Name: ________________________________________________
Period: _____
Unit II: Newton’s Laws
Subunit B: Unbalanced Forces
Variables, Units
Fg
FA
FN
FT
Ff
ΣF or FNET
NOTES:
Equations
Unit II-B Objectives
What you should know when all is said and done
By the time you finish all labs, worksheets and related activities, you should be able to:
1. Use Newton’s 2nd Law to qualitatively describe the relationship between m and a, F and a,
m and F. (e.g., if you double the mass, the acceleration will…)
2. Determine the net force acting on an object by:
a. drawing a force diagram for an object given a written description of the forces acting on it.
b. resolving forces into x and y components, then finding the vector sum of the forces.
c. analysis of the kinematic behavior of the object.
3. Solve quantitative problems involving forces, mass and acceleration using Newton’s 2nd Law.
a. Having determined the net force (as in #3), and given the mass, find the acceleration.
b. Continue to use the kinematical models from Unit I to determine the velocity or
displacement of the object, once the acceleration is known.
4. Differentiate between static and kinetic friction and describe what affects the frictional force.
5. Determine the magnitude of the frictional force and the effect it has on an object’s motion.
Problem-Solving Strategy:
1. Sketch a free-body diagram (FBD). To simplify the diagram, represent the object by a dot. Draw
arrows representing all the forces acting on the object. The direction of each arrow should indicate
the direction of the force.
2. Label each arrow on the FBD with a symbol to indicate the type of force it is.
Use the GUESS method:
3. Write down all Given information in variable form (e.g., m = 2.0 kg; a = 1.5 m//s, right). Write
down the Unknown variable - what the problem asks to be determined or calculated (e.g., FA = ?).
4. Equation: The net force is the vector sum of all the individual forces acting on the object. The
"summing" of individual forces is simplified if the horizontal and vertical forces are summed
separately. Indicate this in the form of equations based upon the FBD.
Horizontal
∑Fx = Fright - Fleft
(assumes that rightward is the + direction)
Vertical
∑Fy = Fup - Fdown
(assumes that up is the + direction)
5. Set the net force equations equal to ma (∑Fx = m ax and ∑Fy = m ay) or equal to zero if there is
no acceleration.
6. Solve the problem for the desired information by relating the #4 and the #5 equations.
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M OP Connection:
Newton's Laws: sublevel 7
1.
The acceleration of an object is ____________________ related to the net force exerted upon it and
_____________________ related to the mass of the object. In equation form: a = Fnet / m.
a. directly, inversely
b. inversely, directly
c. directly, directly
d. inversely, inversely
2.
Use Newton's second law to predict the effect of an alteration in mass or net force upon the
acceleration of an object.
a. An object is accelerating at a rate of 8 m/ s2 when it suddenly has the net force exerted upon
2.
increased
by a factor
2. The new acceleration
be _________
m/ sexerted
1. What
happens
to theofacceleration
of an objectwill
when
the net force
on it is doubled?
Unit II-B: Unbalanced Forces
Worksheet 1
A) It doubles.
B) It is half as much.
C) It remains the same.
A) It doubles.
B) It is half as much.
C) It remains the same.
A) It doubles.
B) It is half as much.
C) It remains the same.
An object is accelerating at a rate of 8 m/ s2 when it suddenly has the net force exerted upon
increased
by a factor
4. The new acceleration
be _________
s2 . object is doubled?
2. What
happens
to theofacceleration
of an objectwill
when
the mass m/
of the
b.
An object is accelerating at a rate of 8 m/ s2 when it suddenly has the net force exerted upon
factor
of 2.is The
new
acceleration
will beto
_________
s2 .
3. If decreased
the massby
of aan
object
cut in
half,
what happens
its weightm/(gravitational
force)?
c.
d. An object is accelerating at a rate of 8 m/ s2 when it suddenly has its mass increased by a factor
2
2. The exerts
new acceleration
will
be _________
4. Aofwoman
a constant
horizontal
forcem/
ons a. large box. As a result, the box moves across a
horizontal floor at a constant velocity. The2constant force by the woman:
e. has
An the
object
is accelerating
at as
a rate
8 m/ s ofwhen
it suddenly has its mass decreased by a factor
A)
same
magnitude
theofweight
the box.
4. The new
be box.
