Transcript forces christina danielle ali

May the Force Be
With You
A lesson on dynamics and forces
By, Christina Germak
Danielle Rosenberg
Ali Larcombe
What are we trying to accomplish?
To model why objects move
 To model forces
 To connect motion to forces
 What is mass? How are mass, force, and
acceleration related?
 To begin solving problems
 To gain an understanding of Newton’s 3
Laws of Motion

How to make a Free-Body Diagram


Start with a dot to represent the object that the forces are acting on
(This is where the mass should be).
Draw arrows from the dot to show the direction of the forces acting
on it.

The upward arrow represents the force of the surface on the object, or
whatever is exerting an upward force on the object (the normal force).
 The downward arrow always represents the force of the Earth on the
object (gravity).
 The arrows in the x direction represent other outside forces, such as
friction, or a push or pull.


If all arrows in the x or y direction are equal in length, the net force is
zero, and the object is traveling at a constant speed.
If one arrow is bigger than the other in either direction, there is a net
force.

Net Force- The difference of forces in two opposite directions. If the
difference is 0, there is no net force.
 If the arrow in the negative direction or positive direction is bigger than
the arrow in the opposite direction, the object is accelerating.
Constant motion or acceleration?
How do you interpret these free-body diagrams?
Acceleration in the
positive or negative x
direction- The arrow to
the left (negative direction)
is bigger than the arrow to
the right. The object could
be slowing down to the
right, or speeding up to
the left.
Constant motionConstant motion- The two upward The net force is zero
forces add up to the downward force in the x direction and
(gravity), which means the net force the y direction. The
object could be in
is zero. The object could be in
motion or at rest.
motion or at rest.
Acceleration in the
positive or negative x
direction- The arrow to the
right (positive direction) is
bigger than the arrow to the
left. The object could be
speeding up to the right, or
slowing down to the left.
Constant motionThe two arrows are
the same size (net
force = 0). The
object could be in
motion or at rest.
Acceleration in the
positive or negative y
direction- The upward
arrow (positive direction) is
bigger than the downward
arrow. The object could be
speeding up to the north, or
slowing down to the south.
Acceleration in the
negative or positive y
direction- The
downward arrow
(negative direction) is
bigger than the upward
arrow. The object
could be speeding up
to the south, or slowing
down to the north.
Try a Problem
Tina and Danielle are
pulling Ali, who
weighs 45 kg, in a
wagon by a string (in
the positive x
direction), across the
street at a constant
speed. (45 kg
includes the mass of
the wagon). Draw a
free-body diagram to
model this scenario.
Ali and wagon =
45 kg
Limitations of Free-Body Diagrams
Can you tell which of these free-body
diagrams represent an object that is
moving down? The real answer is that ALL of these free-body
diagrams could represent an object that is
traveling downwards.
•Free-body diagrams only represent the
magnitude of the forces that are acting on the
object.
Did you say
only this one?
•For example, if the top arrow is larger than
the bottom arrow, it does not mean it is only
moving up. It could also be slowing down in
the negative direction. If the arrows are equal
to each other, it does not only mean it is in
motion, because if an object has a constant
speed of 0 m/s, it has the same free-body
diagram as an object that is traveling at a
constant speed of 10 m/s.
How to make a Motion Diagram






Start off with t = 0 to represent that no time has passed (for the first
dot). Have each proceeding dot represent a certain amount of time.
If the object is traveling at a constant speed, draw the dots equally
apart from each other.
If the object is accelerating, draw each dot a little farther apart than
the last one.
If the object is decelerating, draw each dot a little closer to the last
one.
Depending on the direction of motion, the motion diagram will go to
the left, right, up, or down.
Velocity vectors show the direction of the object and acceleration
vectors show the direction of acceleration (they face in the opposite
direction of motion when the object is decelerating).

