Lab 4
Newton’s First and Second Laws
Objectives:
• To observe what happens to an object’s motion when no force is applied (Newton’s 1st Law).
• To observe what happens to an object’s motion when a force is applied.
• To study the quantitative relationship between force and motion (Newton’s 2nd Law).
Equipment:
• Vernier LabQuest2 interface with LabQuest App software
• Vernier dynamics track and adjustable leveling feet
• Vernier adjustable end stop
• Vernier standard cart
• Vernier cart picket fence
• Vernier photogate and photogate
acket
• Vernier ultra pulley and pulley
acket (one piece and short bolt 1/4” x 20 x 5/8”)
• Vernier Go Direct R© force and acceleration sensor (or dual-range force sensor) with hook
• Lightweight mass hange
• Slotted laboratory masses (30, 40, and 50 g)
• Mass balance or electronic balance
• Length of string (70 cm)
Safety and Care of Equipment:
• Observe standard laboratory safety precautions.
• Absolutely no food or open drink containers are permitted in lab. Water bottles with
a screw-on top are permitted.
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58 LAB 4. NEWTON’S FIRST AND SECOND LAWS
Figure 4.1: The force sensor is attached to the cart and a photogate is positioned mid-way down the track. A
cart picket fence rides in a slot on the cart. In the first and third parts of this lab, the force sensor is pushed
and pulled manually.In the second part, the spring is extended over the pulley and a weight hanger and weights
are attached.
4.1 Theory
4.1.1 Introduction
The relationship between force and motion was particularly difficult to decipher, and has been refe
ed
to by some scholars as the most difficult problem in the history of science. It took the best minds of
Europe nearly 2000 years to discover, so you can expect to work hard to understand it fully. They did
not, however, have the equipment that you have available, and you now have their experience to draw on.
Most people, prior to studying physics, believe that the velocity of an object is directly related to
the force on the object. They will tell you that if the force is doubled, the velocity will be doubled. You
will be able to check out that belief here and discover for yourself that it is not co
ect. You will begin
to study an alternative relationship between force and motion proposed by Isaac Newton over 300 years
ago.
4.1.2 Newton’s Laws of Motion
Newton’s First Law of Motion states that as long as there is no net force on an object, the object will
maintain its constant velocity. This velocity could be zero or any other value. Keep in mind that since
velocity is a vector, with magnitude and direction, constant velocity implies that neither the magnitude
nor the direction is changing.
For the Second Law of Motion Newton proposed that a force applied to an object will cause the
object to undergo an acceleration that is directly proportional to the force. Again, both force and
acceleration are vectors, so the magnitude of the force should be proportional to the magnitude of the
acceleration and the direction of the force should be the same as the direction of the acceleration. In
compact mathematical notation, we write
~F = m~a (4.1)
or, if we are dealing with the simple case of motion in one direction, say along the x-axis, we write
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4.2. PROCEDURE 59
Fx = max (4.2)
This last equation contains the information that the force and the acceleration are both in the same
direction and that the magnitude of the force is proportional to the magnitude of the acceleration. The
constant of proportionality is, according to Newton, the mass m of the object.
4.2 Procedure
4.2.1 Newton’s First Law of Motion
In this section you will use a photogate along with a force sensor to study the relationship between the
force on a cart and its motion.
You will cali
ate the force sensor and should develop the habit of doing so at the beginning of
each experiment. In addition to cali
ation at the beginning of the experiment, the force sensor must
e zeroed before each data collection or run. Do this by tapping Sensors → Zero on the LabQuest2
screen when nothing is pushing or pulling on the hook of the force sensor.
1. Set up the dynamics track with an end stop at one end. Go ahead and attach the pulley to the
other end, but you will not use the pulley until the next section. Attach a photogate with the long
flat photogate
acket to the side of the track near the middle. Secure the force sensor to the cart
and insert the cart picket fence into the slot along the side of the cart. Tie small loops at each end
of a piece of string about 70 cm long. Attach one loop to the hook on the force sensor. The setup
is depicted in Fig. 4.1.
2. Connect the force sensor to the LabQuest Mini’s CH 1 channel and connect the photogate to the
DIG 1 channel. Set the switch on the force sensor to ±10 N.