_________ m/ s2.
B) isofgreater
thanacceleration
the weight will
of the
C) has the same magnitude as the total force
which resists the motion of the box.
f. An object is accelerating at a rate of 8 m/ s2 when it suddenly has the net force exerted upon
D) isincreased
greater than
the
total
force
which
resists
the motion of the box.
by a factor of 2 and its mass decreased by a factor of 4. The new acceleration will be
E) is greater than either
the
weight
of
the
box
or
the total force which resists its motion.
2
_________ m/ s .
5.
theobject
woman
in questionat4asuddenly
stops
applying
a horizontal
to the
box,upon
then the box
g. If An
is accelerating
rate of 8 m/
s2 when
it suddenly
has the force
net force
exerted
A) will
immediately
stop.
increased by a factor of 4 and its mass increased by a factor of 2. The new acceleration will be
B) will
continuem/moving
at a constant speed for a while and then slow to a stop.
_________
s2.
C) will immediately start slowing to a stop.
D)
at a constant
h. will
Ancontinue
object is accelerating
at aspeed.
rate of 8 m/ s2 when it suddenly has the net force exerted upon
D) will
increase
its
speed
for
a
and
then start
to4.a The
stop.new acceleration will be
increased by a factor of 3 and while
its mass
decreased
by slowing
a factor of
_________ m/ s2.
3.
6. These force diagrams depict the magnitudes and directions of the forces acting upon four
These force
diagrams
depict
the magnitudes
andforce
directions
of the Rank
forces these
acting objects
upon four
objects.
In each
case,
the down
force is the
of gravity.
in objects.
order ofIntheir
each case, the down
force is the
force of gravity. _______
Rank these> objects
in order
of their >
acceleration,
acceleration,
from largest
to smallest:
_______
> _______
_______
from largest to smallest:
_______ > _______ > _______ > _______
7. Newton’s 2nd Law of Motion relates the amount of net force and the amount of inertia to the
acceleration or change in motion of an object. It states that larger forces produce ____ (more/less)
acceleration on a given mass, and that the more mass an object has, the ___ (more/less) it will
© The
Physics Classroom,
Page 12
accelerate
for a given2009
net force.
8. Neglecting air resistance, why would an elephant and a mouse fall with the same acceleration?
Use an equation to help explain.
Free Response. Show your work!!
9. What would be the force of gravity of a 60 kg girl on the moon where the acceleration due to
gravity is 1.6 m/s2? What would her mass be?
Fnet=
m=
a=
10. What net force is required to accelerate a car at a rate of 2 m/s2 if the car has a mass of 3,000
kg?
Fnet=
m=
a=
11. What is the mass of a truck if it produces a force of 14,000 N while accelerating at a rate of 5
m/s2 ?
Fnet=
m=
a=
12. What is the acceleration of softball if it has a mass of 0.5 kg and hits the catcher's glove with a
force of 25 N?
Fnet=
m=
a=
13. Sally’s car has a mass of 2000 kg. If her car produces a force of 5000 N, how fast will it
accelerate?
Fnet=
m=
a=
14. Sally wants to accelerate even faster than in problem #13, so she removes 500 kg of mass
from her car. How fast will her 1500 kg car accelerate if it produces 5000 N of force?
Fnet=
m=
a=
Unit II-B: Unbalanced Forces
Worksheet 2
1. Felicia, the ballet dancer has a mass of 45 kg. A) What is her weight on Earth?
B) What is Felicia’s mass on Jupiter, where the acceleration due to gravity is 26 m/s2?
C) What is Felicia’s weight on Jupiter?
2. Butch the 72 kg star quarterback collides with a stationary player and is brought to a stop with
an acceleration of -20 m/s2. A) What force does the stationary player exert on Butch?
B) What force does Butch exert on the stationary player?
Fnet=
m=
a=
3. You push horizontally on a 20-kg crate with a force of 100 N. If the frictional force is 15 N, what
is the acceleration of the crate?
Fnet=
m=
a=
4. Now, instead of just the 20 kg crate, you push on two crates
as shown in the diagram with a 100 N of force. The total force
of friction on the two crates is 20 N.
Fnet=
m=
a=
5. A 70 kg skydiver jumps out of an airplane.
A) Immediately after jumping, how large is the skydiver's acceleration?
Fnet=
m=
a=
B) Upon reaching a downward velocity of 100 miles per hour, 300 Newtons of drag resist the
skydiver's motion (mass = 70 kg). Draw a force diagram for the skydiver. How large is the
skydiver's acceleration?
Fnet=
m=
a=
Newton's Laws
4.
