Newton’s Second Law
Purpose: The purpose of this Lab Activity is to guide you with the experimental verification of Newton’s
second law represented by the equation F = ma, where F is the net force action on an object, m is the mass of
the object, and a is the acceleration of the object as a result of F. This Lab Activity is intended to assist you
to:
• Develop a physical understanding of the relationship between force and acceleration.
• Make experimental measurements and use graphical analysis to confirm Newton’s second law.
Equipment List: PASCO track, Photogate dynamics cart, pulley and clamp, masses, Pickett fence, string,
bumper, paper clips.
Bring
Ruler, pencil, calculator, textbook
Newton’s Second Law
Name (observer):___________________________________________________ Date: ____ / ____ / ____
Name (partner): _______________________________________________Course # and Section_________
Name (partner): _______________________________________________
Activity 1
A cart is made to roll on a horizontal level track. Draw a labeled free body diagram of the cart only and from
it write down an expression from Newton’s II law. Explain what each term in the expression is.
N → normal force
Fapplied is the force due to the weight in the hanger
M is the mass of the cart + picket fence
Fnet = Ma = Fapplied − f s = MaE
Compare with y = mx + b;
y → Fapplied ; x → aE ; b → f s ; m = M total
N
Fapplied
f
Mcart g
Thus if we plot Fnet vs aE, the slope will give the mass of the cart and the intercept will give the friction force,
form which the coefficient of friction can be found.
Activity 2
Using the equipment provided, one can design and conduct an experiment to calculate the acceleration of the
cart for any applied force. Show that one can use kinematics to do this without using the computer. Clearly
state your initial conditions.
1
2∆x
∆x = vi t + at 2 with vi = 0, a = aE = 2
2
t
Thus we have an independent method to check on the acceleration of the cart. If the Photogates are at a fixed
distance apart ∆x, Data studio can will give the time for the cart to travel this distance and hence acceleration
can be calculated.
Activity 3
A cart is made to roll on a horizontal level track with the help of a falling mass as shown in the diagram.
Draw properly labeled free body diagram(s) and derive an expression for the acceleration of the cart. Assume
that the paper clips represent the falling mass for this activity. This expression for acceleration (a T) gives
you the theoretical value. (Hint: your textbook will be useful here)
See example 4.7 of text for derivation
M is the mass of the cart + picket fence
m is the mass of the hanger + mass on the hanger + mass of paper clips if used
mg + µ k Mg
mg + µ k Mg
aT =
= aT =
m+M
mtotal
If paper clips are used to account for friction force and are also used as a hanger than its mass should be
included in the calculations.
Activity 4
Design and conduct an experiment to find acceleration of the cart for various applied forces. Use the
equipment that is available to you including the sensors and the data studio software. Find out how many
paper clips does it take to get the cart just rolling (think why you need to do this). Then use additional
weights to apply various forces and find the acceleration. This will be your experimental value (a E). Note
that the sensors will give you more accurate results (if used properly) than the process of activity 2. Organize
your work in data tables provided here.
Caution: The total of mass on the hanger + on the cart should not exceed 80 grams at any time.
DATA TABLES
Note: You are expected to know and learn how to make appropriate tables to represent scientific data.
However I will provide them to you this time to assist you and as examples for future experiments.
Suggestions
1. Complete column B first of table 3 first. This will tell you what you should be expecting in column
C. If you do just one trial you can save yourself a lot of time by finding potential experimental
problems.
2. Make sure each Photogate is set to read the appropriate flag length and that the computer knows
about that length
3. Pay attention to why one should do odd number of trials and sets in Table 2
4. Pay attention to the system mass.
Table 1: Various Masses
A
1
Item
3
Mass of the cart (m C)
4
Mass of all weights
5
Mass of Pickett Fence (mp)
Mass of the Hanger (paper
clips) (m h)
6
Total of all masses m total
B
Mass (g)
C
Mass (kg)
80
13
0.080
0.013
Table 2: Experimental Acceleration
Distance between Photogates: _________ (cm)
A
*Mass (m)
on hanger
(kg)
B
Mass on
Cart
(kg)
C
a E -Trial 1
m/s2
_________(m)
D
a E -Trial 2
m/s2
E
a E -Trial 3
m/s2
F
Average a E
m/s2
1
2
3
4
5
* This includes the mass of the hanger
Note: Mass of hanger + Mass on hanger + Mass on Cart should be within 80g-85g.
Table 3: Net Force
A
B
*Mass (m) on
aT
hanger (kg)
(m/s2)
1
2
3
4
5
* This includes the mass of the hanger
C
aE
(m/s2)
D
% Error
E
F net =MaE
(N)
Average % Error:
Activity 5
Determine the percentage error (column D of table 3) between your theoretical value and the experimental
value of acceleration. State under what condition (or assumption) this calculation is valid. Do you have a
high or a low percentage error? Explain your results.
If you go back to activity 3, you will notice that the only needed assumption to use the theoretical equation is
that there is no friction between the track and the cart. In fact you did that by finding the number of paper
clips required to move the cart with constant velocity and kept those paper clips all the time on the hanger.
Activity 6
Regardless of the percentage error in activity 5, one can use the experimental data and the analysis in activity
1 to avoid putting conditions (or making assumptions) for calculation in activity 5. Use your experimental
data to plot a graph of net force verses (F net) experimental accelerations (a E). From your graphs deduce the
coefficient of static friction and redo the calculation in activity 5. What is now the new average percentage
error? Show all relevant work here. Include a print out of your graph with any relevant regression performed.
You can do regression in either Data studio or in Excel.
A plot of Fnet = Mtotal aE is a straight line graph. If you compare this with activity 1, you will recognize that
the intercept will give the friction force. From there one can find the coefficient of friction (since f=µN).
Note that since you used paper clips to compensate for friction force the intercept should have been either
zero, very small positive value (over compensation) or very small negative value (under compensation).