Acceleration vectors are all the same length when the acceleration is
constant. Place them above or next to the velocity vectors.
Can you interpret these motion
= 1 second
diagrams?
t=0
t=0
Acceleration- An object is speeding up in the positive x
direction.
Acceleration- An object is slowing
down in the positive x direction.
t=0
Constant / Accelerated
Motion- An object starts out
with constant motion in the
positive x direction, and then
slows down to a stop, and is
stopped for 2 seconds.
t=0
Acceleration- An object is slowing down in
the negative x direction.
Constant
motion- An
object is
traveling at a
constant
speed in the
negative y
direction.
Acceleration- An
object speeds up in
the positive y
direction.
Try a problem

A car is traveling at a constant
speed. He then realizes he is not
going to make the green light, so he
steps on the gas and accelerates
through it. Draw a motion diagram to
model this situation.
t=0
What experiments will provide a
good basis for this chapter?
 Roller
skating experiment
 Bocce ball experiments (1 and 2)
 Fan cart experiments
 2 lab experiments that show the
relationship between acceleration,
force, and mass
 The weight on the scale (in elevator
and elsewhere)
Roller Skating




Make sure you have the appropriate safety
equipment! (helmet, wrist guards, elbow and knee
pads)
Make sure there is nothing on the ground you could
run over and trip on (back packs, etc.).
See how many ways you can get yourself to move on
roller skates.
Pay attention to:

what direction you exert the force, and what direction you
actually move.


The direction in which you exert the force is opposite to the
direction in which you move.
how much of a force you exert and how fast you move.

The speed at which you move depends on how much force
you apply. They are directly proportional.
Bocce Ball Exp. 1


Make sure no body is
around the bocce ball
when it is rolled.
Have person 1 roll the ball at a constant speed
to person 2, who is sitting 5 meters away.
Halfway there, have person 3 push the ball in
the direction of its original motion and observe
the results before person 2 stops it by exerting a
force in the opposite direction of its motion.
You should observe that the speed of the ball
increases in the direction of its motion after it
has been pushed the first time.
Bocce Ball Exp. 2


Make sure no body is around
the bocce ball when it is
rolled.
Have person 1 roll the ball at a constant, fast
speed to person 2, who is sitting 5 meters away.
Halfway there, person 3 should push the ball in
the opposite direction of its original motion, and
observe the results before person 2 stops it by
exerting a force in the opposite direction of its
motion.
The ball should slow down in the original
direction of its motion, after it has been pushed
the first time.
t=0
Fan Cart Scenario 1
• Be careful not to
put your fingers, or
any part of your
body near the fan!
• If you have long
hair, make sure to
tie it back.


There are 2 connected fan carts, A and B. A is
on the left and B is on the right. The positive
direction is to the right, and the negative
direction is to the left. Turn on fan A, and
observe the motion of the two carts.
You should observe that the two carts
accelerate in the positive direction.
Fan Cart Scenario 2
• Be careful not to put your fingers, or
any part of your body near the fan!
• If you have long hair, make sure to tie
it back.


There are 2 connected fan carts, A and B. A is
on the left and B is on the right. The positive
direction is to the right, and the negative
direction is to the left. Turn on fan B, and
observe the motion of the two carts.
You should observe that the two carts
accelerate in the negative direction.
Fan Cart Scenario 3
• Be careful not to put your
fingers, or any part of your
body near the fan!
• If you have long hair, make
sure to tie it back.
There are 2 connected fan carts, A and B.
A is on the left and B is on the right. The
positive direction is to the right, and the
negative direction is to the left. Turn on
fan A and fan B, and observe the motion of
the two carts.
 You should observe that the two carts do
not move.
t=0

