Download UNBALANCED FORCES

Mr. Curl
Example Physics Lab Report
UNBALANCED FORCES
study of elevators quickly leads to a machine called an Atwood’s machine. An
Atwood’s machine involves a string wrapped around a pulley or two pulleys that connect two
masses together, one on each side of the pulley. The machine’s purpose is to provide a
comparison of mass to acceleration. Typically, one mass is greater than the other and the heavier
mass provides the force that moves the entire system. This is a great example of how a machine
can use an unbalanced force to move an object.
Description: A
Purpose: The experiment is testing Newton’s second law. The idea is to place increasing
masses on one side of the pulley system then measure the affect it has on the acceleration rate.
Materials: Stopwatch, tall ring stand or table clamp, Atwood pulley, string, two 50g mass
hangers and washers.
Procedure:
1. Attach the Atwood pulley to the top of a long vertical rod at least a meter above the floor.
Connect one end of the string to a mass hanger, drape the string over the elevated pulley
and attach the other end of the string to another mass hanger as illustrated in figure 1.
Adjust the length of the string so that m1 does not reach the pulley when m2 is on the
floor.
2. Start with m1 equal to the mass of the container plus 3 washers and m2 equal to the mass
of the container plus 3 washers. The washers represent the small masses that can be
shifted to unbalance the system.
3. Elevate m2 and check the system by initiating motion in one direction and then the other
to see if it undergoes a constant acceleration. If it does not, shift one penny from m1 to
m2 so that m2 accelerates smoothly downward when released from rest. Begin with m1
resting on the floor. Release m2 and determine the time it takes to reach the floor.
Record the time t and the distance between the two masses h. Repeat 5 times and record
the average time of fall. Using the last equation in the Theory section, calculate the
acceleration of the system. Shift another washer from m1 to m2 and determine the new
acceleration of the system. Continue this process one washer at-a-time until all of the
washers from m1 have been shifted to m2.
4. Calculate the theoretical accelerations for the various combinations of m1 and m2
using the first equation in the Theory section. Compare the theoretical
accelerations with those experimentally determined for the various
combinations of m1 and m2. Calculate the percentage error (∆%) in each case.
Do you notice any trends?
5. Create a simple graph to plot the mass differences (m2-m1) along the x-axis and
the corresponding accelerations (a) along the y-axis. Add an appropriate title
and descriptive axis labels to the plot. Have the program draw a best fit linear
Mr. Curl
Example Physics Lab Report
line and determine the slope and intercept for the plot. Make a print-out of the
labeled plot with the slope and intercept fully visible.
Data and Observations:
PHYS 101 UNBALANCED FORCES LAB
Today’s date = 11/30
Table # =
Names of group members→
Member 1
Member 2
Drop
Drop
Member 2
2h/t2
2
Theory
∆%
2
M1 (kg)
M2 (kg)
h (m)
t (s)
a (m/s )
a (m/s )
2/4
0.06
0.07
1.0
2.02
0.5
0.75
33
Trial #2 1 / 5
0.055
0.076
1.0
1.3
1.18
1.58
25
Trial #3 0 / 6
0.05
0.081
1.0
1.0
2.0
2.33
14
3-4. Trial #1
Trial #4
Trial #5
5. Slope
Intercept
6. g/m1 + m2
∆%
71 m/s/s/kg
0.15 m/s/s
75 m/s/s/kg
5.3%
Neatly show all calculations performed and answer questions from the lab on a separate sheet
of paper. Don’t forget to include an error analysis, a conclusion, and the printout for procedures 5.
Observations: In operating the Atwood’s machine there were several challenges in the quest to
attain reliable data. Our first attempt included two miss-alligned pulleys that produced erroneous
results. It was decided that switching to a single pulley would result in more reliable numbers.
Other sources of error and awkwardness occurred with the timing of the drop – remaining as
accurate as humanly possible. And, being consistent with the one meter height. All in all,
through several trials, the improvised Atwood’s machine performed satisfactorily and ours
numbers were within an acceptable range.
Mr. Curl
Example Physics Lab Report
Graph
Mass's Affect on Acceleration
2.5
Acceleration m/s/s
2
1.5
1
0.5
0
1
2
3
Mass Difference ( x 0.01) kg
Series1
Series2
Series3
Calculations:
Graph calculations of acceleration due to mass difference ratio;
Theory (g / m1 + m2).
Experimental acceleration
Acceleration = 9.8 m/s/s / 0.065kg + .065 kg
Exp Acc = rise / run
Acc = 75 m/s/s/kg
= 2.0 – 0.5 m/s/s / .031 - .01 kg
Exp Acc = 71 m/s/s / kg
% error = theoretical – experimental x 100
Theoretical
% error = 75 – 71 x 100
75
error = 5.3%
Calculations from Chart; an example from the first trial (2/4 Washer Combination)
Theory acc = m2 – m1 x 9.8m/s/s
m1 + m2
acc = 0.07 – 0.06 x 9.8m/s/s
0.130
acc = 0.75 m/s/s
Mr. Curl
Example Physics Lab Report
Experimental Acceleration and Percent error
2 /4 Washer Combination
Experimental
Acc = 2 (h)
t2
Acc = 2 (1)
(2.02) 2
Acc = 0.5 m/s/s
Percent error = (0.75 – 0.5) x 100
0.75
Percent error = 33 %
Analysis
The numbers revealed a trend in their accuracy; as the mass of m2 increased, the
closer the acceleration rate was to the theoretical number. More than likely, this
was due to the greater force of m2 over-riding any friction or other alignment
problems the assembled machine may have possessed.
With regard to the slope of the line on the graph, it represented how closely the
mass difference (which created the force) affected the rate of acceleration.
The slope intercept represented how the mass difference created the force of
movement for the system.
Additionally, it was noted that the tension in the string was felt equally
throughout the whole string. In other words, according to Newton’s 3rd law, as
m2 pulled on m1; m1 pulled equally back on m2 but in the opposite direction.
Conclusion:
The Atwood’s Machine Lab was an excellent example for illustrating the differences in
balanced versus unbalanced forces. The lab exercise mostly focused on the application of
Newton’s second law. On step one the forces were balance on both sides of the machine because
there was equal mass on each side; f = ma was the same on both sides. The experiment then
required the operator to take a washer from one mass and transfer it to the mass on the other side.
This transfer created an unbalanced force great enough to accelerate both masses at a rate
directly proportional to the applied force. The total mass of the system remained fixed for all
trials, only portions of m1 were transferred to m2.
In the end the numbers did make sense because they seemed to correspond with the
theoretical values. We did verify that the greater the mass difference between m1 and m2
created a greater force for m2 to apply to the system. The increase in force was matched by an
increase in acceleration; just as Newton’s second law states: F = m * a. Here we see if the
overall mass remains the same, we can only increase the acceleration if there is an increase in the
applied force. Or, saying it the other way; an increase in force will result in an increase in
acceleration; the variables of force (F) and acceleration (a) are directly proportional.