8A_Lab2_ForcesAndAccelerations
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LAB
2
Forces And Accelerations
In this laboratory, we will be analyzing a spring scale and a cart and track system with a various assortment of masses.
The goal of this lab is to better familiarize you with Newton’s Laws as well as forces and accelerations in general.
Given Quantities
• Track Length
=
0.8m
• Mass of Weight Hook
=
5g
• Mass of Cart
=
520g
• Mass of Pulley
=
30g
• Mass of String
º
0.5g
• Mass of Rectangular Metal Block
=
500g
2.1
Analyzing Net Force And Accelerations
In this part of the lab, we will try to better understand the relationship between forces and accelerations by using a
mass and a spring scale. As background, a spring scale works in a similar fashion to an ordinary household scale.
When a weight is attached to it, its spring stretches and the scale displays the weight of the attached object in units of
Newtons.
Figure 2.1: 500 Gram Mass on Spring
105
2. F
ORCES
A
ND
A
CCELERATIONS
1.
Take the
500g
mass (or another mass that you have been provided) and attach it to the end of the spring scale.
Because the spring scales may not be totally accurate, record the reading on the scale in the space below.
2.
Draw a
Free Body Diagram
for the mass and spring scale system while it is at rest in the space below. Include
the “Force of the Scale” and “Weight of the Mass”. Indicate the relationship between these two forces.
Figure 2.2: Moving Scale
3.
Before we proceed any farther, let’s do a quick thought experiment. What would happen to the reading of
the scale if you were to move the scale up or down with a constant velocity, while the mass was attached (but
without touching the mass)? Would the reading on the scale increase, decrease, or stay the same? Briefly
explain your reasoning.
4.
Now, with the
500g
mass attached, hold the scale and move it up and then down with a constant velocity.
What happens to the reading of the scale as you do so? Was your group’s hypothesis correct? If not, explain
why.
5.
Draw a
Free Body Diagram
for the mass and scale system as it is moved with constant velocity. Indicate
the relationship between the “Force of the Scale” and “Weight of the Mass” and indicate the direction of
acceleration if applicable.
6.
Before we proceed any farther, let’s do another quick thought experiment. What would happen to the reading
of the scale if you were to move the scale up from the floor to approximately shoulder level rather quickly?
Would the reading on the scale increase, decrease, or stay the same? Briefly explain your reasoning.
7.
With the
500g
mass attached, one teammate will hold the scale (with mass still attached) close to the ground
and then move it up to shoulder level rather quickly. The rest of the team will observe the reading of the scale.
What happens to the reading of the scale as the mass is moved quickly upward? Was your group’s hypothesis
correct? If not, explain why.
106
470g
The
force
of
the
spring
scale
and
the
weight
Force
of
scale
of
the
massare
the
same
magnitude
Gravity's
force
pulls
down
on
the
mass
while
the
spring
pushes
up
on
it
weight
of
masi
Moving
the
entire
system
upward
would
cause
the
weight
tobe
heavier
since
the
object
is
moving
against
gravity
The
scale
read
a
heavier
weight
as
we
moved
the
system
up
showing
that
our
hypothesis
was
correct
1
Egg
L
thereis
zero
acceleration
when
velocity
is
constant
The
reading
on
the
scale
would
increase
since
thenet
force
will
no
longer
be
zero
due
to
the
increase
of
upward
force
on
the
spring
with
upwardacceleration
2.1. Analyzing Net Force And Accelerations
8.
Draw a
Free Body Diagram
for the mass and scale system as it is moved upward quickly from the floor. Indicate
the relationship between the “Force of the Scale” and “Weight of the Mass” and indicate the direction of
acceleration if applicable.
9.
Before we proceed any farther, let’s do another thought experiment. What would happen to the reading of the
scale if you were to move it from shoulder level to the floor rather quickly? Would the reading on the scale
increase, decrease, or stay the same? Briefly explain your reasoning.
10.
With the
500g
mass attached, have one teammate hold the scale and mass at shoulder level then have them
move it toward the ground rather quickly while the rest of the team observes the reading of the scale. What
happens to the reading of the scale as the mass is moved quickly downward? Was your group’s hypothesis
correct? If not, explain why.
11.
Draw a
Free Body Diagram
for the mass and scale system as it is moved downward quickly. Indicate the rela-
tionship between the “Force of the Scale” and “Weight of the Mass” and indicate the direction of acceleration
if applicable.
12.
Using the principles you learned above explain how someone would feel in an elevator as it initially moves
upward, as it is traveling upward, and as it comes to a stop. Specifically, explain whether someone would feel
lighter, heavier, or the same weight at these three points and briefly explain why using a combination of Free
Body Diagrams and brief explanations.
