Slide 1

LAB 4: FORCE AND MOTION

Please list the members of your group:
Zachary O'Rourke and Adri Lila

OBJECTIVES
To learn how to use a force sensor to measure force and to set up a force scale.
To explore how the motion of an object is related to the forces applied to it.
To find a mathematical relationship between the force applied to an object and its acceleration.

OVERVIEW
In the previous labs, you have examined position–time, velocity–time, and acceleration–time graphs of
different motions of the IOLab using the Wheel displays. You were not concerned about how you got the
IOLab to move, i.e., what forces (pushes or pulls) acted on it. (You pushed it with your hand, allowed the
Earth’s gravitational force to pull on it , and also used a hanging mass attached to a string to pull it.)
From your previous experiences, you know that force and motion are related in some way. To start your
bicycle moving, you must apply a force to the pedal. To start up your car, you must step on the
accelerator to get the engine to apply a force to the road through the tires.

But exactly how is force related to the quantities you used in Labs 2 and 3 to describe motion—position,
velocity, and acceleration? In this lab you will pay attention to forces and how they affect motion. You
will learn how to measure forces. By applying forces to the IOLab and observing the nature of its
resulting motion graphically, you will begin to understand the effects of forces on motion as described
by Newton’s Laws.

Copyright © 2018 John Wiley & Sons, Inc.

Slide 2

INVESTIGATION 1: MEASURING FORCES

In this investigation you will explore the concept of a constant force and the combination of forces in
one dimension. You can use these concepts to learn how to set up a force scale and measure forces
with a force sensor. You will need the following materials:

Calibrated IOLab with force sensor hook

computer with IOLab software
five identical rubber bands. Use the ones in the package.
a paper ruler.
a paper clip.
scotch tape.
60 g mass. Five quarters wrapped in a piece of paper is about right.
Slide 3

Activity 1-1: How Large Is a Pull?

If you pull on a rubber band attached at one end, you know it will stretch. The more you pull, the more it
stretches. Try it.

1. Attach one end of the rubber band to something on the table that can’t move. Also tape the
paper ruler to the table so that it doesn’t move. Now stretch the rubber band so it is several
centimeters longer than its relaxed length. Does it always seem to exert the same pull on you
each time it is stretched to the same length? Most people agree that this is obvious. (A good
length to stretch a size 19 rubber band that is 3.5" x 1/16" is no more than 17 cm.)
2. Write down the stretched length you have chosen in the space below. This will be your
standard stretched length for measurements.

Standard stretched length of rubber band:

17cm

3. Attach one end of each of two identical rubber bands in the same way as before to something
that can’t move, and stretch them together side-by-side to the standard stretched length.
Slide 4

Activity 1-1: How Large Is a Pull?

Question 1-1: How does the combined force of two rubber bands compare to what you felt when only
one rubber band was used? Do not use the IOLab, just use you judgement.

The force has increased by a noticable amount.

Repeat this comparison of how strong the forces feel with three, four, and five rubber bands stretched
together to the same standard stretched length.

Question 1-2: Suppose you stretched a rubber band to your standard stretched length by pulling on it.
Now you want to create a force six times as large. How could you create such a force?

Use 6 rubber bands instead of 1.

Question 1-3: Suppose you applied a force with a stretched rubber band one day, and several days later
you wanted to feel the same force or apply it to something. How could you assure that the forces were
the same? Explain.

If you used the same type of rubber band it can be assumed that the forces would be the
same if pulled to the same length.

Question 1-4: Do side-by-side rubber bands provide a convenient way of accurately reproducing forces
of many different sizes that you can apply to objects? Explain.

Yes, the rubber bands allow you to keep adding more rubber bands to create more force.

Comment: Pulling more and more rubber bands to the same length requires a larger pull. To be more
precise about the pulls and pushes you are applying, you need a device to measure forces accurately.
The electronic force sensor that is part of the IOLab is designed to do this.
Slide 5

Activity 1-2: Measuring Forces with a Force Sensor

In this activity you will explore the capability of the IOLab’s electronic force sensor as a force-
measuring device.

