) Calculate the normal force keeping your snack from crumbling to the ground.
Unit II-A: Balanced Forces
Worksheet 8
For each of the problems below, carefully draw a force diagram of the system before attempting
to solve the problem.
1. The cable at left exerts a 30 N force.
a. Write the equation for the sum of the forces in the x-direction.
What is the value of T2?
b. Write the equation for the sum of the forces in the y-direction.
What is the force of gravity acting on the ball?
7.
Draw aforce
force diagram
the child on the swin
2. You pull back your 15-kg brother in preparation for a swinging time. HowLabel
much
mustandforuse
the force vectors
equality marks on
you apply to hold him motionless at an angle of 25 degrees to the vertical?
3. The object hung from the cable has a weight of 25 N. Write the equation for the sum of the
forces in the y-direction. What is the tension in the cable?
8. Draw a force diagram for the climber who has
equality marks on the vectors.
4. Tarzan prepares to swing and much to his dismay, gets his
loincloth stuck on a branch. He's left hanging with the vine pulling
upward at a 40-degree angle and his loincloth pulling him horizontally
to the right.
A) If Tarzan’s mass is 75 kg, calculate the tension in the vine.
7. Tarzan prepares to swing and much to his disma
hanging with the vine pulling upward at a 40-degre
to the right.
a. Draw a
angled fo
are equal
B) Calculate the force of the branch on his loincloth (let’s hope it holds!).
b. Write an equation for the vertical forces
c. Write an equation for the horizontal forc
5. The box on the frictionless ramp is held at rest by the tension force. The mass of the box is
20 kg.
d. Tarzan's mass is 75 kg. Calculate his we
e. Use the appropriate equation for the forc
A) What is the value of the tension force?
f. Determine the tension in his loincloth.
B) What is the value of the normal force?
©2009 Modeling Instruction Program
6. In the system below the pulley and ramp are frictionless and the block is in static equilibrium.
What is the mass of the block on the ramp?
3
7. A man pulls a 25 kg box at constant speed across the floor. He applies a 250 N force at an
angle of 30.
A) Sum the forces in the x-direction. What is the value of the frictional force opposing the
motion?
B) Sum the forces in the y-direction. What is the value of the normal force?
8. A man pushes a 2.0 kg broom at constant speed across the floor. The broom handle makes a
50 angle with the floor. He pushes the broom with a 5.0 N force.
a. Sum the forces in the y-direction. What is the value of the normal
force?
b. Sum of the forces in the x-direction. What is the value of the
frictional force opposing the motion?
c. If the frictional force were suddenly reduced to zero, what would happen to the broom?
Unit II-A: Balanced Forces
Worksheet 9
1. A diver dives off of a raft - what happens to the diver? The raft? How does this relate to
Newton's Third Law?
2. A tennis racquet hits a tennis ball. Why doesn't the racquet swing backwards when the ball
hits it? (Shouldn't it swing back because of action-reaction forces?)
3. What action-reaction forces are involved when a rocket engine fires? Why doesn't a rocket
need air to push on?
Free Particle M
Inter
1. Explain what a normal force is and give an ex
4. What forces are acting on a book sitting on a table? Are action-reaction forces involved in
this situation?
2. Can an inanimate object (such as a table) exe
by an inanimate object change? Explain and giv
5. If two people each standing on a scooter board push off of each other what happens (relate
to Newton's Third Law)?
3. If the acceleration of an object is zero, are no
6. In #5 how would the distance moved by the scooter boards compare if one person had a lot
more mass than the other person?
7. If a person standing on a scooter pushes off of a wall, what happens? Can this situation be
explained in terms of Newton's Third Law (action-reaction)?
4. How does the force block A exerts on block
Draw and label a quantitative force diagram for
8. How does the force block A exerts on block B compare to the force
block B exerts on block A? Draw and label a quantitative force diagram
for each block, using equality marks on the vectors.
5. How does the force block A exerts on block B compare to the
Draw and label a force diagram for each block, using equality ma
9. How does the force block A exerts on block B
compare to the force block B exerts on block A?
Draw and label a force diagram for each block,
using equality marks on the vectors.
6. How does the force block A exerts on block B compar
Draw and label a force diagram for each block, using equ
10. How does the force block A exerts on block B
compare to the force block B exerts on block A? Draw
and label a force diagram for each block, using equality
marks on the vectors.
6. How does the force block A exerts on block B compare to the
Draw and label a force diagram for each block, using equality ma
11. Draw and label all of the action-reaction paired forces for
the person pulling the sled.
6.
cord is 25˚ above the horizontal.
mass of kids and sled = 100 kg
Tension
in cord isInstruction
120 N. Program
©2009 Modeling
Friction force is 15 N.
12. TRUE or FALSE: As you sit in your seat in the physics classroom,
the Earth
pulls
Find the acceleration
of the
sled.down
2
upon your body with a gravitational force; the reaction force is the chair pushing upwards on
your body with an equal magnitude.
If False, correct the answer.
©2009 Modeling Instruction Program
2
Unit II-A: Balanced Forces
Review Worksheet
EQUATION
Fg = (10 N/kg) m
1. State Newton’s 1st Law. (remember 3 things about it…)
2. State Newton’s 3rd Law.
3. What is the difference between mass and weight? What are the units of each?
4. A piece of dry ice is kicked across the floor. If it has little to no friction, what will it do? What
would happen if you exerted a constant force on it?
5. What quantity describes how much inertia an object possesses?
6. When an object is in equilibrium, what must Fnet equal?
7. A) You are in the front of a bus, standing in the isle wearing roller-blades. The bus suddenly
starts to accelerate forward. What happens to you? Why?
B) Now the bus is moving at a constant velocity. What is your motion relative to the bus? Explain.
8. When you fire a rifle, why do you feel the kick-back? (Explain using Newton’s 3rd Law).
9. When you push on a book, the book pushes back on you with the same force. So why does
the book move, and not you?
10. A 1000-N crate is dragged across a factory floor at a constant velocity by pulling on a rope
with a force of 400 N, as shown in the picture.
30
A) Draw a force diagram of the forces acting on the crate and label them.
B) Write equations for the vertical and horizontal components of the forces.
C) Find the force of friction on the crate.
D) Find the normal force on the crate.
8. A 90 kg skier takes to the slopes and re
E) With what force does the block pull on the rope?
a. D
coo
sur
12. A 90 kg skier takes to the slopes and reaches a constant velocity.
A) Draw a force diagram for the skier. (Hint: use a coordinate axis parallel
and perpendicular to the hill's surface)
B) Determine the skier's weight.
C) Determine the Normal Force.
b. Determine the skier's weight.
D) Determine the Frictional Force.
c. Determine the component of the
d. Determine the component of the