For each force diagram, determine the net or resultant force (! F), the mass and the acceleration of
the object. Identify the direction (the second blank) of the two vector quantities. NOTE: Fgrav
6. For stands
each force
diagram,
for the
weight ofdetermine
the object.the net or resultant force (∑F), the mass and the acceleration
of the object. Identify the direction (the second blank) of the two vector quantities.
a.
b.
! F=
,
! F=
m =
a=
m =
,
c.
a=
,
d.
! F=
,
! F=
m =
a=
,
m =
,
e.
a=
,
f.
! F=
,
! F=
m =
a=
,
,
m =
,
a=
,
Unit II-B: Unbalanced Forces
Worksheet 3
1. An elevator is moving up at a constant velocity of 2.5 m/s, as illustrated in the diagram. The man
has a mass of 85 kg.
A) Construct a force diagram for the man.
B) How much force does the floor exert on the man?
2. The elevator now accelerates upward at 2 m/s2.
A) Construct a force diagram for the man.
B) How much force does the floor now exert on the man?
Fnet=
m=
a=
3. Upon reaching the top of the building, the elevator accelerates downward at 3 m/s2.
A) Construct a force diagram for the man.
B) How much force does the floor now exert on the man?
Fnet=
m=
a=
C) While descending in the elevator, the cable suddenly breaks. What is the force of the floor on
the man?
4. A jumbo jet has a mass of 30,000 kg. The horizontal thrust for each of four engines is 15,000 N.
What is the jet’s acceleration when taking off on a level runway?
Fnet=
m=
a=
5. A tow truck exerts a force of 3000 N on a car, accelerating it at 2 m/s2. Draw a force diagram.
A) Find the mass of the car. B) If the force of friction on the car is now 1000 N and the tow truck
still pulls with 3000 N, what will be the acceleration of the car?
Fnet=
m=
a=
6. A rocket weighs 2 x 107 N. Its engines exert 25 x 106 N of force at lift-off. Draw a force diagram!
A) What is the mass of the rocket? B) What is its acceleration when it lifts off?
Fnet=
m=
a=
7. An unbalanced force of 30 N gives an object an acceleration of 5 m/s2. What force would be
needed to give it an acceleration of 1 m/s2?
Fnet=
m=
a=
8. A firefighter with a mass of 80 kg slides down a vertical pole with an acceleration of 4 m/s2.
What is the frictional force that acts on the firefighter?
Fnet=
m=
a=
9. A 900 kg car exerts 5000 N of traction force on a level road while being opposed by 1000 N of
friction and drag forces combined. What is the acceleration of the car?
Fnet=
m=
a=
Unit II-B: Unbalanced Forces
Worksheet 4
1. During a head-on collision, a passenger in the front seat of a car accelerates from 13.3 m/s (30
mph) to rest in 0.10 s.
A) What is the acceleration of the passenger?
Δx =
Equation:
v0 =
v=
a=
t=
B) The driver of the car holds out his arm to keep his 25 kg child (who is not wearing a seat belt)
from smashing into the dashboard. What force must he exert on the child?
F=
m=
a=
C) Convert this forces from Newtons to pounds (1 lb = 4.45 N). What are the chances the driver
will be able to stop the child?
2. The maximum force that a grocery bag can withstand without ripping is 250 N. Suppose that the
bag is filled with 20 kg of groceries and lifted with an acceleration of 5.0 m/s2. Draw a force
diagram. Do the groceries stay in the bag?
Fnet=
m=
a=
3. A 4-kg helicopter accelerates upward at 2 m/s2. Draw a force diagram. How much lift force is
exerted by the air on the propellers?
Fnet=
m=
a=
4. A racecar has a mass of 710 kg. It starts from rest and travels 40 m in 3 s. The car is uniformly
accelerated during the entire time. What net force is acting on the car?
Δx =
Equation:
Fnet=
v0 =
m=
v=
a=
a=
t=
6. Suppose that a 1,000 kg car is traveling at 25 m/s (55 mph). Its brakes can apply a force of
5,000 N. What is the minimum distance required for the car to stop?
Δx =
Equation:
Fnet=
v0 =
m=
v=
a=
a=
t=
7. A 65 kg person dives into the water from the 10-m platform.
A) What is her speed as she enters the water?
Δx =
Equation:
v0 =
v=
a=
t=
B) She comes to a stop 2 m below the surface of the water. Calculate the net force the water
exerted on the swimmer.
Δx =
Equation:
Fnet=
v0 =
m=
v=
a=
a=
t=
8. While chopping down his father’s cherry tree, George discovered that if he swung the axe with a
speed of 5 m/s, it would embed itself 2.3 cm into the tree before coming to a stop.
A) If the axe head had a mass of 2.5 kg, how much force was the tree exerting on the axe head
upon impact?
Δx =
Equation:
Fnet=
v0 =
m=
v=
a=
a=
t=
Unit II-B: Unbalanced Forces
Worksheet 5
Physics Tip: Whenever you encounter a situation involving a force directed diagonally, immediately convert the
diagonal force into two perpendicular components (BREAK IT DOWN!). Use SOH CAH TOA to resolve any
uncooperative force into two components - one being in the direction of the acceleration (or the motion) and the other
being at right angles to it. In the case of inclined planes, resolve the uncooperative force into components parallel
and perpendicular to the inclined plane. Then IGNORE the uncooperative (diagonal) force and treat it as though it
has been replaced by the two components.
1. You are dragging your desk again, but this time you remembered to empty the drawers so that
it is light enough to move. The desk has a mass of 30 kg and the friction is 100 N. You pull with
250 N of force at a 30-degree angle.
A) Write the equation for the forces in the y-direction. Calculate
the Normal force.
B) Calculate the frictional force resisting your pull.
C) Write the equation for the forces acting in the horizontal direction. Calculate the acceleration of
the desk.
2. Now you decide to push that same blankety-blank desk instead of pull, but use the same 250 N
force at an angle of 30 degrees above the horizontal. The desk still has a mass of 30 kg, but since
you are pushing down into the floor, the friction force has increased to 200 N.
A) Write the equation for the forces in the y-direction and calculate
the Normal force.
B) Write the equation for the forces acting in the horizontal direction.
Calculate the acceleration of the desk. Is it better to push or pull the
desk?
3. An applied 25 N force pushes on a 5.0 kg block resting on a frictionless horizontal surface. The
force is directed downwards at an angle of 20º.
A) Draw a force diagram of the block.
B) Determine the sum of the forces in each direction (ΣFx and ΣFy).
C) Use one of the equations to calculate the acceleration of the block.
D) Use one of the equations to calculate the normal force on the block.
4. A 70-kg box is pulled by a 400 N force at an angle of 30º to the horizontal. The force of friction is
75 N. A) Draw the force diagram for the box.
B) Determine the sum of the forces in each direction (ΣFx and ΣFy).
C) Use one of the equations to calculate the acceleration of the box.
Unit II-B: Unbalanced Forces
Worksheet 6
1. A classroom desk is stationary in the room. A really cool science teacher comes around and
pushes upon the desk in an effort to start it into a state of motion. The desk does not budge. The
desk remains at rest because
A) there is a force of static friction opposing its motion
B) there is a force of kinetic or sliding friction opposing its motion
C) there is a force of rolling friction opposing its motion
D) there are small dust mites at the desk's feet which push back on the desk to keep it at rest
2. Now when the really cool science teacher comes around and pushes upon the desk in an effort
to start it into a state of motion, the desk is finally accelerated from rest and then moves at a
constant speed of 0.5 m/s. The desk maintains this constant speed because
A) there is a force of static friction balancing the teacher's forward push
B) there is a force of kinetic or sliding friction balancing the teacher's forward push
C) there is a force of rolling friction balancing the teacher's forward push
D) the teacher must have stopped pushing
3. The symbol μ stands for the
A) coefficient of friction
B) force of friction
C) normal force
4. The units on μ are
A) Newton
C) m/s/s
B) kg
D) There are no units!
5. A 50-kg sled is pulled horizontally along snow-covered, flat ground. The static friction coefficient
is 0.30, and the kinetic friction coefficient is 0.10.
A) What force is needed to start the sled moving?
B) What force is needed to keep the sled moving at a constant velocity?
6. A 5 kg box on a horizontal table is pushed by a horizontal force of 15 N as
shown. If the coefficient of friction is 0.4, will the box move?
7. A 400-gram package lying on a horizontal surface is attached to a horizontal
string that passes over a smooth pulley. When a mass of 200 grams is
attached to the other end of the string, the package is on the point of moving.
Find the coefficient of friction.
8. A freshman is walking through the school cafeteria but does not realize that
the person in front of him has just spilled his glass of chocolate milk. As the freshman, who has a
mass of 42 kg, steps in the milk, the coefficient of friction between his feet and the floor is suddenly
reduced to 0.040. What is the force of friction between his feet and the floor?
9. Unbeknownst to the students at AHHS, every time the school floors are waxed, Mr. Collins likes
to slide down the hallway in his socks. Mr. Collins weighs 850 N and the force of kinetic friction
between his socks and the floor is 102 N. What is the coefficient of kinetic friction that opposes Mr.