1. Screw the hook into the IOLab Force Sensor until it is tight. Bend a paper clip to make a hook
you can attach rubber bands to. Plug the IOLab dongle into the computer and turn on the
IOLab.
2. Calibrate the IOLab by selecting from the menu at the top, and then selecting Force
from the pulldown menu. Follow the instructions.
Slide 6
Force (4800 Hz) Remote 1

11
10
9
8
7
Fᵧ (N)

6
5
4
3
2
1
0
-1
0 1 2 3 4 5 6 7 8 9 10
  Rezero sensor Time (s)

Activity 1-2: Measuring Forces with a Force Sensor

3. The axes on the right should display Force vs. Time.
4. Test your calibration by:
a. holding the IOLab with the hook and attached paper clip pointed down
b. clicking Rezero sensor under the axes
c. hanging the 60 g mass from the paper clip and clicking Record
d. measuring the force using
If the measurement is not close to 0.6 N, check the mass you made and adjust it to get it
within 0.05 N of 0.6 N.
5. Attach three rubber bands to the hook.
6. Place the IOLab upside down on a horizontal table (with its wheels pointing upwards), and
the rubber bands lying on the table (not pulling on the hook).

Note: Since forces are detected by the computer system as changes in an electronic signal, it
is important to first have the computer “read” the signal when the force sensor has no force
pushing or pulling on it. This process is called “zeroing” the force sensor. This is also
necessary because the electronic signal from the force sensor can change slightly as the
temperature changes or when the IOLab collides with something. It is a good idea to click on
Rezero sensor (below the axes) with nothing pulling or pushing on the force sensor, before
you collect data.

7. Click Remove next to the Run(s) on the Data Acquisitions list used to test the calibration.
This will erase those runs and set up the IOLab for a new data collection.
8. Click Record. Then—while holding the IOLab in place—pull the three rubber bands to the
standard stretched length from Activity 1-1, and hold. Be sure to graph for the entire 10 s.
Make sure you understand what part of the graph represents when the data were taken with
the rubber bands stretched. Repeat the graph by using +Add Run, as many times as
necessary to get a good run. Then Remove all but the run you want to use.
9. Record the average force sensor reading from the graph only during the time interval when
the three rubber bands are stretched. (Do not include the period before you start pulling or
after you stop pulling) Use the analysis feature of the software to get an accurate value for
the average force reading.
Average reading:

10.8N
Slide 7
Force (4800 Hz) Remote 1

5
4
3
2
1
Fᵧ (N)

0
-1
-2
-3
-4
-5
0 1 2 3 4 5 6 7 8 9 10
  Rezero sensor Time (s)

Activity 1-2: Measuring Forces with a Force Sensor

10. Remove one rubber band from the hook. (You will still have two rubber bands connected to
the hook.)
11. Click +Add Run. With the rubber bands loose, Rezero the force sensor and then click Record.
Then—while holding the IOLab in place—pull the two rubber bands to the standard stretched
length and hold. Be sure to graph for the entire 10 s.
12. Again record the average force sensor reading from the graph
Average reading with two rubber bands:

8.0N

13. Repeat the process in step 11, with just one rubber band stretched to your standard
stretched length. Be sure to graph for the entire 10 s.
Average reading with one rubber band:

4.0N
 The data has been saved to file:
C:/Users/orourkez/Documents/IOLab-
Slide 8 WorkFiles/export/20230915-132227_Force.csv

Force (4800 Hz) Remote 1

5
4
3
2
1
Fᵧ (N)

0
-1
-2
-3
-4
-5
0 1 2 3 4 5 6 7 8 9 10
  Rezero sensor Time (s)

Activity 1-2: Measuring Forces with a Force Sensor

14. Use Excel or another graphing program to plot a graph of F vs. N, the number of rubber bands.

Question 1-5: How are force sensor readings related to the size of the pull exerted on the force sensor
hook by the rubber bands? Describe the mathematical relationship in words. ×
The more rubber bands we add to the hook the more the force is applied when pulling and
the force sensor hook will read a greater number
Question 1-6: Based on your analysis (and/or graph), what force sensor reading would correspond to
the pull of five rubber bands when stretched to yourThe
standard length? How did you determine this?
data has been saved to file:
C:/Users/orourkez/Documents/IOLab-
Using the equation given by the graph: 3.4x+0.8 we can WorkFiles/export/20230915-132227_Force.csv
determine that the force of 5
rubber bands is 17.8 N
 The data has been saved to file: ×
C:/Users/orourkez/Documents/IOLab-
Slide 9 WorkFiles/export/20230915-132227_Force.csv