3. Open the LabQuest App software. The computer should automatically detect both the force senso
and the photogate and give you position vs time, velocity vs time, and force vs time graphs (only
two are displayed at the time). Change the position axis-label to acceleration. You may adjust
the experiment Duration after you begin collecting data, if necessary.
4. Cali
ate the force sensor in a horizontal orientation using a 100 g mass. We generally use a 500
g mass, but in this case we prefer to have greater accuracy over a smaller range of values. See
Appendix C for instructions on cali
ating the force sensor.
5. Check the cali
ation of the force sensor by zeroing it, placing it in a horizontal orientation,
extending a string out and over a pulley, and then hanging a 100 g mass from the string and
collecting data. If the resulting graph is not a force line at 0.98 N, recali
ate the sensor.
6. Zero the force sensor now and prior to each run.
7. To collect data for Trial 1, position the cart on the track near the end stop. Extend the string that
is tied to the force sensor, along the track and grasp the string on the far side of the photogate.
Smoothly pull on the string and thus pull the cart along the track through the photogate. Keep
the string parallel to the track and maintain tension in the string. Practice a few times if necessary.
You are looking for a reasonably smooth force graph and acceleration graph.
8. Draw the force, acceleration, and velocity graphs in the Trial 1 column of Fig. 4.2. Make sure
that the time axis is the same on all three graphs so that a vertical line running through all three
graphs marks the same event.
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60 LAB 4. NEWTON’S FIRST AND SECOND LAWS
9. To collect data for Trial 2, pile the string on top of the cart and start the cart near the end of
the track with the pulley. Zero the force sensor now and prior to each run. Start data collection
and give the hook on the force sensor a quick push with your finger or pencil eraser. The cart
will travel through the photogate. There is no force acting on the force sensor during the time it
travels through the photogate.
10. Sketch the force, acceleration, and velocity graphs in the Trial 2 column of Fig. 4.2.
4.2.2 Newton’s Second Law of Motion
Your observations in the previous section should have provided evidence that it is the acceleration, and
not the velocity, that is directly related to the applied force. In this section you will examine this
elationship more fully, and check out Newton’s Second Law of Motion. For the measurements in this
section the x-axis is along the track.
1. Using the mass balance in the lab, measure the mass of the cart and the attached force sensor.
Record this mass as m in Table 4.1.
2. Set up the dynamics track, as shown in Fig. 4.1, with an end stop at one end and a pulley at the
other end. Attach a photogate with the long flat photogate
acket to the side of the track nea
the middle. Secure the force sensor to the cart and insert the cart picket fence into the slot along
the side of the cart. Tie small loops at each end of a piece of string about 70 cm long. Attach one
loop to the hook on the force sensor. Place the other loop on the weight hanger. With the cart on
the track, the string should pass over the pulley so that the weight hanger hangs vertically.
3. Check the cali
ation of the force sensor by zeroing it, placing it in a horizontal orientation,
extending a string out and over a pulley, and then hanging a 100 g mass from the string and
collecting data. If the resulting graph is not a force line at 0.98 N, recali
ate the sensor.
4. Zero the force sensor now and before each run. Attach a 30 g mass to the weight hanger at the
end of the string. When the cart is released from rest, the weight of the hanging mass should
cause the cart to accelerate. With the cart starting near the end stop and before the photogate,
collect data as the cart travels through the photogate. You should see a range of time over which
the acceleration and force graphs are approximately constant (after the release and before the cart
hits the end stop). If not, adjust the length of the string and repeat the trial.
5. Select a time range over which the force and acceleration are approximately constant. Use the
Analyze → Statistics feature on the force graph to find the average values for the force. Use
the Analyze → Curve Fit → Linear Fit feature on the velocity graph to find the acceleration.
Record this data in Table 4.2. From the average values, calculate the force to acceleration ratio
and record this as well.
6. Repeat the data collection, changing the value of the hanging mass to 40 g and to 50 g. Make
sure that you zero the force sensor prior to each run. Enter this data in Table 4.2.
7. Calculate the mean of the three F/a ratios in Table 4.2, and record this mean as Average F/a in
the last row of Table 4.2.
If the ratio F/a is approximately the same for each of the three cases, your data
indicates a proportional relationship, F ∝ a. Another way to show that force and
acceleration are proportional is to graph