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Unformatted text preview: NAME LAB PARTNERS Station Number Newton's Second Law of Motion Experiment 10 INTRODUCTION A net force Fnet acting on an object produces an acceleration a in the direction of the force
directly proportional to the force and inversely proportional to the mass m of the object. In
equation form this statement becomes, Fnet = 2F = ma. Notice that both F and a are vectors, but
m is a scalar (number). The objects of this experiment are to learn to apply Newton's second law
of motion and to use to ﬁnd useful information about the forces acting. You will measure both
the coefﬁcients of rolling friction and sliding friction. THEORY The system to be studied is shown in the
ﬁgure. A mass M rests on an inclined track and
is attached to a second mass m by a string that
passes over a pulley. The pulley and the string
are so light that their mass or rotational inertia
may be neglected. The forces that act on each
mass are shown and identiﬁed as follows: T is
the tension in the string, mg is the weight of mass m, N is the normal force of contact between
the track and M, Mg is the weight of mass M, and f is the force due to friction (rolling or sliding).
The equation of motion parallel to the track for mass M, a dynamics cart (or wooden block) in
this experiment, is given by TMgsinHf=Ma. (1)
The equation of motion for the hanging mass is given by
mg — T = ma, (2) where we have assumed quantities positive up along the track and down from the pulley. The
equation of motion for the mass M perpendicular to the track is given by N—Mg cos 6:0. (3) For both rolling friction and sliding friction, it is possible to relate the magnitude of the friction
force f to the normal force of contact between the surfaces so that f = Mr N for rolling friction and 65 f = Mk N for sliding (kinetic) friction. By measuring a, M, m, and 6. one can calculate f, T, N and
ﬁnally ,ur and ,uk. The forces that act in this experiment may be considered constant so that one can use the
equations for constant velocity and constant acceleration. The acceleration will be calculated
from the position versus time curve for the motion of the masses m and M. EXPERllVIENT N O. 10 1. Level the track by adjusting the screws on the feet of the track. 2. Remove the feet on the initial side of the track. The track will remain inclined during the
experiment; we will record data as the cart and wooden block move up the inclined track. 3. Carefully measure the angle of inclination of the track. Angle = 4. In the ﬁrst part of the experiment, we will obtain data to calculate the coefﬁcient of rolling
friction for the dynamics cart. Use the balance to ﬁnd the mass of the cart and the weight
hanger. Add about 15 grams to the weight hanger. This should be enough to cause the cart
to accelerate up the track. The mass of the weight hanger plus the added 15gram mass
corresponds to the mass m in the drawing. Record these values below Weight hanger mass + Added mass = total mass (m) mass of the cart (M) =
5. Log into the Student account and open the exp9 ﬁle from the Start Menu.
6. Before each time data are acquired, place the cart at the starting position, release it and click Start to record data. Click again to stop recording data before the cart reaches the end of the
track. Collect your ﬁrst data set. 10. 11. 12. 13. 14. Your data set contains the position as a function time of the cart as it moved up the track. To
view a graph of your data, drag the data set Run #1 onto the Graph header in the Display window below.
You should now see a graph of position vs. time. Since these data represent motion with
constant acceleration the graph will not be a straight line. If your data look ﬁne close the graph. We now want to look at the graph of velocity as a function of time. Remember that velocity
is deﬁned as v = dx/dt. Before we create the graph of v vs. t Click on the Calculate button at the top of the screen and select New. Under Deﬁnition type
“dx = xlast(1,x)”, as shown in the ﬁgure below, and click Accept. This deﬁnition uses the
special function “last” to calculate the difference between two adjacent values of the variable
x, (x2 — x1). If you are asked to deﬁne the variable x, simply drag x (m) to where it says
“Please import the variable x” under Variables Now set the variable name and the units of dx, click Properties in the Calculator window
then type “m” under Units. Under Variable Name type “dx”. Click OK. Similarly, we are going to create the variable dt. Click on New in the Calculator window.
Type “dt = tlast(1,t)” under deﬁnition and click Accept. If asked to deﬁne the t, click on “t =
timeof(x)” in the Data window and drag it to deﬁne the variable. Click Properties in the Calculator window and type “s” under Units. Click on the drop
down button besides Variable Name and select Y, erase it and type “dt”. Click OK. Create the variable v by clicking New in the Calculate window and typing “V =dx/dt” under
Deﬁnition. To set the units of v click Properties in the Calculator window and type “m/s”
under Units. Click the button besides Variable Name and select Y, erase it and type “v”. cc 39
S Then click the button again, this time select X, erase it type “time”. Then type under Units. Click OK. To plot the graph of v vs. t drag “v = dx/dt” on the Data window and drop it on Graph in the
Display window. The graph should be a straight line since it is described by the equationv = v0 + at. Eliminate the line connecting the data points, click Display on the menu at the top of your
screen and select Settings. Uncheck the box that says “Connect Data Points” and click OK. Print the graph, draw the best ﬁt line through it and calculate the slope. Record both the slope
and the vintercept. Show all your calculations on the graph print out. 67 Slope = vintercept = 15. We are now going to use the computer to ﬁt the data. DataStudio will ﬁt the data to the
“best” straight line, thereby minimizing the error you might make in eyeballing the best
straight line. Such a process is called the least squares ﬁt to a straight line. Click Fit on the
graph window and select Linear Fit, a small window will appear with information the values
of the ﬁtting parameters. Write down the value of the slope and intercept, the results should
be very close to the ones obtained in the previous step. If you only want to ﬁt part of the data
highlight the interval that you want to consider and then use Linear Fit. Slope = vintercept = 16. Print your graph again, now showing the least squares ﬁt obtained. The equation 1) = 130 + at
describes velocity as a function of time for an object moving with constant acceleration. What do the slope and vintercept represent? Calculate the percent of difference between the values for acceleration and initial velocity
found by constructing the best ﬁt by hand and the values generated by DataStudio.
Show your work. %diﬂina= %diﬂinv0= 68 17. Use Equations (1) and (2) to eliminate T and show that the expression for f is given by f=g(mMsin8)(m+M)a (4) 18. Use all the data you have acquired, set g = 9.8 III/52, and ﬁnd the rolling friction force f. Use
Equation (3) to ﬁnd the normal force and calculate the coefﬁcient of rolling friction Hr Fill
in the spaces below and show all work in the space below. f = ___.__~__ N = _— ,ur =
19. Now we will carry out the same procedure to calculate the coefﬁcient of sliding friction for
the wooden block (felt side down). Determine the mass (M) of the wooden block and record
it. Then replace the cart with the wooden block.
Mass of wooden block 20. Add about 40 grams to the weight hanger and record the total hanging mass m. 69 Hanging mass (m) = 21. Record a data run now using the wooden block. The graph of velocity vs. time will be created
automatically. Use this graph to obtain the acceleration of the block as it moves up the track using the
Linear Fit function only. Find the friction force, normal force, and coefﬁcient of sliding
friction Mk Record these values below and show all work in the space below. f=___.__ N=____ Mk: Logout of the computer. QUESTIONS 1. Calculate the tensions in the string for both the cart and the wooden block. 70 w.“ 2. Use the value obtained for the cart's coefﬁcient of rolling friction and determine how far it
will travel if given an initial speed of 20 cm/s across a ﬂat, level surface. 71 ...
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 Fall '10
 LOWELLWOOD

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