INVESTIGATION 2: MOTION AND FORCE

Now you can use the IOLab to explore the effects of forces applied to it by using the measurements of
the Wheel and Force Sensor together. You will be able to explore the relationship between motion and
force. You will need the following materials:

Calibrated IOLab with force sensor hook

computer with IOLab software
smooth tabletop or other flat surface at least 0.5 m long
20 g and 60 g masses
string
Slide 10

Activity 2-1: Pushing and Pulling a Cart

In this activity you will move the low friction IOLab by pushing and pulling it with your hand. You will
measure the force, velocity, and acceleration vs. time. Then you will be able to look for mathematical
relationships between the force applied to the IOLab and the velocity and/or acceleration, to see
whether either velocity or acceleration (or neither) is related to the force.

Set up the IOLab and force sensor hook on a smooth level surface as shown below.

Prediction 2-1: Suppose you grasp the force sensor hook and move the IOLab forward and backward.
Do you think that either the velocity graph, the acceleration graph or neither will look like the force
graph?

velocity acceleration neither velocity nor

acceleration

Prediction 2-2: Explain the basis for your Prediction 2-1.

The amount of force applied will relate to the velocity because when you increase the
velocity will increase at a constant rate then the force will increase at a constant rate
hypothetically
Slide 11
Force (200 Hz) Remote 1

0
Fᵧ (N)

-1
-2
-3
-4
0 1 2 3 4 5 6 7 8 9 10
  Rezero sensor Time (s)

Wheel - Velocity (100 Hz) Remote 1

1.0
0.5
vᵧ (m/s)

0.0
-0.5
-1.0
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Wheel - Acceleration (100 Hz) Remote 1

4
aᵧ (m/s²)

2
0
-2
-4
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Activity 2-1: Pushing and Pulling a Cart

Test your prediction.

1. The IOLab should be supported by its wheels. The IOLab force sensor should have already
been calibrated. The IOLab dongle should have remained plugged into the USB port on your
computer, and the IOLab should have remained on since the calibration. If you are not sure,
check the calibration by:
a. holding the IOLab with the hook pointed down
b. clicking Rezero sensor under the axes
c. clicking Record
d. hanging 60 g from the force sensor hook for the remainder of the 5 s
e. measuring the force using
If the measurement is not close to your previous value, check your iOLab zeroing.
2. Zero the force sensor by clicking on Rezero sensor with nothing pulling or pushing on the
sensor.
3. Click +Add Run and then click Record. Then grasp the force sensor hook and give the IOLab
a quick jerk towards you and without letting go then stop it quickly. Wait a second and then
give it a quick jerk away from you and again stop it quickly. Repeat both of these motions
one more time.
 Note: Try to get sudden starts and stops, and to pull and push the force sensor hook along a
straight line without lifting the IOLab off the tabletop.

4. Repeat until you get a good, clear set of graphs. Adjust the force, acceleration and velocity
axes to display the graphs as clearly as possible. Remove all sets of graphs except the best
set.
Slide 12
Force (200 Hz) Remote 1

0
Fᵧ (N)

-1
-2
-3
-4
0 1 2 3 4 5 6 7 8 9 10
  Rezero sensor Time (s)

Wheel - Velocity (100 Hz) Remote 1

1.0
0.5
vᵧ (m/s)

0.0
-0.5
-1.0
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Wheel - Acceleration (100 Hz) Remote 1

4
aᵧ (m/s²)

2
0
-2
-4
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Activity 2-1: Pushing and Pulling a Cart

Read the times off the graphs when each of these occurred:

A: You first began pulling the IOLab towards you the first time

0.3s

B: You stopped the IOLab as it was moving towards you the first time.