107
My
hypothesis
was
correct
since
the
reading
on
the
scale
increases
quite
rapidly
and
by
a
large
margin
as
the
scale
is
quickly
moved
upwards
acceleration
is
present
in
the
upwards
I
force
of
scale
direction
force
of
mass
The
reading
on
the
scale
will
decrease
because
the
net
force
will
no
longer
be
zero
because
the
downward
forcewhich
used
tobe
just
the
weight
ofthe
mass
mxg
would
now
include
the
downward acceleration
My
hypothesis
was
correct
because
the
reading
on
the
scale
decreases
rapidly
When
we
move
the
scale
downwards
acceleration
is
force
of
scale
present
in
the
downwards
direction
weight
of
mass
initially
movesupward
travellingupward
coming
to
a
stop
force
of
elevator
f
In
elevator
of
long
of
elevator
mass
force
is
greater
in
downwards
direction
The
movement
would
be
at
a
constant
making
net
force
negative
which
makes
velocitymeaning
zero
acceleration
in
Acceleration
is
in
the
upwards
dirite
either
direction
andthat
both
present
causing
you
to
feel
heavier
than
you
feel
lighter
thannormal
forces
are
equal
You
will
feel
the
same normal
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2. F
ORCES
A
ND
A
CCELERATIONS
2.2
Newton’s First Law / Analyzing Simple Accelerations
Take your track and place it flat against the table, and then place your cart on the track. Ensure that the track is
flat and level, and that the cart can remain at rest while on the track. Adjust the track as necessary. Ensure that the
“Bubble Level” is securely attached to the cart using the piece of putty, and that the bubble is centered between the lines
when the cart is at rest i.e. that the level is parallel to the table. Assume that all surfaces are perfectly smooth, which
means the cart does not slow down due to friction. Refer to the picture below.
Figure 2.3: Cart on Level Track
1. Briefly explain Newton’s First Law and provide an every-day example below.
2.
Before we begin the next part of the lab, let us briefly think about what is inside of a bubble level. Consider
that a bubble level contains some sort of fluid, and some sort of gas. For our purposes, we can assume that
the level contains a combination of water and air. Which of these components likely has more mass, the water
or the air bubble?
Now we are going to try and make some predictions. For each of the motions described below,
predict
where the
bubble will be in the level and sketch the location of the bubble within each box. For each case, try and briefly explain
your prediction. It may also be helpful to think about what happens to the fluid that is in the level during these time
periods.
Case 1: Cart moves to the right and
is speeding up.
Case 2: Cart moves to the right with
constant velocity.
Case 3: Cart moves to the right and
is slowing down.
Explanation:
Explanation:
Explanation:
Now you will try it out. Take your cart and place it at the end of the track farthest away from the bumper. With
your hand, give the cart a gentle but quick tap toward the end of the track with the bumper.
1.
While your hand is pushing the cart, sketch the position of the bubble. What can you say about the cart’s
108
an
object
stays
in
motion
or
at
rest
unless
acted
upon
by
an
outside
force
16
skating
An
object
stays
at
motionor
at
rest
unless
acted
upon
by
an
outside
force
ie
Ice
skating
Water
has
a
higher
mass
than
the
air
bubble
iii
EEd.name
immuna
shift
shifting
it
mass
shift
2.2. Newton’s First Law / Analyzing Simple Accelerations
acceleration during this time, is it zero or nonzero? Draw a
Free Body Diagram
of the cart at this time and if
applicable, draw an arrow that points in the direction of the cart’s acceleration.
2.
After your hand is no longer touching the cart and it is moving toward the bumper, sketch the position of the
bubble. What can you say about the cart’s acceleration during this time, is it zero or nonzero? Draw a
Free
Body Diagram
of the cart at this time and if applicable, draw an arrow that points in the direction of the cart’s
acceleration.
3.
What happens to the position of the bubble the moment the cart hits the bumper? Sketch the position of the
bubble. What can you say about the cart’s acceleration during this time, is it zero or nonzero? Draw a
Free
Body Diagram
of the cart at this time and if applicable, draw an arrow that points in the direction of the cart’s
acceleration.
4.
Using Newton’s first law, try to explain what is happening to both the bubble and the fluid during the different
periods of motion. Were your predictions correct?
2.2.1
Newton’S First Law / Analyzing Accelerations Due to Gravity
Take your track and place it on the metal bar so that it is inclined at a small angle of about 15 degrees. Make sure that
the black bumpers underneath the track are behind the metal bar, to ensure that the track will not slide off during the
next part of the laboratory. While the cart is resting on the inclined track against the bumper, adjust your Bubble level
so that the bubble is positioned in the center between the two lines while the cart is at rest. Meaning, the level should
be parallel to the table, even though the cart is now on an incline. Assume that all surfaces are perfectly smooth, which
means the cart does not slow down due to friction.