Collin’s motion down the hall?
10. A car on a level surface of asphalt has a coefficient of static friction of 0.75 and a coefficient of
kinetic friction of 0.67. When a driver starts a car by "flooring it," the tires grind on the road
producing a smoke of burning rubber and pavement. Since the tires are slipping, the coefficient of
kinetic friction determines the maximum acceleration. Under normal circumstances, however, most
drivers are not willing to subject their tires to such extreme punishment. Typical car tires rotate
over the surface of the road without slipping, thus the coefficient of static friction determines a car's
maximum acceleration in most situations.
A) Find the force of static friction between the car and the road if the car has a mass of 2000 kg.
B) Find the force of kinetic friction between the car and the road.
C) Which way would give you better acceleration, by flooring it or by having a more gradual
approach?
Unit II-B: Unbalanced Forces
Worksheet 7
1. A block weighing 300 N is moved at a constant speed over a horizontal surface by a force of 50N applied parallel to the surface.
A) Construct a force diagram for the block.
B) Determine the sum of the forces in each direction (ΣFx and ΣFy).
C) Use one of the equations to calculate the coefficient of kinetic friction μk.
D) What would be the acceleration of the block if the μk = 0?
2. A horizontal 100-N force is applied to a 50-kg crate resting on a level floor. The coefficient of
kinetic friction μk is 0.15.
A) Draw a force diagram to represent the situation.
B) Determine the sum of the forces in each direction (ΣFx and ΣFy).
C) Calculate the force of friction acting on the crate.
D) Use one of the equations to calculate the acceleration of the crate.
3. During a football workout, two lineman are pushing the coach on the sled. The combined mass
of the sled and the coach is 300 kg. The coefficient of friction between the sled and the grass is
0.800. The sled accelerates at a rate of 0.580 m/s/s.
A) Draw a force diagram to represent the situation.
B) Determine the sum of the forces in each direction (ΣFx and ΣFy).
C) Calculate the force of friction acting on the crate.
Friction
Read from Lessons 2 and 3 of the N ewton's Laws chapter at The Physics Classroom:
Read from Lessons 2 and 3 of the Newton's Laws chapter at The Physics Classroom:
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1. A classroom desk supported by long legs is stationary in the room. A teacher comes around and
1. theAdesk
classroom
desk to
supported
by along
is stationary
in thedoes
room.
teacher
comes around and
pushes upon
in an effort
start it into
statelegs
of motion.
The desk
notAbudge.
The
D) Determine
the______.
force
applied
to thetosled
the lineman.
upon
the
desk
in an effort
startby
it into
a state of motion. The desk does not budge. The
desk remains
at pushes
rest because
desk
remains
at rest
becauseits
______.
a. there is a force
of static
friction
opposing
motion
a. ofthere
is aor
force
of static
friction
opposing
its motion
b. there is a force
kinetic
sliding
friction
opposing
its motion
is afriction
force ofopposing
kinetic oritssliding
friction opposing its motion
c. there is a forceb.ofthere
rolling
motion
c. dust
theremites
is a force
rollingfeet
friction
its on
motion
d. there are small
at theofdesk's
whichopposing
push back
the desk to keep it at rest
d. there are small dust mites at the desk's feet which push back on the desk to keep it at rest
2. A classroom
desk are
supported
by
legs is
stationary
in the room.
comes
4.2.You
drivingdesk
a long
2500-kg
car
at long
a constant
speed Aofteacher
14the
m/s
alongaround
an
icy,and
but
straight
and
classroom
supported
by
is stationary
in
teacher
comes
around
andlevel,
pushes upon
theAdesk
in an effort to
start it into
a statelegs
of motion.
The desk
isroom.
finallyAaccelerated
road. pushes
You approach
a
traffic
light
that
turns
red,
and
slam
on
the
brakes.
Your
wheels
lock,
and
upon
desk inspeed
an effort
start
into
a state
of motion.