0.69s

C: You began to push the IOLab away from you the first time

2.9s

D: You stopped the IOLab as it was moving away from you the first time.

3.3s

Question 2-1: Explain how you identified each of the points A, B, C and D.
A is when the velocity graph started to increase, B is when the velocity graph went back to
zero, C is when the velocity graph increased in the negative direction, D when it went back
to zero
Slide 13
Force (200 Hz) Remote 1

0
Fᵧ (N)

-1
-2
-3
-4
0 1 2 3 4 5 6 7 8 9 10
  Rezero sensor Time (s)

Wheel - Velocity (100 Hz) Remote 1

1.0
0.5
vᵧ (m/s)

0.0
-0.5
-1.0
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Wheel - Acceleration (100 Hz) Remote 1

4
aᵧ (m/s²)

2
0
-2
-4
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Activity 2-1: Pushing and Pulling a Cart

Question 2-2A: Does either graph—velocity or acceleration—resemble the force graph?

velocity acceleration

neither

Question 2-2B: Explain how you reached this conclusion.

There are similiar based on the values of the graphs. There is a bit of human error in the
beggining of moving the IOLab.

Question 2-3A: Based on your observations, does it appear that there is a direct mathematical
relationship between either

force and velocity force and acceleration

both neither
Question 2-3B: Explain based on your graphs.

They look similiar.

Slide 14

Activity 2-2: Speeding Up Again

You have seen in the previous activity that force and acceleration seem to be related. But just what is
the mathematical relationship between force and acceleration?

Predictions: Suppose that you have a cart (e.g., the IOLab) with very little friction and you pull it with a
constant force as shown on the force–time graph below.

Prediction 2-3: Which of the following graphs would represent velocity vs. time as the cart with very
little friction is pulled by the force above.

A B C

D E

Prediction 2-4: Describe in words the predicted shape of the velocity vs. time graph that you selected.

It's a straight line in the positive direction

Slide 15

Activity 2-2: Speeding Up Again

Prediction 2-5: Which of the following graphs would represent acceleration vs. time as the cart with very
little friction is pulled by the force above.

A B C

D E

Prediction 2-6: Describe in words the predicted shape of the acceleration vs. time graph that you
selected.

it's a straight horizontal line

Slide 16

Activity 2-2: Speeding Up Again

To test your predictions, you will need the following:

Calibrated IOLab and hook

IOLab software
smooth tabletop or other flat surface at least 0.5 m long
string about 0.6 m long
paper clip bent into a hook
20, 40, and 60 g masses
Slide 17
Force (200 Hz) Remote 1

1.0
0.5
Fᵧ (N)

0.0
-0.5
-1.0
0 1 2 3 4 5 6 7 8 9 10
  Rezero sensor Time (s)

Wheel - Velocity (100 Hz) Remote 1

1.0
0.5
vᵧ (m/s)

0.0
-0.5
-1.0
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Wheel - Acceleration (100 Hz) Remote 1

3
2
aᵧ (m/s²)

1
0
-1
-2
-3
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Activity 2-2: Speeding Up Again

1. Set up the IOLab on the tabletop or ramp as shown below, with the string attached to the
hook and hung over the edge of the table with a mass of about 20 g hanging from it. The
mass should have around 0.75 m to fall to the floor.

2. The IOLab force sensor should have already been calibrated. The IOLab dongle should have
remained plugged into the USB port on your computer, and the IOLab should have remained
on since the calibration. You can check the calibration by:
a. holding the IOLab with the hook pointed down
b. clicking Record
c. hanging 60 g from the force sensor hook for the remainder of the 10 s
d. measuring the force using
If the measurement is not close to your previous value, check your iOLab a zeroing.
3. Ensure the graph axes on the right are displaying velocity, acceleration and Force vs. time.
4. Zero the force sensor by clicking on Rezero sensor with nothing pulling or pushing on the
sensor.
5. Begin with the mass hung over the edge, holding the IOLab to prevent it from moving. The
mass should have at least 0.75m to fall. Make sure the mass is not swinging.
6. Click +Add Run and then click Record. Then immediately release the IOLab, and let the
falling mass pull it across the table. Stop the IOLab just before it falls off the edge of the
tabletop.
7. If necessary, repeat until you get good graphs for the entire motion of the IOLab.
8. Adjust the axes to display the graphs as clearly as possible, then continue on to the next
slide. (If you need to zoom out, click the zoom icon, then double-click the graph.)
Slide 18
Force (200 Hz) Remote 1
∆t: 2.33267 s
0.3 μ: 0.091 N — σ: 0.0099 N a: 0.213 Ns s: -0.01 N/s (r²: 0.28)
0.2
Fᵧ (N)