Mass is Constant






You will need a small cart, a spring
scale, 1500 grams, a meter stick,
and a stop watch.
Measure 1 meter from the start
point to the end point.
Put the 1500 grams onto the cart
and attach the spring scale to the
cart as well.
Place the cart at the start point
and start the stop watch as some
one pulls the spring scale with a
constant force until the end point,
where you stop the watch.
Do this, increasing the force by 10
N each trial. Find the acceleration
of each trial and see how the force
is related to the acceleration.
You should find that acceleration
and force are directly proportional.
Make sure you are wearing
closed-toed shoes!
Force (N)
Time (s)
Acceleration
(m/s/s)
10
8.28
0.03
20
7.27
0.04
30
4.48
0.1
40
3.36
0.18
50
2.93
0.23
60
2.70
0.27
70
2.48
0.33
80
2.13
0.44
90
2.09
0.46
100
1.65
0.73
Due to human error, results may vary.
Force is Constant





You will need different masses,
a meter stick, a small cart and
hanger (pulley), and
stopwatch.
The cart is connected to a
pulley which has a constant
mass at the end of it resulting
in a constant force
Load different masses onto the
cart and set it down on the lab
table
See what happens to the
acceleration when more mass
is added to the cart
You should find that mass and
acceleration are inversely
proportional.
Make sure you are wearing
closed-toed shoes!
Mass (g)
Time (s)
Acceleration
(m/s/s)
500
1.78
0.63
700
2.03
0.49
1000
2.25
0.4
1200
2.50
0.32
1500
2.69
0.28
1700
2.87
0.24
2000
3.25
0.19
2200
3.50
0.16
2500
3.52
0.16
2700
3.65
0.15
Due to human error, results may vary.


From the last two
experiments, it can be
seen that acceleration is
directly proportional to the
net force, and inversely
proportional to the mass.
From this, we can derive
this equation, which
represents Newton’s
Second Law.
a
F

m
Scale in Elevator





Place a 100 gram weight on a scale in an
elevator, and hit the up button in the elevator.
What do you notice about the reading on the
scale as the elevator speeds up? When it stays
at a constant speed? When it slows to a stop?
When the elevator is accelerating upward you
should notice that the force on the scale
increases (the reading on the scale should
increase over 100 g).
When the elevator stays at a constant speed,
the force on the scale remains constant (it
should read the final mass that it increased to
from the previous scenario).
When the elevator slows down while traveling
upward, the force should decrease (it should
slowly decrease to 100 g).
Fstring
Weight on Scale 1


scale
100 g
Take a 100 gram mass and place it on the scale.
First, attach a string to the side of the mass and
pull upward in a diagonal direction while sliding it
across the surface of the scale. What do you
notice happens to the force on the scale?
You should notice that the force on the scale
decreases because the force of you pulling on
the mass alleviates some of the force on the
scale.
Fstring
Weight on Scale 2


scale
100 g
Take that same 100 gram mass and place it on
the scale. Using your finger, press down on a
corner of the mass in a downward diagonal
direction and push the mass across the surface
of the scale. What do you notice happens to the
force on the scale as you push it across?
You should notice that the force on the scale
increases as you push it down and across the
surface of the scale.
First Law (Law of Inertia)

An object at rest will stay at rest, and an
object in motion will stay in motion, unless
an unbalanced force acts upon it. An
object with more mass has more inertia,
which means its resistance to motion is
greater than an object with less mass.
Because the rock was only in
the way of the skateboard,
the skateboard stopped, but
the skateboarder continued
his motion in the positive x
direction.
First Law (Law of Inertia)
Skateboard before hitting rock
Skateboard after hitting rock
Fsurface
Fsurface
skateboard
Frock
skateboard
Fearth
Fearth
skateboard
skateboard
The force of the rock on the
skateboard is an unbalanced force
(the net force is no longer 0 N), and
caused the skateboard to stop
moving.
skateboard
Second Law (

a
F
m
)
The Net force on an object is directly
proportional to the acceleration of the
object and is indirectly proportional to the
mass of the object.
Because the ball has less
mass than the wall, it
accelerates more.
Second Law (
(wall)
a
F
Fperson
Fearth
wall
(ball)
Fperson
Fearth
ball
ball
m
wall
)
The amount of force
exerted on the wall by
the person and the
ball by the person is
the same. However, if
you look at Newton’s
2nd law equation, if the
mass increases, the
acceleration will
decrease, since they
are inversely
proportional. This is
why the wall does not
move, and the ball
does.
Third Law

