PHYSICSLAB2
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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
4959,4.94N
force
of
weight
of
scale
↓
Fi
Many
↑
F
Eq
The
reading
of
the
scale
won't
change
because
the
scale
moves
with
a
constant
velocity
so
there
no
force
acting
on
the
scale.
Since
constant
velocity
150,
th
19
means
acceleration
is
0,
therefore
causing
the
force
I
maCF
=
m(0)
to
be
0.
-weight
increases
it
fuctuates
in
guns
as
the
scale
moves
up
a
down.
Yes,
our
hypothesis
was
correct.
L
the
weight
decreases
rent)
I
/
Force
of
scale
to
The
reading
of
the
scale
would
increase
because
the
system
accelerates,
which
means
there
must
be
a
force
acting
on
the
system
per
newtons
and
law:
IF
ma
Yes,
our
hypothek
was
correct.
The
mass
went
up.
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
hi
ote"
meant
f
scale
1944
Eg
*
The
scale
reading
would
decrease
because
the
weight
of
the
mass
has
Yes,
it
decreased.
Our
hypothesis
was
correct.
Face
for
west
of
the
e
when
the
elevator
initially
moves
upward,
you
feel
heavier
because
there
is
a
force
upwards
that
is
greater
than
the
weigh
of
you.
The
force
needs
to
be
greater
than
youre
weight
so
it
can
pull
up.
As
you're
traveling,
you
feel
the
same
because
the
elevator
starts
traveling
at
a
constant
velocity.
Asitsomes
to
astop,
you
feel
lighter
because
there
in
more
force
downwards
on
the
elevator.
FN
FN
↑
Y
a
9
97q
Ea
Eg
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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
Newton's
first
law
states
that
an
object
at
rest
will
stay
a
treat
or
an
object
thats
moving
will
continue
moving
at
a
constant
velocity
unless
a
force
acts
on
it.
An
example
of
this
Is
your
body
turning
to
the
side
when
you
make
a
turn
a
car.
the
water
has
more
mass
The
bubbles
The
bubble
The
bubble
more
light
because
the
will
stay
in
the
middle
will
be
on
the
left
and
120
moves
left.
because
5
0
so
there
Had
will
be
on
the
no
externating
to
it.
right.
#Im
/
An
I
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
If
a
atnonzer
The
acceleration
is
0.
Tazo
Acceleration
starts
-Imper
decreasing
til
the
cart
stops.
So
the
a
nonzero
based
on
120
potential
&
equilibria
when
motion
is
constant
(speed),
the
bubble
doesn't
more.
When
the
speed
of
motion
increases,
the
fluid
tries
to
remain
in
equilibrium
(Y)
so
the
alguid
moves
backwards
bubbles
move
forward
toward
direction
of
motion.
When
thespeed
of
motion
is
decreasing,
the
liquid
tries
to
continue
keeping
constant
movement,
so
it
shifts
forward
bubbles
move
backwards
in
the
direction
of
acceleration.
Yes,
our
predictions
were
correct.
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
-
-
The
bubble
The
bubble
moves
in
the
direction
The
bubbles
of
the
motion
in
moves
opposite
to
the
motion
moves
toward
the
the
incline.
The
lower
incline
water
pushes
away
in
the
of
the
because
Hao
moves
direction
upward
is
of
Inclue
and
in
A
backwards.
motOn.
the
motion
of
the
down
hill.
The
acceleration
of
the
bubble
is
nonzor
an
the
bubbles
go
backwards.
*
↑
Eq
the
acceleration
of
the
cart
becomes
0,
the
bubbles
stay
at
the
middle
of
the
box
and
the
cart
moves
at
a
constant
velocity.
Since
Go,
E=0
because
IF
=
m10]
0
N
*
when
the
cart
starts
to
rollback
down
the
inclue,
the
bubbles
move
toward
and
the
acceleration
starts
to
increase
int
he
negative
x-direction.
e
based
on
120
potential
&
equilibria
when
motion
is
constant
(speed),
the
bubble
doesn't
more.
When
the
speed
of
motion
increases,
the
fluid
tries
to
remain
in
equilibrium
(Y)
so
the
liquid
moves
backwards
bubbles
move
forward
toward
direction
of
motion.
When
thespeed
of
motion
is
decreasing,
the
liquid
tries
to
continue
keeping
constant
movement,
so
it
shifts
forward
bubbles
move
backwards
in
the
direction
of
acceleration.
Yes,
our
predictions
were
correct.
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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
it
Bubble
stays
moves
toward
Bubble
stays
In
the
center
In
center.
-
of
the
-
center.
S
1
circle.
An
he
water
moves
toward
the
outside
of
the
circle
because
it
has
more
mass
but
the
bubbles
more
toward
the
motion.
During
constant
velocity,
the
bubble
stays
in
the
middle
but
when
acceleration
goes
up,
the
bubble
goes
into
the
circle
$
420
goes
away
from
motion
to
gain
equilibrium.
When
its
constant
theres
no
force
acting
on
the
system.
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
⑰
-
a
m
m,
79
a
=
mm,
5-ton
00103)-ls"
its
equal
to
each
other
because
the
weight
of
the
porosis
I
tal
system
doesn't
change
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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College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning