#$&*
Phy 201
Your 'conservation of momentum' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Conservation of Momentum_labelMessages **
** **
Proceed to adjust the height of the 'tee' until the balls collide with their centers at the same vertical altitude. In the space below, give in the first line the measurement from the edge of the paper to the mark made by the ball as it strikes the vertical object, and from the edge of the paper to the mark made by the collision of the two balls. In the second line give the height of the top of the 'tee' above the tabletop. In the third line give the distance from tabletop to floor. Make both all measurements as accurate as possible, and indicate in the fourth line the uncertainty in each of your measurements and how these were estimated:
-------->>>>>>>> collision pt 1 ball against vert and coll pt 2 balls, ht of top of tee above tabletop, tabletop to floor, uncertainties
Your answer (start in the next line):
2.0
2.0
1.5
I beleive my values are accurate.
#$&*
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):
10.75, 11.0, 10.9, 10,95, 11.5
10.95, .09716
I measured the distance from the edge to where the ball ended.
#$&*
Now place the target ball at the edge of the table, as described earlier. Measure the distance in cm from the edge of the ramp to the closest point on the straw.
Align the target ball so that after the collision, the 'forward' paths of both balls are in the same direction as that of the uninterrupted first ball. That is, make sure the collision is 'head-on' so that one ball doesn't go to one side and the other to the opposite side of the original path.
Divide the carbon paper into two pieces, and position the two in such a way that after collision the two balls will leave clear marks when they land. Do this until you get marks for five trials. Be sure to note which second-ball position corresponds to which first-ball position (e.g., number the marks).
Using your marks, determine the horizontal ranges of the two balls after collision.
In the first line of the space below, give the five horizontal ranges observed for the second ball, using comma-delimited format. In the second line give the corresponding first-ball ranges. In the third line give the mean and standard deviation of the second-ball ranges, and in the fourth line give the same information for the first ball. Starting in the fifth line specify how you made your measurements, and as before specify the positions with respect to which you found your ranges, as well as how you measured those positions.
-------->>>>>>>> five ranges target ball, five ranges first ball, mean and std second, mean and std dev first ball, details
Your answer (start in the next line):
20.5, 21.4, 21.4, 22, 22.4
8.7, 8.75, 8.0, 8.5, 9.0
21.5, .702
8.9, .15
I measured the distance from the edge to the final postion.
#$&*
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):
12
.16
Using the equation`dt=sqrt(2*`ds/a), where a=gravity
#$&*
In the space below give in the first line the velocity of the first ball immediately before collision, the velocity of the first ball immediately after collision and the velocity of the second ball immediately after collision, basing your calculations on the time of fall and the mean observed horizontal ranges. In the second line give the before-collision velocities of the first ball based on (mean + standard deviation) and (mean - standard deviation) of its uninterrupted ranges. In the third line do the same for the first ball after collision, and in the fourth line for the second ball after collision.
-------->>>>>>>> velocity first ball before, first ball after, second ball after collision; mean +- std dev first ball before, after, 2d ball after
Your answer (start in the next line):
79.5, 63.12, 175
80.12, 78.7
63.22, 62.2
180.3, 168.1
#$&*
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):
M1* 79
M1*63.12
M2*175
M1*&795+m2*0
M1*63.12+m2*175
M1*79+m2*175
Ma*79+m2*0=m1*63.12+m2*175
#$&*
Rearrange your equation so that all terms containing m1 are on the left-hand side, and all terms containing m2 are on the right-hand side. Report this equation in line 1 below.
Divide both sides by the appropriate quantity so that m1 appears by itself on the left-hand side. Report the resulting equation in line 2.
Divide both sides of the equation by m2, and report the resulting equation in line 3.
Simplify the right-hand side, if you have not already done so, to obtain a single number. If you have done your calculation correctly, the units will cancel out. Report the resulting equation in line 4. The left-hand side will be m1 / m2 and the right-hand side will be a single decimal number or, if you prefer, a reduced fraction.
Starting in the fifth line discuss the meaning of the ratio m1 / m2.
-------->>>>>>>> equation solution in steps, meaning of ratio m1 / m2
Your answer (start in the next line):
m1 * 79 - m1 * 63.12 = m2 * 175
m1 = (m2 * 175)/ (16.5)
m1/ m2 = 175 / 16.5
m1/ m2 = 11
#$&*
Measure and report the diameter of ball 1 and the diameter of ball 2, in comma-delimited format in the first line below.
Calculate the volumes of the two balls and report them in the second line.
-------->>>>>>>> diameters, volumes
Your answer (start in the next line):
2.5, 8
9.2, .25
#$&*
Physics 121 students are not required to continue, but may do so
Error Analysis for First Setup:
If at collision the center of the first ball is higher than the center of the second, how will this affect the magnitude and direction of the velocity of the first ball immediately after collision? Will the speed be greater or less than if the centers are at the same height? Will the direction of the after-collision velocity differ, and if so how?
In the space below answer this question, and also answer the same questions for the second ball.
-------->>>>>>>> if first ball higher what is effect on its motion, same question for second ball
Your answer (start in the next line):
The speed of the first ball would be the same and the direction would change after the collisoin.
If the second ball were lower, it would be greater than if hit in center.
#$&*
How do you think this will affect the horizontal range of the first ball? How will it affect the horizontal range of the second?
-------->>>>>>>> effect on horizontal ranges
Your answer (start in the next line):
The velocity would be the same but the range would be shorter
The second ball would have a greater range.
#$&*
For the first ball before collision you reported an interval of velocities based on mean + std dev and mean - std dev of observed horizontal ranges. You did the same for the first ball after collision, and the second ball after collision. Each of these intervals includes a minimum and a maximum possible velocity.
What do you get for the ratio of masses if you use the minimum before-collision velocity in the interval reported for the first ball, the maximum after-collision velocity for the first ball, and the minimum after-collision velocity of the second? Report how you determined this ratio in the space below:
-------->>>>>>>> mass ratio using min before, max after 1st ball, min after 2d
Your answer (start in the next line):
11.5
#$&*
What percent uncertainty in mass ratio is suggested by comparing this result to your original result?
-------->>>>>>>> % uncertainty suggested by previous
Your answer (start in the next line):
8.5%
#$&*
*#&!
&#Your work on this lab exercise looks very good. Let me know if you have any questions. &#