Figure 2.4: Cart on a Sloped Track
Like before, we are going to try and make some predictions. For each of the motions described below,
predict
where
the bubble will be in the level and sketch the location of the bubble within each box. For each case, try and briefly
explain your prediction. It may also be helpful to think about what happens to the fluid that is in the level during
these time periods.
109
The
acceleration
is
nonzero
positive
Fhand
dairy
oh
I
1mg
The
acceleration
iszero
offing
The
acceleration
is
nonzero
negative
Fumff
Ing
s
direction
of
deacceleration
My
predictions
werecorrect
2. F
ORCES
A
ND
A
CCELERATIONS
Case 1: The cart moves up the
incline as someone is pushing the
cart.
Case 2: After being released, the
cart travels up the incline
Case 3: The cart reaches the top of the
incline and travels back down the
ramp.
Explanation:
Explanation:
Explanation:
Now we will try it out. With your hand, give your cart a gentle but quick tap up the incline.
1.
While your hand is pushing the cart, sketch the position of the bubble. What can you say about the cart’s
acceleration during this time, is it zero or nonzero? Draw a
Free Body Diagram
of the cart at this time and if
applicable, draw an arrow that points in the direction of the cart’s acceleration.
2.
After your hand is no longer touching the cart, sketch the position of the bubble. What can you say about the
cart’s acceleration during this time, is it zero or nonzero? Draw a
Free Body Diagram
of the cart at this time
and if applicable, draw an arrow that points in the direction of the cart’s acceleration.
3.
What happens to the position of the bubble when the cart starts to roll back down the incline? Sketch the
position of the bubble. Draw a
Free Body Diagram
of the cart at this time and if applicable, draw an arrow that
points in the direction of the cart’s acceleration.
4.
Using Newton’s 1st law, try to explain what is happening to both the bubble and the fluid during the different
periods of motion. Were your predictions correct?
110
Tnth
isbeig
pushed
lay
in
the
c
filing
is
team
to
shift
left
thecart's
acceleration
is
nonzero
positive
L
Ency
dkfimm.gg
my
initial
if
aeration
E
d
s
Dorrition
mg
the
carts
acceleration
is
Ency
nonzero
negative
initial
My
predictions
were
correct
because
we
see
Newton's
first
law
applied
in
the
results
The
external
force
causes
the
bubble
to
shift tothe
right
because
wateris
heavier
than
gas
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2.2. Newton’s First Law / Analyzing Simple Accelerations
2.2.2
Circular Motion
Using the same principles as earlier, we will now make some predictions and observations regarding circular motion.
In the front of the room, there is a rotating chair with a bubble level attached to it.
Figure 2.5: Chair
Like before, we are going to try and make some predictions. For each of the motions described below,
predict
where
the bubble will be in the level and sketch the location of the bubble within each box and indicate which direction the
center of the circle is relative to the level by drawing an arrow. For each case, try and briefly explain your prediction. It
may also be helpful to think about what happens to the fluid that is in the level during these time periods.
Case 1: The chair is being slowly
spun clockwise with a constant
speed.
Case 2: The chair is released
and continues rotating
clockwise.
Case 3: The chair is being slowly spun
counter clockwise with a constant
speed.
Explanation:
Explanation:
Explanation:
Now we will try it out. Go to the front of the room and make sure that the bubble is in the center of the level (i.e. the
level is level) while the chair is at rest. Take your hand and gently spin the chair in the clockwise direction. Stop it and
then slowly spin it again in the counter clockwise direction.
1.
Using Newton’s first law, try to explain what is happening to both the bubble and the fluid during the different
periods of motion. Were your predictions correct?
2.
Briefly describe what happens to the speed and velocity of the bubble level during its circular motion. In
particular, are they constant or changing? How does this influence the position of the bubble?
111
begin
in
the
miauandmn.my
iiffI
itEi
Endian
push
bubble
towards
center
a
mar
1st
period
of
motion
centrifugal
force
shifts
bubble
towards
center
2nd
and3rd
period
of
motion
moves
bubble
toward
center
of
chair
My
predictions
were
comet
2. F
ORCES
A
ND
A
CCELERATIONS
2.3
Analyzing Forces And Accelerations
For the remainder of this section, take off the Bubble Level and putty and refer to the figure below.
Move the
bumper to the opposite edge of the track. The bumper should be next to the pulley, near the edge of the table, and
positioned at approximately 100 cm. Remove the track from the raised bar, and place it flat against the table, and then
place your cart on the track. Place the
500g
mass bar on top of the cart, and put on an additional 30 grams of mass
onto the cart using the small circular masses. Attach one loop on your string to the plastic screw on the end of the cart.
Hook the weighted hook onto the other end of the string, and place the string over the pulley.
Your cart may begin to
move, if this is the case just place the hook on the table for now, and keep the system at rest.
