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course Phy 241
1/9 10
Ramp & Ball
You allowed a ball to roll from rest down a ramp on a tabletop. The lower end of the ramp was positioned so that the ball could roll continuously off the ramp and into free fall.
You observed the horizontal range of the falling ball and the distance of fall.
Insert a copy of your data here, along with any previously submitted work you wish to include:
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Finding Velocity, acceleration of steel ball rolling down ramp with varying slopesHere we had a 60cm long ramp and the large steel ball. we had varying heights of one side of the ramp. started the ball from rest, and measured how long it took to roll to the bottom of the ramp. simple.
And here just calculated the vel, vel_avg, accel. I know you dont want calculated data in here so here is just raw data
Ramp slope | time taken
1.7deg 6s
4.2deg 3.5s
8.3deg 2.5s
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Your data should include the horizontal range of the projectile.
For every angle of elevation, you will then need to find the horizontal velocity of the projectile, which will very nearly equal the final velocity of the ball on the ramp.
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You did trials for three ramps.
Analysis based on projectile motion:
Phy 201 students may assume that the initial projectile velocity is horizontal.
University Physics students can do the same as a first approximation, but are expected to also then solve assuming that the initial projectile velocity is parallel to the ramp.
What was the horizontal velocity of the ball as it fell to the floor?
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the question didn't ask for all 3, but i have a feeling you want them.
final vel * cos ( ramp deg) = horizontal vel.
ramp final horizont vel
1 19.99 cm/s
2 34 cm/s
3 47.4cm/s
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What was the final velocity for each ramp slope?
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20cm/s
34.4 cm/s
48 cm/s
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Based on your result and the length of the ramp, what would have been the acceleration of the ball on the ramp?
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dividing the final vel by the time it took to get accel.
3.33 cm/s^2
9.77 cm/s^2
19.2 cm/s^2
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Graph acceleration vs. ramp slope and find the slope of this graph.
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slope is 2.4 in this situation
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2.4 what? Units are essential.
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What do you think is the percent uncertainty in your measurement of the horizontal distance traveled by the ball from the end of the ramp to the floor?
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probly less than 2%. We had hard data of the ball hitting the floor, so our error would have been in the ramp not being exactly at the edge of the table. or the paper moving slightly when the ball hits it. getting our measurement
a little off, but barely. Now compared to our data, we can figure out the horizontal distance, and given the % uncertainty in our actuall timing of the ball going down the ramp, this is quite large. because time is very very hard to get under 5%
uncertainty without the proper equiptment. I'd say we are within a half second on our time. which is about 8 % uncertainty. ( .5s / 6s) = about 8.33 % and this is directly proportional to our percent uncertainty in our horizontal velocity, which
is again directly proportional to our horizontal distance. so compiled onto eachother, about 12% uncertain.
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What do you think is the percent uncertainty in your measurement of the vertical distance traveled by the ball from the end of the ramp to the floor?
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just answered with decent explanation, 12%
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What do you think is the percent uncertainty in your measurement of the distance traveled by the ball from release to the end of the ramp?
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Very small. the only thing affecting this is the % error in the printing of the ink on the ruler, and our eyes making the judgement of how long the ramp is, and mainly our release on the ball at the top of the ramp, by the time it
completely wa released from our hands, it could have been a few milimeters down the ramp, but a few mm compared to 60cm, is only about 1%. so we very well could have release it more than a few mm down the ramp, i'd say a maximum of 2%
uncertainty. which again is directly related to every calculation from there on out. compliling to the other % uncertainty's or errors in our other calculations.
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What therefore do you think is the percent uncertainty in each of the following quantities, as you have calculated them?
· the time required to fall to the floor
· the horizontal velocity of the ball during its fall
· the acceleration of the ball on the ramp
· the slope of your graph of acceleration vs. ramp slope
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fall to floor, less than 2% because constant force of gravity,
horiz vel. about 12% because of human error in timing down ramp
again about 12% because of timing.
Something like 15% off from real slope based on our obscured data.
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Analysis based on timing:
Based on the time down the ramp and the distance the ball traveled from rest as it accelerated down the ramp, what was the acceleration on each ramp, and what is the slope of the graph of acceleration vs. ramp slope?
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answered this just a second ago. a few questions up the page.
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What do you think is the percent uncertainty in your measurement of the time required to travel down the ramp?
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again 12%, answered twice now.
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For each ramp:
What was the change in the gravitational PE of the ball? You may assume a 70 gram mass.
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ramp
1 88,290 g cm^2/s^2
2 171,675 g cm^2/s^2
3 343,350 g cm^2/s^2
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What velocity would have been attained if all the lost PE went into translational KE?
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I'm having trouble finding this. first, I'm not sure if my previous calculation is correct because I used accel of gravity as 981 cm/s^2. I""m not sure if i was supposed to use that * ramp slope. if so, these numbers would be a little closer to my actual esimates.
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Your values for the PE loss appear to be fine.
What would be the KE of the ball for each slope, based on its mass and your values for the PE?
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University Physics students: Account for the difference between the loss of gravitational PE and the translational KE which corresponds to your results. Use your results to find the acceleration of gravity.
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using the equations, i'm getting accel of gravity to be about 90% higher, so it looks like I might should have done that in the first place. Either way, The steps involved are good, just bad number values.
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You didn't report, and apparently did not use, the observed horizontal ranges of the ball after leaving the ramp.
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