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course PHY 231
10/12 4:00 pm The asterisks above are to remind me that there are some questions I need to do after I get answers to questions in the document. I want to go ahead and get what I can of this work posted as it's behind and the missing parts aren't very significant.
Lab Activities 101006•Deflection_of_ball_down_ramp_from_path
• Acceleration_of_gravity measured in stairwell
• Ball_off_ramp_to_floor,_at_angle:__University_Physics_Students_Only
Deflection of ball down ramp from path
`qx001. How far did the ball travel after leaving the end of the ramp, in the trial without the magnet, and what therefore was its horizontal velocity during the fall, assuming a fall time of .4 second?
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13.25, 33.125
This is measured in cm from the drop ball point and units are cm and cm/s respectively.
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`qx002. What is the maximum deflection of the ball, due to the presence of the magnet, from its original straight-line path?
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My max deflection point was 9 cm to the left, the side where we held the magnet.
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`qx003. What velocity does the ball therefore attain, in the direction perpendicular to its original straight-line path, as a result of the magnet?
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Perp. direction velocity is 22.5 cm/s. Just used ∆x/∆ts.
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`qx004. Assume the ball was close enough to the magnet to have its motion significantly influenced for a distance of 5 centimeters. How long did it take for the ball to travel this distance?
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I assume this asking if the deflection was 5 cm not how long was the ball under the magnets influence if the magnet was 5 cm in length, the latter being a much more complex problem as the magnet also affects the velocity in the x direction and y direction while the ball is within its force field. And wouldn't the time for the former scenario still be 0.4 seconds? So maybe it is asking the about the latter, in a general way, and this time would be about 0.22 s.
The ball is moving as 33 cm/s when it passes the magnet. It is close enough to the magnet to have its path significantly affected for 5 cm, which is about the length of the magnet. So the question is effectively asking how long it takes the ball to pass the magnet.
From this you would get about 0.15 seconds.
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`qx005. Assume that the ball has a mass of 60 grams. How much momentum did it gain, in the direction perpendicular to its original line of motion, as a result of the magnet?
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p=mv= 60*22.5=1350 g cm/s.
Just using the formula for momentum with my max deflect. ball velocity and the mass provided.
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`qx006. What therefore was the average rate of change of its momentum with respect to clock time, for the 5-cm interval during which the magnet significantly affected its motion?
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∆p/∆t= mv/t= 1350/0.22= 6075 g cm/s/s. Here I just used the typical equation for change wrt clock time.
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`qx007. What were the measurements by which you can calculate the slope of your ramp? What was the slope of the ramp?
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It was 30 cm long (hyp of the triangle) and 2 cm high. sin = opp/hyp -----> arcsin (2/30) ≈ 3.82º
You're better off sticking with the slope, which is 1/15, but the angle is OK too.
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Acceleration of gravity
`qx008. What was your count for the object dropped in the stairwell? To what time interval in seconds does your count correspond?
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I had 5 counts. I re-calibrated my counts as they used to be to slow for any accuracy and now I have 0.25 sec/count. So 1.25 seconds.
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`qx009. What was your count for the object dropped in the stairwell? To what time interval in seconds does your count correspond?
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Well this seems duplicated but I also had 4 counts twice. So that interval was 1 second.
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`qx010. What was the distance the object fell (1 block = 8 inches or about 20 centimeters)?
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It fell 27*20= 540 cm
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`qx011. Using the distance of fall and the time interval in seconds, find the acceleration of the falling object.
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v0=0 vf= 540/1.25= 432 ---->∆v = 432 ---> 432/1.25= 346 cm/s. This is pretty far off as it should be more like 980 or 1000 cm/s.
vAve = 432 cm/s
vf would be 864 cm/s, since the ball was released from rest
so you're not that far off
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Ball off ramp to floor, at angle: University Physics Students Only
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I'm not sure what this next section is referring to. I don't remember taking these measurements unless you mean the magnet deflection or just a regular roll off a ramp. I have ball off ramp measurements somewhere. When you explain this I will submit this last part separately.
you reported at the beginning of this document that the ball traveled about 13 cm in the horizontal direction while falling, so x - x0 would be 13 cm
y - y0 would be the displacement of the ball as it falls
theta is the angle of a displacement down the ramp, which is the same as the angle of the initial velocity of the ball (according to your calculation theta would be 3.82 deg below horizontal); sin(theta) and cos(theta) could be calculated from this angle but you would be better off calculating them based on the rise and length of the ramp
`qx012. Find the initial velocity of the falling ball, based on your measurements of x, y, x0, y0 and your determination of sin(theta) and cos(theta).
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`qx013. Find the time of fall of the ball.
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`qx014. Questions about uncertainties:
• What is your estimated uncertainty in the measurements you used to determine sin(theta)?
• What therefore is your uncertainty in sin(theta)?
• What uncertainty does this introduce into your determination of v0?
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`qx015. Based on a single trapezoid of the graph of F vs. x for magnet forces, explain the meaning of the slope and the area of this graph.
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`qx016. Based on a single trapezoid of the graph of PE vs. x for magnet forces, explain the meaning of the slope and the area of this graph.
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The last two questions are related to the F vs. x and PE vs. x graphs for the car-and-magnet experiment. See also my notes, posted today previous to this document, on that situation. You pretty much had the interpretation of the slope of the PE vs. x graph.
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