The deskspeed
is finally accelerated
from rest and then moves
at athe
constant
of 0.5tom/
s. it
The
desk
maintains
this constant
the car skids to a halt in a distance of 25 m. What is the coefficient of friction between your tires
because ______. from rest and then moves at a constant speed of 0.5 m/ s. The desk maintains this constant speed
and the
icy road?
because
a. there is a force
of static______.
friction balancing the teacher's forward push
Δx
=
Equation:
Fnetpush
= push
a.
there
is aor
force
of
static
friction
balancing
the teacher's
forward
b. there is a force of kinetic
sliding
friction
balancing
the teacher's
forward
v
=
m
=
0
b.
there
is
a
force
of
kinetic
or
sliding
friction
balancing
the
teacher's
forward push
c. there is a force of rolling friction balancing the teacher's forward push
v
=
a
=
c.
there
is
a
force
of
rolling
friction
balancing
the
teacher's
forward
push
d. the teacher must have stopped pushing
a = d. the teacher must have stopped pushing
3. The symbol
t =µ stands for the _____
3. of The
symbol µ stands
for the
_____
a. coefficient
friction
b. force
of friction
c. normal force
a. coefficient of friction
b. force of friction
c. normal force
4. The units on µ are _____
units on µ are
a. Newton 4. The
b. kg
c. _____
m/ s/ s
d. ... nonsense! There are no units on µ.
a. Newton
b. kg
c. m/ s/ s
d. ... nonsense! There are no units on µ.
5. Use the friction
equation
and Fnetin
= the
m•afollowing
to fill in the
blanks in the following situations.
10.
Fill
in
the
blanks
situations.
5. Use the friction equation and Fnet = m•a to fill in the blanks in the following situations.
© The Physics Classroom,
2009Classroom, 2009
© The Physics
Page 19
Page 19
Unit II-B: Unbalanced Forces
Review Worksheet
EQUATIONS
F = Fnet = ma
Fg = mg = Weight
Ff = μ FN
Fnet = the sum of all forces, m = mass, a = acceleration
Fg = the force of gravity, g = 10 m/s2
Ff = Friction, μ = the coefficient of friction, FN = Normal force
1. The acceleration of an object is ____________________ related to the net force exerted upon it
and _____________________ related to the mass of the object. In equation form: a = Fnet / m.
2. Use Newton's 2nd law to predict the effect of an change in mass or net force upon the
acceleration of an object.
A) An object is accelerating at a rate of 8 m/s2 when it suddenly has the net force exerted upon
increased by a factor of 2. The new acceleration will be _________ m/s2.
B) An object is accelerating at a rate of 8 m/s2 when it suddenly has the net force exerted upon
decreased by a factor of 2. The new acceleration will be _________ m/s2.
C) An object is accelerating at a rate of 8 m/s2 when it suddenly has its mass increased by a factor
of 2. The new acceleration will be _________ m/s2.
D) An object is accelerating at a rate of 8 m/s2 when it suddenly has its mass decreased by a factor
of 4. The new acceleration will be _________ m/s2.
3. A 10kg armadillo and a 5 kg armadillo both fall from the same tall building at the same time.
Which will have a greater acceleration? Why?
4. Is it harder to start an object moving or to keep it moving when there is friction? What about
when there is no friction?
5. How much would a 60 kg girl weigh on the Mars, where the acceleration due to gravity is 3.6
m/s2? What would her mass be?
6. A net force of 250 N accelerates a bike and rider at 2.0 m/s2. What is the combined mass of bike
and rider?
Fnet =
m=
a=
7. The most massive train was put together in South Africa in 1989 and was over 7 km long and
had a total mass of 6.94 x 107 kg. Suppose the train’s acceleration from rest was 0.2 m/s2. What
would then be the size of the unbalanced force that the locomotives exerted on the cars of the
train?
8. The largest acceleration that a human has ever endured occurred when a racecar accidentally
crashed into a wall. The car was traveling at a speed of 48 m/s (107 mph) when it hit the wall. The
car came to a complete stop 0.0272 s later. Assume the driver had a mass of 70 kg. What was the
unbalanced force on his body as the car underwent negative acceleration?
Δx =
Equation:
Fnet =
v0 =
m=
v=
a=
a=
t=
9. A falling skydiver is experiencing 402 N of drag force on his parachute. The mass of the skydiver
(including parachute gear) is 67.2 kg.
A) Draw a force diagram.
B) Write the equation for the forces acting vertically.
C) Find the acceleration of the skydiver.
10. A 5-kg bunny is sliding to the right on a frozen lake and encountering a friction force that slows
it down. The coefficient of friction μ between the bunny and the ice is 0.1.
A) Draw a force diagram.
B) Write the equation for the forces acting in each direction.
C) Calculate the friction acting on the bunny.
D) Find the bunny’s acceleration.
11. Wile E. Coyote is pulling a crate of anvils down the
dusty highway. Use the force diagram and the net force
equations to fill in the blanks.