#$&*
PHY 121
Your 'conservation of momentum' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Your optional message or comment: **
5.13.11 at 10:39pm
#$&* Distances from edge of the paper to the two marks made in adjusting the 'tee'. **
Proceed to adjust the height of the 'tee' until the balls collide with their centers at the same vertical altitude. In the
space below, give in the first line the measurement from the edge of the paper to the mark made by the ball as it strikes the
vertical object, and from the edge of the paper to the mark made by the collision of the two balls. In the second line give
the height of the top of the 'tee' above the tabletop. In the third line give the distance from tabletop to floor. Make
both all measurements as accurate as possible, and indicate in the fourth line the uncertainty in each of your measurements
and how these were estimated:
-------->>>>>>>> collision pt 1 ball against vert and coll pt 2 balls, ht of top of tee above tabletop, tabletop to floor,
uncertainties
Your answer (start in the next line):
4.3cm, 4.2cm
2.5cm
70.1cm
All are accurate to 0.05cm
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Run your first set of trials:
Now you will remove the 'tee' and release the ball from the rest at the high end of the sloped track. You will use the same
procedures as in previous experiments for observing the horizontal range of the ball as it falls to the floor.
Be sure the ramps remain well aligned, and if necessary 'shim' the end of the inclined ramp to ensure that there is no 'bump'
when the ball moves from one ramp to the next.
Conduct 5 trials, and in the first line give 5 horizontal ranges; in the second line give the mean and standard deviation of
the range of the ball. Starting in the third line explain in detail how you got your results.
-------->>>>>>>> 5 ranges uninterrupted, mean & sdev, explanation
Your answer (start in the next line):
10.1, 10.4, 10.5, 10.6, 10.7
10.46, 0.2302
Measurements were entered into data program and mean and std dev were calculated via the program.
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Now place the target ball at the edge of the table, as described earlier. Measure the distance in cm from the edge of the
ramp to the closest point on the straw.
Align the target ball so that after the collision, the 'forward' paths of both balls are in the same direction as that of the
uninterrupted first ball. That is, make sure the collision is 'head-on' so that one ball doesn't go to one side and the
other to the opposite side of the original path.
Divide the carbon paper into two pieces, and position the two in such a way that after collision the two balls will leave
clear marks when they land. Do this until you get marks for five trials. Be sure to note which second-ball position
corresponds to which first-ball position (e.g., number the marks).
Using your marks, determine the horizontal ranges of the two balls after collision.
In the first line of the space below, give the five horizontal ranges observed for the second ball, using comma-delimited
format. In the second line give the corresponding first-ball ranges. In the third line give the mean and standard deviation
of the second-ball ranges, and in the fourth line give the same information for the first ball. Starting in the fifth line
specify how you made your measurements, and as before specify the positions with respect to which you found your ranges, as
well as how you measured those positions.
-------->>>>>>>> five ranges target ball, five ranges first ball, mean and std second, mean and std dev first ball, details
Your answer (start in the next line):
5.8, 5, 5.5, 5.15, 5.4
7.6, 7.25, 8, 7.1, 6.6
5.37, 0.3114
7.31, 0.5273
Measurements were taken from where the balls landed. Carbon paper would not mark the spot so ihad to estimate just by
looking at the balls as they fell.
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Do not disassemble the system until you are sure you are done with it. General College Physics and University Physics
students will use the system again in subsequent activities, and should leave it as it is.
Analysis of Results from First Setup:
Give in the first line below the vertical distance through which the two balls fell after collision, and in the second line
the time required to fall this distance from rest. Starting in the third line, explain precisely how you determined these
distances, how you determined the time of fall and what assumptions you made in determining the time of fall:
-------->>>>>>>> vertical fall, time to fall, explanation
Your answer (start in the next line):
5.37, 7.31
0.4219sec
USed timer program to time the drop. Distances were measured earlier.
#$&*
In the space below give in the first line the velocity of the first ball immediately before collision, the velocity of the
first ball immediately after collision and the velocity of the second ball immediately after collision, basing your
calculations on the time of fall and the mean observed horizontal ranges. In the second line give the before-collision
velocities of the first ball based on (mean + standard deviation) and (mean - standard deviation) of its uninterrupted
ranges. In the third line do the same for the first ball after collision, and in the fourth line for the second ball after
collision.
-------->>>>>>>> velocity first ball before, first ball after, second ball after collision; mean +- std dev first ball
before, after, 2d ball after
Your answer (start in the next line):
18.463cm/sec, 17.326, 12.728
25.247, 24.338
#$&*
The masses of both balls are unknown. Using momentum conservation, you will determine the ratio of their masses:
Let m1 stand for the mass of the large ball and m2 the mass of the small ball. In terms of m1 and m2 write expressions for
each of the following:
The momentum of the first ball immediately before collision, using the velocity you reported above (the velocity based on the
mean range and distance of fall). Be sure to use both the numerical value of the velocity and its units. This will be
reported in the first line below.
The momentum of the first ball immediately after collision, using the velocity you reported above. This will be reported in
the second line below.
The momentum of the second ball immediately after collision, using the velocity you reported above. This will be reported in
the third line below.
The total momentum of the two balls immediately before collision. This will be reported in the fourth line below.
The total momentum of the two balls immediately after collision. This will be reported in the fifth line below.
The total momentum immediately before collision is equal to the total momentum immediately after collision. Set the two
expressions equal to obtain an equation. Report this equation in the sixth line below.
-------->>>>>>>> equation for momentum conservation
Your answer (start in the next line):
p=m1*18.463
p=m1*17.326
p=m2*12.728
p=(m1*18.463) + (m2*0)
p=(m1*17.325) + (m2*12.728)
(m1*18.463) + (m2*0) = (m1*17.325) + (m2*12.728)
#$&*
Rearrange your equation so that all terms containing m1 are on the left-hand side, and all terms containing m2 are on the
right-hand side. Report this equation in line 1 below.
Divide both sides by the appropriate quantity so that m1 appears by itself on the left-hand side. Report the resulting
equation in line 2.
Divide both sides of the equation by m2, and report the resulting equation in line 3.
Simplify the right-hand side, if you have not already done so, to obtain a single number. If you have done your calculation
correctly, the units will cancel out. Report the resulting equation in line 4. The left-hand side will be m1 / m2 and the
right-hand side will be a single decimal number or, if you prefer, a reduced fraction.
Starting in the fifth line discuss the meaning of the ratio m1 / m2.
-------->>>>>>>> equation solution in steps, meaning of ratio m1 / m2
Your answer (start in the next line):
(m1*18.463)-(m1*17.321) = m2*12.728
Not sure how to solve this from here.
#$&*
@& You're just about got it. The left-hand side becomes
m1 * (18.5 - 17.3)
which is equal to about 1.2 m1.
Thus
1.2 m1 = 12.7 m2
and
m1 / m2 = 12.7 / 1.2 = 10, approx..*@
*#&!*#&!
&#Good responses on this lab exercise. See my notes and let me know if you have questions.
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