Download Newton`s Second Law of Motion

Newton's Second Law of Motion
Experimental Objectives: To
verify Newton's
2nd law of motion for ar system. This law is
r
commonly written as Fnet = ma . m is the
r
total system mass, a represents r its
acceleration - - the result of a net force Fnet
(the vector sum of all the forces) acting on
it.
This lab employs an "almost frictionless
cart" placed on a ramp (which includes
metric markings). The cart is connected over
a pulley to a hanging mass as shown in
Figure 1 (below).
M
Track and pulley, "frictionless"
cart, various masses, and timer /stopwatch.
Apparatus:
x
Newton's 2nd law is
arguably the most important relationship in
introductory physics, because it successfully
describes how our everyday world works. It
is not derived from basic principles, but
stands on its own as a fundamental
relationship between force, mass and
acceleration.
r r
Rewriting it as a = Fnet m , one can see that
this law predicts that a system's acceleration
is inversely related to its mass if the net
force acting on it is constant. More mass,
less acceleration.
if the mass is
r Instead,
r
constant, then Fnet ∝ a . That is, the system's
acceleration should be directly proportional
to the net force acting on it. More net force,
more acceleration.
Fundamentals:
x
Figure 1: Car, Ramp and Hanging Mass
Note the ramp is tilted downward. This
compensates for the friction present. Before
starting, remove the hanging mass and
adjust the ramp angle so the cart alone (mass
M) moves downward at constant speed,
determined by eyeball. This in effect makes
the cart "frictionless" and the net force is
due only to the gravitational force on the
hanging mass, m. Thus the net force on the
system is Fnet = mg . Express the mass in
kilograms and recall that g = 9.80 m s2 to
ensure the net force is in newtons.
During any one run, the forces on our
system will be constant, therefore the net
force and acceleration will be constant. Thus
our constant acceleration equations are
applicable. The most useful one for this
laboratory is the one that relates location to
Procedure for Constant Mass:
1. Here you will keep the mass of the system
constant and vary the net force. First add
a 500 g block to the cart. Then place six
5.0 g masses and the paper clip on the
cart. Measure the total mass. (It should a
bit more than 1 kg).
acceleration, that is: x = xo + vot + at 2 2 .
Our system will start at rest and we choose
the initial location to be the origin. Thus the
displacement is given by x = at 2 2 or,
solving for acceleration:
a = 2x t 2
m
floor
(1)
(over)
Hence by measuring the time t it takes for a
system to move a distance x we can compute
its acceleration.
Apparatus and Preliminaries:
1
Starting from rest, let the cart roll a
distance x, (perhaps 60 to 80 cm) making
sure the dangling mass does not hit the
floor. Measure the roll time t. Now add
one 200 g slotted mass to the cart,
calculating the total system mass (in kg).
Repeat this four more times, each time
adding an additional 200 g slotted mass to
the cart. Arrange your data in column
form with the following suggested
column headings: Mtotal, x, t, a (calculated
from Eq. 1) and 1/a. Be sure to include
units. Your instructor will tell you if the
data should be displayed on paper or in a
computer spreadsheet such as EXCEL.
Constant Mass (continued):
2. Now move one of the 5.0 g masses to the
paper clip holder. Determine the mass of
the paper clip and combine the two to get
the dangling mass m (in kg). Starting
from rest, let the cart roll a distance x,
(perhaps 60 to 80 cm) making sure the
dangling mass does not hit the floor.
Measure the roll time t. Repeat this five
more times, each time moving another
5.0 g mass to the paper clip holder.
Arrange your data in column form with
the
following
suggested
column
headings: m, Fnet, x, t, and a (calculated
from Eq. 1). Be sure to include units.
Your instructor will tell you if the data
should be displayed on paper or in a
computer spreadsheet such as EXCEL.
Verifying the 2nd Law [constant Fnet]:
1. Graph the total system mass (in kg) on the
vertical axis and the inverse of the
acceleration (1/a in s2/m) on the
horizontal axis. Your graph may be done
on paper or on the computer, depending
on how you were told to accumulate the
data. Regardless, Newton's second law
predicts that this should be a straight line.
Is yours? Comment.
Verifying the 2nd Law [Constant Mass]:
1. Graph the net force on the vertical axis
and the acceleration on the horizontal
axis. Your graph may be done on paper or
on the computer, depending on how you
were told to accumulate the data.
Regardless, Newton's second law predicts
that this should be a straight line. Is
yours? Comment.
2. Either by eyeball slope-intercept method
or using computer software, determine
the equation of the line. Since we expect
1
M total = (Fnet ) , if the net force is
a
constant, this is of the form Y = AX
where A = constant = Fnet . Thus not only
should the data plot as a straight line, but
the slope should equal the net force on
the system. Are they in agreement (to
within 10%)? Comment.
2. Now either by eyeball slope-intercept
method or using computer software,
determine the equation of the line. Since
we expect Fnet = M total a , with the total
mass constant, this is of the form Y = AX
where A = constant = M total . Thus not
only should the data plot as a straight
line, but the slope should equal the total
system mass. Are they in agreement (to
within 10%)? Comment.
(next page)
Procedure for Constant Net Force:
1. Here you keep the net force on the system
(mg) constant and vary the total mass
(M+m) by changing the cart's mass. A
convenient value for the dangling mass is
30 g. Be sure to add the paper clip mass
to determine the value of m.
(Your instructor may
or may not require some or all of these).
Follow-Up Questions:
A.
2. Remove the 500 g block that was on the
cart. Measure the mass of the cart itself.
2
To start the experiment the ramp was
tilted downward until the cart rolled at
constant velocity - - the cart was not
accelerating. For this situation, draw the
free body diagram of the forces on the
cart. Use it to explain how the forces
canceled out.
B.
To start the experiment you tilted the
ramp downward until the cart rolled at
constant velocity. Suppose the required
angle was 2.0o. Use this to estimate the
force of rolling friction on your cart.
(HINT: Draw the free body diagram of
the cart, or see Follow-Up Question A.
You will also need the mass of the cart.)
C.
For the constant mass section of this
experiment, how would your graph
change, if at all, if you had not placed
the additional 500 g mass in the cart at
the beginning? Explain.
D.
For the constant net force experiment,
how would your graph change, if at all,
if you had not removed the 500 g mass
before you started. Explain.
E.
Using the constant mass data with the
largest dangling mass used, to predict
the roll time measured if the roll distance
was 20 cm. Show your work.
F.
Using the constant net force data to
predict the roll time measured if the roll
distance was 40 cm and the cart had 300
g extra on it. Show your work.
G.
Suppose you had a horizontal ramp and
a cart with a mass of 1.00 kg, connected
to a 50 g mass dangling over a pulley. If
the force of rolling friction were 5.0% of
the normal force on the cart, use
Newton's 2nd law and the cart's free body
diagram to determine the cart's
acceleration.
[Rev. 6/07]
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