0.1
0.0
-0.1
0 1 2 3 4 5 6 7 8 9 10
  Rezero sensor Time (s)

Wheel - Velocity (100 Hz) Remote 1

1.0
∆t: 2.32767 s
μ: 0.308 m/s — σ: 0.14 m/s a: 0.716 m s: 0.21 m/s² (r²: 1.00)
0.5
vᵧ (m/s)

0.0
-0.5
-1.0
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Wheel - Acceleration (100 Hz) Remote 1

3
∆t: 2.32767 s
2 μ: 0.212 m/s² — σ: 0.11 m/s² a: 0.493 m/s s: -0.01 m/s³ (r²: 0.00)
aᵧ (m/s²)

1
0
-1
-2
-3
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Activity 2-2: Speeding Up Again

Record the times for the following:

Question 2-4A: the time interval before the mass is released

0-0.3s

Question 2-4B: the exact moment it is released

0.3s

Question 2-4C: the moment you stop the IOLab at the edge of the table.

3.2s

Question 2-5A: Measure the average force only including the time interval during which the IOLab was
being pulled by the falling mass across the table (not including the time interval before you released it,
or the time interval after you first touched it to stop it).

0.091N
Question 2-5B: Measure the average acceleration during the same time interval as the average force.

0.212m/s2
Slide 19
Force (200 Hz) Remote 1
∆t: 2.33267 s
0.3 μ: 0.091 N — σ: 0.0099 N a: 0.213 Ns s: -0.01 N/s (r²: 0.28)
0.2
Fᵧ (N)

0.1
0.0
-0.1
0 1 2 3 4 5 6 7 8 9 10
  Rezero sensor Time (s)

Wheel - Velocity (100 Hz) Remote 1

1.0
∆t: 2.32767 s
μ: 0.308 m/s — σ: 0.14 m/s a: 0.716 m s: 0.21 m/s² (r²: 1.00)
0.5
vᵧ (m/s)

0.0
-0.5
-1.0
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Wheel - Acceleration (100 Hz) Remote 1

3
∆t: 2.32767 s
2 μ: 0.212 m/s² — σ: 0.11 m/s² a: 0.493 m/s s: -0.01 m/s³ (r²: 0.00)
aᵧ (m/s²)

1
0
-1
-2
-3
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Activity 2-2: Speeding Up Again

Question 2-6A: After the cart is moving, is the force that is applied to the IOLab by the fishing line
constant, increasing, or decreasing?

constant increasing decreasing

Question 2-6B: Explain based on your graph.

The force is a flat horizontal line with an avarage of 0.091 N

Question 2-7: How does the acceleration vary in time? Does this agree with your prediction? Does a
constant force applied to the IOLab produce a constant acceleration?
 The acceleration is a flat line like we producted. And yes because the constant force is the
force of gravity applied on the mass.

Question 2-8: How does the velocity vary in time? Does this agree with your prediction? What kind of
change in velocity corresponds to a constant force applied to the IOLab?

The velocity is a straight line increasing in the posoitive direction. yes it agrees with our
prediction.
Slide 20

Activity 2-3: Acceleration from Different Forces

In the previous activity you examined the motion of the IOLab with a constant force applied to it. But
what is the relationship between acceleration and force? If you apply a larger force to the same IOLab
(with the same mass) how will the acceleration change? In this activity you will try to answer these
questions by applying different forces to the IOLab, and measuring the corresponding accelerations.

If you accelerate the same IOLab with two other different forces, you will then have enough data to plot
a graph of acceleration vs. force. You can then find the mathematical relationship between acceleration
and force (with the mass of the IOLab kept constant).