For every force, there is an equal and
opposite force.
The rocket’s
engine pushes on
the ground with
the same force as
the ground
pushes back on
the rocket,
causing it to
launch.
Third Law
Fground
rocket
(ground)
(rocket)
Frocket
The amount of force exerted on
the ground by the rocket is the
same as the amount of force
exerted on the rocket by the
ground.
ground
Environmental Examples

There are several examples of Newton’s 3 Laws
in your everyday life.
1st Law: Imagine you are playing in a soccer game, and
you kick the ball at the goal, and think it is going to go in.
However, the goalie blocks it and keeps it from continuing
in its original path of motion, so you don’t score a goal.
 2nd Law: If you go to the grocery store and you grab an
empty cart, you will notice that it is really easy to push
around and go fast with. Once the cart starts to get full you
should notice that it gets harder to push and is harder to
accelerate.
 3rd Law: If you see a car driving down the highway and a
truck is coming in the other direction, on the wrong side of
the road, and they collide, the car will exert the same
amount of force on the truck as the truck will exert on the
car, even though the truck is bigger.

Exemplary Problem 2

Elevator problem
A
50 kg person stands on a scale in an
elevator. What does the scale read when:
A) The elevator is at rest?
 B) The elevator is going up at a constant speed of
6 m/s?
 C) The elevator is going down at a constant speed
of 6 m/s?
 D) The elevator is accelerating upward at 6 m/s/s?
 E) The elevator is accelerating downward at 6
m/s/s?

Felevator
Answer 1
A, B, and C) 9.8m / s / s 
490 N = Fearth
person
Fearth  person
50kg
person = Felevator
person
Fearth
person
Because scenarios A, B, and C are all traveling a constant speed / at rest, the
force of the elevator on the person will remain the same.
D)
6m / s / s 
Felevator  person  490 N
50kg
300 N = Felevator
Felevator
E)
 6m / s / s 
person - 490 N
person = 790 N
Felevator  person  490 N
50kg
-300 N = Felevator
Felevator
person - 490 N
person = 190 N
Exemplary Problem 2

What is the acceleration of a pulley system
with two masses attached to each end,
one weighing 45 kg and 15 kg?
45 kg
15 kg
F45kg
15kg
Answer 2
Step 1
Fearth  15kg
9.8m / s / s 
15kg
F15kg
147 N = Fearth
Step 2
Fearth  45kg
9.8m / s / s 
45kg
441 N = Fearth
Step 3
15 kg
45 kg
147 N  441N
a
60kg
a = +/- 4.90 m/s/s
earth
Exemplary Problem 3
Remember this problem?
• Tina and Danielle are pulling Ali, who weighs 45 kg in a
wagon by a string (in the positive x direction), across the
street at a constant speed. Draw a free-body diagram to
model this scenario. (45 kg includes mass of wagon)
• Now, Ali is accelerating. The force of Tina and Danielle on Ali
is 12 N, and the force of friction on Ali is 7 N. Find the
acceleration of Ali.
Fsurface
Ali
Answer 3
7N
12 N
FTandD  Ali  Ffriction  Ali
a
45kg
Fearth
12 N  7 N
a
45kg
a= 0.1 m/s/s
Ali
Exemplary Problem 4

A 50 kg man fell out of a plane and is
hurtling towards the ground. What is the
force of the earth on the man as he
accelerates downward?
Answer 4
(air resistance negligible)
Fearth  person
9.8m / s / s 
50kg
50kg
Fearth
490 N
person
Chapter 8 Summary

We model why objects move using freebody diagrams and motion diagrams.
 Objects
move because of the forces that act
upon them.

We model forces using free-body
diagrams.
 Net
Force is the difference of forces that are
acting on an object in opposite directions.

