Download Lab 2 Force and Acceleration

Lab 2 Force and Acceleration - Newton’s Second Law
Objective:
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To observe the relationship between force and acceleration and to test the hypothesis that
the force is equal to the mass times the acceleration (Newton’s Second Law).
Equipment:
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Track with cart, accessory weights
Smart pulley timer
Force Sensor
Triple beam balance
Physical principles:
A net force, F, applied to an object
with a mass, M, will cause the mass
to accelerate with an acceleration,
a. Newton's law of motion asserts
that the net force is directly
proportional to the acceleration
produced. The proportionality
constant is denoted by the inertial
mass, M. In equation form, this
law can be written as
F'M a
(1) Figure 1 Diagram of the experiment.
In this experiment a dynamics cart is accelerated by a string that passes over a smart pulley. The
smart pulley records the position and velocity of the cart as time passes. The acceleration of the
cart is determined from the slope of a graph of the cart velocity versus time. The string loops
under a second pulley that supports an accelerating mass, m, and then is connected to the force
sensor. The force sensor measures the tension in the string which is the force that accelerates the
cart. For accelerations small compared to g this tension is about half of the weight of the
accelerating mass.
Procedure:
Setup Science Workshop:
1. Open Science Workshop.
2. Plug in the smart pulley into digital channels 1 and 2.
3. Drag the digital plug icon over digital channel 1 and
select smart pulley (linear). Double click on the smart
pulley to calibrate it. Enter the average of 0.0155 as
the average radius of the pulley.
4. Plug the force sensor into analog channel A.
5. Drag the analog plug icon over analog channel A and
select force sensor. Double click on the force sensor
to calibrate it. Set the low value to zero, and click on
low value read with no mass hanging from the force
sensor. Set the high value to 4.9N and click on the
high value read with a 500g mass (weight = 4.9N)
hanging from the force sensor.
6. Click on Sampling Options to change the sampling
rate to 1000 Hz and the stop time to 5 sec.
7. Make a graph of velocity versus time by clicking on
the graph icon, dragging it over the smart pulley icon, Figure 2 Force sensor, support
selecting velocity, and clicking on OK. Add the force pulley and smart pulley.
sensor graph to the graph window by
clicking on the multiple graph icon
(lower right icon in the lower left
corner of the graph) and selecting
analog A and force sensor.
8. Start statistics by clicking on the E
button in the graph window, then click
on the E button beside the smart pulley
graph and select curve fit and then
linear fit. Click on the E button beside
the force sensor graph and select mean
and standard deviation.
Figure 3 Force sensor, smart pulley and cart.
Setup system:
1. Measure and record in your journal the mass of the cart, Mcart including the masses of any
blocks on the cart.
2. Place the cart on the track and level the track so that the cart does not accelerate toward the
smart pulley.
3. With a table clamp, position the smart pulley (see figure 3) at the aisle end of the track. Run
the cable through the second, free-hanging pulley and back up to a force sensor mounted
vertically.
Data Collection:
Part 1: Cart with one mass block
1. Place one block on the cart and hang a 20 g mass from the free-hanging pulley, and position
the cart so that the free-hanging pulley is just below the smart pulley. Click on the REC
button as your lab partner releases the cart.
2. Include Table 1 in your journal. Click and drag the curser to select the best data from the
velocity vs. time graph. The statistics section will fit a straight line to the selected data. The
slope of the line, a2, is the acceleration of the cart. Record the value of the acceleration in the
column titled a in Table 1. Click and drag the curser to select the same data on the force vs.
time graph. Record the mean value of the force in the Fmea column of Table 1.
3. Take a series of five more measurements, with masses indicated in Table 1. Record the value
of the acceleration from the slope and the average force for each mass.
4. Print out one of the data graphs and place in the data section of your journal as a “sample”
raw data measurement.
Part 2: Cart with two mass blocks
1. Place two blocks on the cart and repeat the experiment.
2. Fill in a second table in your journal in a similar manner to Table 1 as given above.
Analysis of Data:
1. Use Graphical Analysis to plot a graph of measured tension F (y axis) vs. acceleration a (x
axis) for the data in Table 1. Click on the y axis and change the setting to Autoscale at 0.
Repeat for the x axis. This will include the origin (0,0) point in the graph. Put a title and
label the axes of the graph.
2. To fit the data to a straight line click on Analyze and Automatic Curve Fit and select function
y = M*x + B to select a linear (straight-line) function. Since we have F given as y, and a
given as x, the slope M should be equal to the mass of the cart and block. Theoretically, the
value of the intercept B should be zero, since no F0 appears in Eq. (1). However, F0 can be
thought of as the tension required to cause the cart to move with zero acceleration, that is, the
tension required to overcome kinetic friction. Thus the intercept B provides a measure of the
friction of the system. Print your graph.
3. Record in your journal the slope M and the intercept B . As equation (4) predicts, this slope
should be very close to the mass of the cart (Mcart) in the case of Table 1. In the case of Table
2 the slope should be very close to the total mass (Mtotal). Calculate the percent error for both
cases by using
%Err '
4. Repeat the above analysis for Table 2.
In your conclusions you should:
*slope & M *
× 100
M
(1)
1. Discuss how your data agrees or disagrees with Newton’s Second Law. Is the relation of
force and acceleration linear? To within the percent error that you calculated for both graphs is
the slope of the graph equal to the mass of the cart and blocks?
2. Interpret the value of the intercept. How does the presence of a frictional force affect the
results of the experiment?
3. Speculate on the origin(s) of error.
4. Describe what you learned in this experiment.
Mcart = ______________
Mcart+block = ______________
Table 1 Cart with one mass block
m (kg)
a (m/s2)
Fave (N)
a (m/s2)
Fave (N)
.05
.07
.1
.12
.15
.2
Mcart+blocks = ______________
Table 2 Cart with two mass blocks
m (kg)
.05
.07
.1
.12
.15
.2