Figure 2.6: Cart and Pulley System
1. Draw a Free Body Diagram for both the cart on the track, and the hook hanging from the pulley.
Before we physically do anything with the cart and our masses, let’s first think about what will happen. Recall that
at the start of the lab, you are given all of the necessary information regarding the mass of the cart, hook etc. You may
continue to ignore the effects of friction.
2.
Using the Free Body Diagrams you drew in part (1), derive an expression for the acceleration of the hook and
the cart in terms of the mass of the hook, the mass of the cart, and the gravitational constant of acceleration
g
.
3.
Using the expression you derived in part (2) calculate the acceleration of the cart and the hook. Assume the
mass of the hook is 30 grams, the mass of the cart is 1.05 kg, and that
g
=
9.8
m
/
s
2
4.
Using the expression you derived in part (2) calculate the acceleration. This time, assume the mass of the
hook is 60 grams, the mass of the cart is 1.02 kg, and that
g
=
9
.
8
m
/
s
2
.
How does this acceleration compare to
the value you just calculated above, is it greater than, less than or equal to the acceleration you calculated in
part (3)? Explain your reasoning.
112
2.3. Analyzing Forces And Accelerations
Now we will take our cart (with the metal mass bar and an additional 30 grams of mass on top of it), and our hook
(with a total mass of 30 grams) and position them so we can conduct experiments to observe the motion of the cart.
Place the cart so that the front is
80cm
away from the bumper (i.e. approximately at position
20cm
). Have one person
hold the cart still, keeping it at rest. Add
25g
of mass to the end of the string with the hook and place it over the top of
the pulley. Have someone in your group take the stopwatch and reset it so that it reads a value of zero. When your
teammate is ready, let go of the cart and time how long it takes from the moment the cart is released, to the moment
the cart hits the Styrofoam bumper.
5. Repeat this process three times, record the times below and then calculate the average time:
Mass Attached to the Hook 25g (Total: 30g)
Time (s)
Trial 1
Trial 2
Trial 3
Average Time
6.
Using the kinematic equation for position and the average time you just recorded, calculate the acceleration
of the cart and the hook.
Mass Attached to the Hook
Acceleration of the Cart / Hook
(
m
/
s
2
)
25 grams (30 grams total)
Now we will take the 30 grams of additional mass that is on top of the cart, and place it on the hook. Just like before,
have someone in your group take the stopwatch and reset it so that it reads a value of zero. When your teammate is
ready, let go of the cart and time how long it takes from the moment the cart is released, to the moment the cart hits
the bumper.
7. Repeat this process three times, record the times below and then calculate the average time:
Mass Attached to the Hook 55g (Total: 60g)
Time (s)
Trial 1
Trial 2
Trial 3
Average Time
8.
Using the kinematic equation for position and the average time you just recorded, calculate the acceleration
of the cart and the hook.
Mass Attached to the Hook
Acceleration of the Cart / Hook
(
m
/
s
2
)
25 grams (30 grams total)
9.
What is the ratio of the acceleration you calculated from part (8) over the rate of acceleration you calculated
in part (6)? Is this ratio what you would expect?
113
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2. F
ORCES
A
ND
A
CCELERATIONS
10.
How do your observed rates of acceleration compare to the theoretical values of acceleration you calculated
in parts (3) and (4)? Are they higher than, lower than, or about the same as your predictions?
11.
What things might have affected the acceleration of the cart in real life that we did not account for in our
simplified calculations?
2.3.1
Statics And Motion On An Inclined Ramp
Remove the
500g
mass bar from the top of your cart. Remove the extra circular masses form your hook. Take your
track and place it on the metal bar so that it is inclined again. Make sure that the black bumpers on the bottom of the
track are behind the metal bar, to ensure that the track will not slide off during the next part the laboratory. Again take
the string and attach it to the cart; take the other end of the string with the hook attached and place it over the pulley.
Figure 2.7: Cart and Pulley on a Sloped Track
1. Draw a Free Body Diagram for the Cart and the Hook separately for this positioning.
2.
Theoretically, it is possible to place the cart on the middle of the ramp and have the system be at equilibrium
(at rest). How could this be done?
3.
Calculate what angle you would need to incline the ramp at, to have the system of the cart (mass = 520 grams)
and the hook with 100 grams of added mass (105 gram total mass) to remain at rest. What angle would be
needed?
114
2.4. Friction Is Fun!!
4.
Based on your above calculations, try to put the system into balance. Was the angle you calculated in part (3)
the correct angle needed to balance the system? Explain any differences you might have observed.
2.4
Friction Is Fun!!
Bonus Questions
: When the track is flat against the table, what type of friction is acting on the cart? Is friction
helping or hindering the motion of the cart? What about when the track in on an incline? Briefly explain:
115
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