Download Composition and Resolution of Forces

Name: _______________________________________ Date: ____/____/_____ Course/Session: _________
PreLab
Newton’s Second Law: F = ma
Instructions: : Prepare for this lab activity by answering the questions below. Note that this is a PreLab. It
must be turned in at the start of the lab period. Time cannot be given in lab to perform PreLab activities. After
the start of lab activities, PreLabs cannot be accepted.
Q1. Newton’s second law indicates that when a net force acts on an object, it must accelerate. Does it mean
that when two or more forces are applied to an object simultaneously, it must accelerate? Explain.
Q2. The net external force acting on an object is zero. Is it possible for the object to be traveling with a
velocity that is not zero? If your answer is yes, state whether any conditions must be placed on the magnitude
and direction of the velocity. If your answer is no, provide a reason for your answer.
Q3. All of the following, except one, cause the acceleration of an object to be reduced by a factor of two.
Which one is it?
(a) The net force acting on an object is reduced by a factor of two.
(b) The net force acting on the object is doubled.
(c) All forces acting on the object are reduced by a factor of two.
(d) The mass of the object is doubled.
Q4. When the net force that acts on a hockey puck is 10 N, the puck accelerates at a rate of 50 m/s2. What is
the mass of the puck? Show your work.
(a) 0.2 kg
(b) 1.0 kg
(c) 5.0 kg
(d) 10 kg
(e) 50 kg
Q5. A car has a mass of 1500 kg. It is stuck in the snow and is being pulled out by a cable that applies a
force of 7660 N due north. The resistance of the snow and mud also applies a force to the car, which has a
magnitude of 7510 N and points due south. What is the acceleration of the car? Show your work.
(a) 15 m/s2 north
(b) 10 m/s2 south
c) 0.15 m/s2 south
d) 0.10 m/s2 north
(e) zero
Newton’s Second Law: F = ma
Purpose: The purpose of this lab activity is to guide you to an 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, dynamics cart (and platform), pulley and clamp, masses (blue box),
stopwatch, string, bumper, paper clips.
Introduction: In the figure below, a small mass m is connected to the dynamics cart via a string that passes
over a pulley at one end of the PASCO track. The fall of m pulls and accelerates the cart on the track.
Assuming that the string is not elastic and that there is no slack in it, the acceleration of the cart on the track
is the same as the acceleration of the falling mass. Our goal is to measure this acceleration experimentally
and then compare it with the expected theoretical result. Let the experimental acceleration be aE. If the cart
accelerates from rest (zero initial speed, vi=0), and covers a distance x in t seconds, from the equation of
motion x= vi t + ½ aE t 2 we can write aE = 2 x t 2. On the other hand, the theoretical acceleration aT can be
obtained from the Newton’s second law F = m aT , namely, aT = F/m.
Procedure
Part I: Setup
a. Set up the pulley and the bumper as shown in the figure.
b. Adjust the level of the track until the cart has no particular tendency to drift or accelerate in either
direction along the track.
c. Make a loop at one end of the string and place it over the spring-release trigger on the dynamics cart.
Drape the string over the pulley. Adjust the pulley so that the string is leveled. You can use the sprit
level to assist you in this setup.
d. Adjust the length of the string so that it does not touch the ground before the cart hits the bumper,
and make a loop at the other end. Attach one open paper clip to this end to serve as a hanger. Note: If
the falling mass hits the ground the cart stops being pulled and its acceleration becomes zero. It may
continue its motion until reaching the bumper, but it will do so with a uniform (constant speed)
motion.
Part II: Friction
The equation for aT displayed above assumes that there is no friction involved in the setup. However, small
as it may be, there is friction between the track and the edges of the cart wheels, and between the wheels and
the axles. In order to take into account the friction effect in this setup, proceed as follows:
a. Attach a few paper clips to the hanger until the cart moves without apparent acceleration when
barely nudged. You have to use trial and error to figure out how many paper clips it will take.
b. The idea here is that the weight of the paper clips is just enough to counteract the friction force
holding the cart, and therefore, equal in magnitude to it.
c. Ignore the weight of the paper clips in the calculations.
Part III: Measuring Mass
a. The mass of the platform is printed on the label (blue sticker tape) on top of the cart between the two
brass pins. It is between 90 and 100 grams. Write the number in cell B2 of Table 1. Convert to
kilograms (1 kg = 1000 grams) and write it in cell C2.
b. The mass of the cart is labeled on the real longer side to the cart with a blue stick tape. It is between
450 and 490 grams. Write it down in cell B3 of Table 1, convert it to kilograms and write it in cell
C3.
c. Add all the masses in column B and write the result in cell B5. Do the same in column C.
d. The value in cell C5 is your mcart that you will use later in the calculations.
Part IV: Practice Run
a. From the blue box collect the following masses and place them on the platform of the cart: Two 10 g
and three 20 g masses (80 g total). Slide the masses on the brass pins attached to the platform. Do not
borrow masses from another setup. If your set up does not have the masses, contact the lab
instructor.
b. Take one 10 g mass from the platform and place it on the hanger.
c. Pick a distance x (about 40 or 50 cm) on the yellow scale on the track along which you want to
measure the acceleration. Use the V mark on the blue label on the side of the cart for this purpose.