Prediction 2-7A: Suppose you pull the IOLab with a force about twice as large as before. What would
happen to the acceleration of the IOLab?

acceleration unchanged acceleration twice as large

acceleration half as large none of the above

Prediction 2-7B: Explain your Prediction.

The acceleration would increase because the force is what increases the accerlation in the
first place.
Slide 21
Force (200 Hz) Remote 1

1.0
∆t: 1.29500 s
μ: 0.071 N — σ: 0.014 N a: 0.092 Ns s: -0.01 N/s (r²: 0.07)
0.5
Fᵧ (N)

0.0
-0.5
-1.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
  Rezero sensor Time (s)

Wheel - Velocity (100 Hz) Remote 1

1.0
∆t: 1.30000 s
μ: 0.600 m/s — σ: 0.25 m/s a: 0.780 m s: 0.67 m/s² (r²: 1.00)
0.5
vᵧ (m/s)

0.0
-0.5
-1.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
  Time (s)

Wheel - Acceleration (100 Hz) Remote 1

3
∆t: 1.30000 s
2 μ: 0.655 m/s² — σ: 0.13 m/s² a: 0.851 m/s s: -0.03 m/s³ (r²: 0.01)
aᵧ (m/s²)

1
0
-1
-2
-3
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
  Time (s)

Activity 2-3: Acceleration from Different Forces

To test your prediction, accelerate the IOLab with a larger force than before. To produce a larger force,
hang a mass from the fishing line two times as large as in the previous activity. Don’t forget to follow
the same steps as before:

1. The IOLab force sensor should have already been calibrated. The IOLab dongle should have
remained plugged into the USB port on your computer, and the IOLab should have remained
on since the calibration. You can check the calibration by:
a. holding the IOLab with the hook pointed down
b. clicking Rezero sensor under the axes
c. clicking Record
d. hanging 60 g from the force sensor hook for the remainder of the 10 s
e. measuring the force using
If the measurement is not close to 0.6 N, return to previous slide and re-calibrate.
2. Ensure the graph axes on the right are displaying velocity, acceleration and Force vs. time.
3. Zero the force sensor by clicking on Rezero sensor with nothing pulling or pushing on the
sensor.
4. Begin with the 40g mass hung over the edge, holding the IOLab to prevent it from moving.
The mass should have at least 0.75m to fall. Make sure the mass is not swinging.
5. Click +Add Run and then click Record. Then immediately release the IOLab, and let the
falling mass pull it across the table. Stop the IOLab just before it falls off the edge of the
 tabletop.
6. If necessary, repeat until you get good graphs for the entire motion of the IOLab.
7. Adjust the axes to display the graphs as clearly as possible, then continue on to the next
slide.
Slide 22
Force (200 Hz) Remote 1

1.0
∆t: 1.51500 s
μ: 0.255 N — σ: 0.014 N a: 0.386 Ns s: -0.01 N/s (r²: 0.05)
0.5
Fᵧ (N)

0.0
-0.5
-1.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
  Rezero sensor Time (s)

Wheel - Velocity (100 Hz) Remote 1

∆t: 1.52000 s
1.0 μ: 0.560 m/s — σ: 0.30 m/s a: 0.851 m s: 0.67 m/s² (r²: 1.00)
vᵧ (m/s)

0.5
0.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
  Time (s)

Wheel - Acceleration (100 Hz) Remote 1

3
∆t: 1.52000 s
2 μ: 0.651 m/s² — σ: 0.14 m/s² a: 0.989 m/s s: -0.06 m/s³ (r²: 0.04)
aᵧ (m/s²)

1
0
-1
-2
-3
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
  Time (s)

Activity 2-3: Acceleration from Different Forces

Record the times for the following:

Question 2-9A: the time interval before the mass is released

0s

Question 2-9B: the exact moment it is released

0.01s

Question 2-9C: the moment you stop the IOLab at the edge of the table.

1.71s

Question 2-10A: Measure the average force only including the time interval during which the IOLab was
being pulled by the falling mass across the table (not including the time interval before you released it,
or the time interval after you first touched it to stop it).