There is no net force if the object is moving at a
constant speed or motionless.
Chapter 8 Summary
Mass
is the amount of inertia an object
has, or how much it resists a change in
motion.
 Weight
is the amount of force with which an
object pushes down on the Earth.
Mass
is inversely proportional to
acceleration. Force is directly
proportional to acceleration.
Chapter 8 Summary

Newton’s 3 Laws of Motion model how
and why objects move.

First Law (Law of Inertia): An object at rest will stay at rest,
and an object in motion will stay in motion, unless an
unbalanced force acts upon it. An object with more mass
has more inertia, which means it will resist motion more.
a
F

Second Law (
m ): The Net force is directly proportional
to the acceleration of an object and indirectly proportional
to the mass of an object.

Third Law: For every force, there is an equal and opposite
force.
Practice Problems
1.
2.
An object sits on a frictionless surface.
There is a 20 N force being applied to
the object in the right direction and its
acceleration is at 2 m/s/s. What is its
mass?
A 25 kg mass pulled along a frictionless
surface by a horizontal force of 150 N will
have what acceleration?
Practice Problems
3. A shopper in a supermarket pushes a loaded
cart with a horizontal force of 15 N. The cart
has a mass of 40kg.


a. What is the resulting force? Ignore friction.
b. What will the resulting force if shopper places
their 30N child in the cart before they begin to push
it?
4. A 35 kg block is pulled along a frictionless
horizontal surface by a string The string is
pulled by a 110 N force. What is the
acceleration of the block?
Practice Problems
5. A professional wrestler pushes his small son on a sled
from behind along a horizontal surface.
a. As they accelerate from rest, which force is larger: the force
of the boy on the wrestler or the force of the wrestler on the boy?
b. Once they are traveling at a constant velocity, which force is
larger: the force of the wrestler on his son, or the force of the
surface, due to friction on the boy?
c. As they slow down what is the larger force: the force of the
wrestler on his son, or the force of the surface, due to friction on the
boy?
6. What force is required to accelerate an object having a
mass of 3 kg at 10 m/s/s?
7. What is the mass of an object which is accelerated at
15 m/s/s due to a force of 70 N?
8. A rope is lifting a heavy bucket with a force of 20N and it
is accelerating upward at 5 m/s/s. What is the mass of
the bucket?
Practice Problems
9.
10.
11.
12.
13.
Amanda is pulling a 50 kg cart with a force of 10N across a
carpet with friction of 7N. How much is it accelerating?
There is a frictionless pulley with a 5.5 kg mass and a 6.5
kg mass attached on either end. What will the acceleration
of this system be?
You are pulling your suitcase, with a mass of 20 kg, across
a carpet to the right (there is a force of friction of 6 N to the
left). The suitcase is moving at a constant speed. Draw a
free-body diagram for this situation, and what is the force of
you that is pulling the suitcase?
A man standing on a scale in an elevator usually weighs
850 N but the scale he is standing on reads 15 N. He is
traveling upward to the 50th floor. What is his acceleration?
A man in an elevator weighs 75 kg. He is accelerating
downwards at 5 m/s/s. What is the force of the elevator on
the man?
1.) 10 kg
2.) 6 kg

3.)
 A.)
0.375 m/s/s
 B.) 0.35 m/s/s
4.) 3.14 m/s/s

5.)
 A.)
The force of the wrestler on the son is the
same as the force of the son on the wrestler.
 B.) Fwrestler
son
 C.) Fwrestler
son

6.) 30 N

7.) 4.67 kg

8.) 4 kg

9.) 0.06 m/s/s

10.) 0.82 m/s/s
Fsurface

11.) 6 N
6N
?
Fearth
15 N

12.) -9.53 m/s/s
?
?
850 N
75 kg

you
13.) 360 N
735 N
you
Works Cited
www.sciencebyjones.com/force_problems.
htm
 www.physics247.com/physics-homeworkhelp/net-force.php