Have the V mark on the same side as the yellow scale on the track so that lining it up is easy. For
example, the starting point for the cart could be 140 cm and the stopping point could be 190 cm (x =
50 cm). When the cart is at the stopping point, the V mark should line up with the 190 cm point, and
the plunger of the cart should be just touching the bumper. Record the distance x on top of Table 2.
d. Pull the cart back to the chosen starting point. Release the cart being careful not go give it any push
or pull. One way of doing it is by just slightly pressing your finger on the track in front of the cart
thereby blocking the motion of the cart. Quickly pull your finger away in the direction that the cart
wants to move. Start the stopwatch simultaneously with the pull of your finger and stop the
stopwatch when the cart hits the bumper. To reduce reaction time errors, the person that releases the
cart should also do the timing. Practice a few times until you feel comfortable about timing the
motion of the cart.
Part V: Force and Acceleration Measurements
a. With the 10 g mass on the hanger, let the cart run three times, and determine the average time for the
cart to move through the distance x after being released from rest. Record the run times of the three
trials and the average time on Table 2.
b. Keep the 10 g mass on the hanger and move the other 10 g mass from the platform to the hanger.
Repeat the previous step and record the run times and the average time of the three trials on Table 2.
c. Keep the two 10 g masses on the hanger and move one 20 g mass from the platform to the hanger.
Repeat the previous step and record the run times and the average time of the three trials on Table 2.
d. Keep the two 10 g and one 20 g masses on the hanger and move the second 20 g mass from the
platform to the hanger. Repeat the previous step and record the run times and the average time of the
three trials on Table 2.
e. Keep the two 10 g and two 20 g masses on the hanger and move the third 20 g mass from the
platform to the hanger. Repeat the previous step and record the run times and the average time of the
three trials on Table 2.
f. Place the masses back in the blue box.
g. Complete Table 2 and Table 3 using the equations as indicated.
Newton’s Second Law
Part VI: Mass and Acceleration Measurements
a. Collect the following masses from the blue box: Two 10 g, two 20 g, one 50 g, and three 100g.
b. Place one 10 g mass on the hanger and one 100 g mass on the cart platform. Proceed as before,
recording the run times and the average time of three trials on Table 4.
c. Keep the 10 g mass on the hanger and the 100 g mass on the platform, and add another 100 g mass to
the platform. Proceed as before, recording the run times and the average time of three trials on Table
4.
d. Keep the 10 g mass on the hanger and the two 100 g masses on the platform, and add the third 100 g
mass to the platform. Proceed as before, recording the run times and the average time of three trials
on Table 4.
e. Keep the 10 g mass on the hanger and the three 100 g masses on the platform, and add 100 g mass
(use 10 g + 20 g + 20 g + 50 g) to the platform. Proceed as before, recording the run times and the
average time of three trials on Table 4.
h. Place the masses back in the blue box.
f. Complete Table 5 using the equations as indicated.
Final Analysis:
1. Use the data from Table 3 to make a plot of acceleration (column B) versus force (column E).
a. Determine the slope and the intercept of the straight line connecting the points. Obtain the equation
of this line.
b. What does the intercept represent? Whys is it nonzero?
c. Identify the terms in your equation with the corresponding ones in Newton’s second law.
d. Compute the percent difference between the slope in your graph and the total mass mtotal .
2. Use the data from Table 5 to make a plot of acceleration (column E) versus mass (column F).
a. Determine the slope and the intercept of the straight line connecting the points. Obtain the equation
of this line.
b. What physical quantities do the slope and the intercept represent?
c. What is the relationship between the acceleration aE and the mass mtotal?
d. Show how you can compare the slope of this plot with the values in column F of table 5.
Newton’s Second Law - DATA TABLES
Name (observer):___________________________________________________
Date: ____ / ____ / ____
Name (partner): ____________________________________________________
Course/Session: _________
Table 1: Masses
1
2
3
4
5
A
Item
Mass of the platform (mP)
Mass of the cart (mC)
Mass of all brass weights
Total of all masses (add rows 2 to 4)
Table 2: Experimental Acceleration
A
B
1 Mass on hanger
Trial 1
(kg)
time (s)
2
0.010
3
0.020
4
0.040
5
0.060
6
0.080
Table 3: Net Force
A
1 Mass on hanger
(kg)
2
0.010
3
0.020
4
0.040
5
0.060
6
0.080
B
aT = (m/mtotal)g
(m/s2)
Table 4: Experimental Acceleration
A
B
1
Mass on
Trial 1
platform (kg)
time (s)
2
0.10
3
0.20
4
0.30
5
0.40
Table 5: Net Force
A
1
Mass mh on
hanger (kg)
2
0.010
3
0.010
4
0.010
5
0.010
B
Mass mp on
platform (kg)
0.100
0.200
0.300
0.400
B
Mass (g)
C
Mass (kg)
80
0.080
Distance x: _________ (cm)
_________(m)
C
D
E
Trial 2
Trial 3
Average time (s)
time (s)
time (s)
(B2+C2+D2)/3 =
(B3+C3+D3)/3 =
(B4+C4+D4)/3 =
(B5+C5+D5)/3 =
(B6+C6+D6)/3 =
C
aE = 2 x t2
(m/s2)
D
% difference
(| aT - aE | / aT) 100
Distance x: _________ (cm)
C
D
Trial 2
Trial 3
time (s)
time (s)
_________(m)
E
Average time (s)
F
aE = 2 x t2
(m/s2)
E
Fnet = m aE
(N)
F
aE = 2 x t2
(m/s2)
(B2+C2+D2)/3 =
(B3+C3+D3)/3 =
(B4+C4+D4)/3 =
(B5+C5+D5)/3 =
C
Total mass M = mh+ mp+ mcart
of cart (kg)
D
1/M
(1/kg)
E
aE = 2 x t2
(m/s2)
F
Fnet = mh g
(N)