RipStik energy conservation and banana leaf marble ramp notes
On Monday I tried to show that energy is conserved by trading GPE at the top of a slope for KE at the bottom. I used the covered walkway between the A and F buildings. My final velocity was difficult to obtain, I could only time the final 303 post-to-post centimeters to estimate my velocity. The real complication proved to be the height h. Without a level I could not accurately level the line I used to determine the height h. Memo to self: obtain a level before trying this again.
Although I started in centimeters, the numbers generated by working in cgs (70000 g, 14140000 g cm/s of momentum) appeared to be clouding the physics for the students and worked against rounding to mentally comprehensible numbers. So I switched to MKS.
A mass of 70 kg (myself plus my RipStik measured using a metric spring scale), a g of 9.70 m/s², and a height of 0.09 meters yielded 62 Joules of GPE. A final speed of 3.03 meters/1.4 seconds (2.02 m/s) yielded a kinetic energy of 141 Joules. Thus my line was low. I had tried to level the line against the roof line of the north faculty building, I obviously failed. I was not wearing pants conducive to laying on the ground. More notes to self - wear grunge next time, bring that level. The "right" height is somewhere near 20 cm.
Wednesday I modified the marble ramp. By bringing extra meter sticks I was able to set up a T at the end of the 100 cm run. The leaf was hung low, only a 50 cm max height possible. I did heights at 5, 10, 15, 20 ,25 and 50, timing from 0 cm to when the marble slapped the end stick. This eliminated the sharp speed losses seen when I would shift from 100 cm to 200 cm lengths. I did all at 100 cm. The fastest marble, the 50 cm drop, timed in at 0.31 seconds. I was able to consistently and repeatedly repeat times in the low 0.30s for this marble.
The use of the end stick has generated numbers closest to theoretic yet generated - somewhat coincidental/accidental given that the loss of energy due to spin up was not factored in. The corrected coefficient is down around 34 times the square root of the height.
Although I started in centimeters, the numbers generated by working in cgs (70000 g, 14140000 g cm/s of momentum) appeared to be clouding the physics for the students and worked against rounding to mentally comprehensible numbers. So I switched to MKS.
A mass of 70 kg (myself plus my RipStik measured using a metric spring scale), a g of 9.70 m/s², and a height of 0.09 meters yielded 62 Joules of GPE. A final speed of 3.03 meters/1.4 seconds (2.02 m/s) yielded a kinetic energy of 141 Joules. Thus my line was low. I had tried to level the line against the roof line of the north faculty building, I obviously failed. I was not wearing pants conducive to laying on the ground. More notes to self - wear grunge next time, bring that level. The "right" height is somewhere near 20 cm.
Wednesday I modified the marble ramp. By bringing extra meter sticks I was able to set up a T at the end of the 100 cm run. The leaf was hung low, only a 50 cm max height possible. I did heights at 5, 10, 15, 20 ,25 and 50, timing from 0 cm to when the marble slapped the end stick. This eliminated the sharp speed losses seen when I would shift from 100 cm to 200 cm lengths. I did all at 100 cm. The fastest marble, the 50 cm drop, timed in at 0.31 seconds. I was able to consistently and repeatedly repeat times in the low 0.30s for this marble.
height actual linear energy (cm) velocit predict prediction (cm/s) (cm/s) (cm/s) 0 0 0 0 5 71 71 98 10 109 143 139 15 139 214 170 20 169 197 25 189 220 50 323 311
The use of the end stick has generated numbers closest to theoretic yet generated - somewhat coincidental/accidental given that the loss of energy due to spin up was not factored in. The corrected coefficient is down around 34 times the square root of the height.
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