0.255N
Question 2-10B: Measure the average acceleration during the same time interval as the average force.

0.651m/s2

Question 2-11: How did the force applied to the cart compare to that with the smaller mass in Activity 2-
2 (Slide 18)?

it was almost the same

Question 2-12: How did the acceleration of the cart compare to that caused by the smaller force in
Activity 2-2? Did this agree with your prediction? Explain.

Our prediction was right. The acceleration was twice as large but the force stayed the
same and that was not part of our prediction.
Slide 23
Force (200 Hz) Remote 1

1.0
∆t: 1.14386 s
μ: 0.336 N — σ: 0.032 N a: 0.385 Ns s: -0.03 N/s (r²: 0.10)
0.5
Fᵧ (N)

0.0
-0.5
-1.0
0 1 2 3 4 5 6 7 8 9 10
  Rezero sensor Time (s)

Wheel - Velocity (100 Hz) Remote 1

1.0
∆t: 1.14542 s
μ: 0.640 m/s — σ: 0.34 m/s a: 0.734 m s: 1.00 m/s² (r²: 1.00)
0.5
vᵧ (m/s)

0.0
-0.5
-1.0
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Wheel - Acceleration (100 Hz) Remote 1

3
∆t: 1.14542 s
2 μ: 1.012 m/s² — σ: 0.18 m/s² a: 1.159 m/s s: -0.18 m/s³ (r²: 0.12)
aᵧ (m/s²)

1
0
-1
-2
-3
0 1 2 3 4 5 6 7 8 9 10
  Time (s)

Activity 2-3: Acceleration from Different Forces

Repeat using larger (60g) mass:

8. Zero the force sensor by clicking on Rezero sensor with nothing pulling or pushing on the
sensor.
9. Begin with the 60g mass hung over the edge, holding the IOLab to prevent it from moving.
The mass should have at least 0.75m to fall. Make sure the mass is not swinging.
10. Click +Add Run and then click Record. Then immediately release the IOLab, and let the
falling mass pull it across the table. Stop the IOLab just before it falls off the edge of the
tabletop.
11. If necessary, repeat until you get good graphs for the entire motion of the IOLab.
12. Adjust the axes to display the graphs as clearly as possible.

13. Measure the average force only including the time interval during which the IOLab was being
pulled by the falling mass across the table (not including the time interval before you
released it, or the time interval after you first touched it to stop it).
0.336s

14. Measure the average acceleration during the same time interval as for average force.
1.012m/s2
Slide 24

Activity 2-3: Acceleration from Different Forces

15. Use Excel or another graphing program to plot a graph of average Force vs. average Acceleration.

Question 2-13: Does there appear to be a simple mathematical relationship between the acceleration of
the IOLab (with fixed mass and small friction) and the force applied to the IOLab (measured by the force
sensor)? Write down the equation you found and describe the mathematical relationship in words.(You
may want to refer to the Comment about mathematical relationships on slide 8)

y=3.1796x-0.0978

Question 2-14: If you increased the force applied to the IOLab by a factor of 10, how would you expect
the acceleration to change? How would you expect the acceleration–time graph of the IOLab’s motion
to change? Explain based on your graphs.

Based on the graph the acceleration would grow a lot.

Question 2-15: If you increased the force applied to the IOLab by a factor of 10, how would you expect
the velocity–time graph of the IOLab’s motion to change? Explain based on your graphs.

Since the acceleration would be so high the velocity would increase rapidly.

Comment: The mathematical relationship that you have been examining between the acceleration of
the cart and the force applied to it is known as Newton’s second law. In words, when there is only one
force acting on an object, the force is equal to the mass of the object times its acceleration. (Note: You
will see in the next lab that when more than one force is acting on an object, it is the vector sum of the
forces--or "net force"--that is equal to mass times acceleration.)
Slide 25

ALL DONE!
Please remember to edit the report (insert your name - and if necessary your partners), export the report
and submit it on Blackboard.

Now do the homework associated with this lab.

Copyright © 2018 John Wiley & Sons, Inc. and David Sokoloff, Erik Jensen, and Erik Bodegom.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any
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