course phy231
I need an actual length for the ramp and the weight of the marble to get more accurate calculations but i beleive i did them all correctly by assuming the marble weighed .1kg and the length of the ramp being 20cm and a horizontal drop off of the table being 94cm. The height of one domino is .9cm and the height of the ramp plus magnet is 1.5 cm. I used excel for all of the calculations if you like that file email me and I will send it to via e-mail so you can check my work and formula entry.
Your calculations look great. However they are based on a 20 cm ramp, and it's longer than that. That will change your predictions a bit. Change that in your spreadsheet and see how your predictions are modified.
The predictions are consistent with your data, and will probably be more so when you have completed the revisions.
Note that you can copy the actual spreadsheet into your form and I'll get a pretty good copy of it. If you have good column headings I won't have much trouble interpreting it. But do attach an email copy also.
You also need to do the symbolic solution because we're going to have to take some derivatives, which you won't be able to do with just the numbers. Let me know if you have questions with those calculations.
I need an actual length for the ramp and the weight of the marble to get more accurate calculations but i beleive i did them all correctly by assuming the marble weighed .1kg and the length of the ramp being 20cm and a horizontal drop off of the table being 94cm. The height of one domino is .9cm and the height of the ramp plus magnet is 1.5 cm. I used excel for all of the calculations if you like that file email me and I will send it to via e-mail so you can check my work and formula entry.
ramp hieght
2.4,
3.3,
4.2,
5.1,
6,
6.9,
horizontal distance ball travels on ramp
calculated by pythagorean theorem c^2=a^2+b^2
19.93990973,
19.91732914,
19.89472292,
19.87209098,
19.84943324,
19.82674961,
angle of ramp with respect to the x-axis in degrees
tan^-1(vy/vx)
6.863198175,
9.407580801,
11.92074664,
14.39381707,
16.8187877,
19.18864705,
The ramp is a foot long, but the distance between supports was probably a bit less than this. My guess is that it was around 29 cm between supports, and that is what you would use along with the change in vertical position for the hypotenuse.
`dPEgrav at end of ramp joules
mass*gravity*`dy
-0.02352,
-0.03234,
-0.04116,
-0.04998,
-0.0588,
-0.06762,
`dKE joules
assuming no loss of energy anywhere else
0.024,
0.032,
0.041,
0.05,
0.059,
0.068,
actual `dKE
assuming that only 5/7 of `dPE is transferred into KE
0.017142857,
0.022857143,
0.029285714,
0.035714286,
0.042142857,
0.048571429,
v0 m/s
sqrt(`dKE/(.5*.1kg)
0.692820323,
0.8,
0.905538514,
1,
1.086278049,
1.166190379,
corrected v0
sqrt((corrected)`dKE/(.5*.1kg)
0.585540044,,
0.676123404,
0.765319728,
0.845154255,
0.918072515,
0.985610761,
vertical velocity component m/s
velocity vector*sin(theta)
0.163498668,
0.254504,
0.357017614,
0.46376,
0.571610372,
0.678361282,
corrected vertical velocity in m/s
corrected velocity vector*sin(theta)
0.138181595,
0.215095138,
0.301734956,
0.391948737,
0.483098938,
0.573319923,
Horizontal component m/s
velocity vector*cosin(theta)
0.67328279,
0.7584,
0.8321,89894,
0.886,
0.923662225,
0.948579254,
corrected horizontal component
corrected velocity vector*cosin(theta)
0.569027815,
0.640964987,
0.70332883,
0.74880667,
0.78063706,
0.801695793,
vf=sqrt(v0^2 + 2a`ds)vertical
4.295431505,
4.29985724,
4.307140766,
4.317299311,
4.330212283,
4.345592483,
corrected vertical vf
4.294542368,
4.297704727,,
4.302911106,
4.310176773,
4.319419473,
4.330438284,
`dt=(vf-vo)/a
0.4216258,
0.412791147,
0.403073791,
0.393218297,
0.383530807,
0.374207265,
actual
0.424118446,
0.416592815,
0.408283281,
0.399819187,
0.391461279,
0.383379425,
Predicted horizontal range meters
0.283873395,
0.313060806,
0.335433935,
0.348391411,
0.354252919,
0.354965249,
predicted horizonatl range in cm
28.38733947,
31.30608059,
33.54339355,
34.83914111,
35.42529188,
35.49652488,
corrected predicted horizontal range in m
0.241335193,
0.267021408,
0.287157402,
0.299387274,
0.305589182,
0.307353672,
corrected predicted horizontal range in cm
24.13351926,
26.70214082,
28.7157402,
29.93872741,
30.55891818,
30.73536717,
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