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Submitting Assignment: Motion in a Force Field
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In this experiment you will roll a ball down an incline, then onto a nearly level surface, and off the edge of that surface, from which point it will fall to the floor. You will infer its velocity and direction from its behavior as a projectile. This procedure should be familiar to you.
In this case we will also situate a magnet near the edge of the table or countertop, at a measured distance from the path of the ball. You will measure the effect of the magnet on the velocity and on the path of the ball.
This experiment will not require as many repetitions as previous experiments using similar setups.
Instead of the grooved metal ramps, which would interact with the magnet and would also prevent the ball from deviating from its original path, you will use two books as inclines. Any two hard-cover books will suffice, provided they are of nearly the same thickness and have good flat covers which are not warped or bent. The ball will roll from rest down one book, which will be inclined, onto the other, which will be very nearly horizontal.
To keep the ball on a straight-line path prior to reaching the vicinity of the magnet, you will use two creased sheets of paper, as described below.
The setup is illustrated below. The figure below refers to a marble, but glass marbles don't interact with magnetic fields, and in this experiment the smaller of the steel balls will be used instead.
End view of book, viewed from the higher end, with creased paper just to the right of the ball. There is a very slight slope to the right, just enough to prevent the ball from rolling away from the crease, but not enough that it rolls over the crease:
An actual setup is shown below. The ball shown in this setup is larger than the one you will use in the experiment. The only function of the grooved track is to steady the magnet and hold it in a fixed position. The books are not actually blue and green, but in accordance with the diagram above will be referred to as the 'blue' and 'green' book.
In the first figure below the corner of a piece of paper is positioned just to the left of the ball's path along the creased paper. In the second figure the piece of paper has been moved so that the ball just barely brushes its edge as it passes, and the position of the corner has been marked on the paper. The position of the magnet has also been marked. More description of this process is given below.
The position of the magnet and the path of the ball will be marked on a piece of paper lying on the 'green' book. The paper should be taped to the book to prevent movement from one trial to the next.
At the end of the experiment the paper will look something like the one below, showing the line made by the creased edge, the path of the 'edge' of the ball (a path through four short line segments made in the manner described above), the positions of the magnet through 5 different setups (indicated in the picture by 'trial 1' thru 'trial 5'; the word 'setup' should probably have been used rather than 'trial'), and the distance of the magnet from the edge over which the ball rolls before falling.
The magnet should lie on its narrowest edge, with its longest side parallel to the path of the ball. The magnet should not be further than 3 cm from the edge off of which the ball will roll. If it helps to place It closer to the edge that is permissible.
By noting the points at which the ball hits the floor in the absence of the magnet, and the points at which it hits when the magnet is present, you should be able to adjust the slope of the 'blue' book and the position of the magnet so as to achieve the maximum possible deflection of the ball from its original path.
In the space below describe how you set up the system to optimize the deflection of the ball from its original path:
:
#$&* how set up to optimize deflection
Once you have the incline and the magnet position set to achieve good deflection from the path, begin taking measurements:
Measure the diameter of the ball. Make sure you are accurate to the nearest millimeter. You will use a regular piece of paper with non-rounded right angles at its corners (a typical sheet of typing paper would be fine). You really only need one corner and a few centimeters the two edges that meet in that corner (i.e. a corner torn off a sheet of typing paper would be fine). Place this paper in the path of the ball so that one edge is on the second book, the paper itself is in a vertical plane and its corner is in the path of the ball; thus if the ball were to travel along its usual path it would flatten the paper and roll over the corner. Don't let it actually do this. Now move the paper back a little from the path of the ball, so that the ball will pass near it but will not touch the paper. Roll the ball down the incline as usual. Repeat, with the paper a little closer to the path of the ball. Keep repeating until the ball just barely brushes the paper as it passes. Mark the position of the corner of the paper. Do this with near the edge, 5 cm back from the edge, 10 cm back from the edge, and also just after the ball has rolled off the first book and onto the second. Sketch the straight line or smooth curve you believe best indicates the path of extreme 'edge' the ball along the second book, in the absence of the magnet (the word 'edge' isn't quite right because round objects don't have edges, but any other term would involve bigger and potentially more confusing phrases).
Measure the diameter of the ball. Make sure you are accurate to the nearest millimeter.
You will use a regular piece of paper with non-rounded right angles at its corners (a typical sheet of typing paper would be fine). You really only need one corner and a few centimeters the two edges that meet in that corner (i.e. a corner torn off a sheet of typing paper would be fine).
Place this paper in the path of the ball so that one edge is on the second book, the paper itself is in a vertical plane and its corner is in the path of the ball; thus if the ball were to travel along its usual path it would flatten the paper and roll over the corner. Don't let it actually do this.
Now move the paper back a little from the path of the ball, so that the ball will pass near it but will not touch the paper. Roll the ball down the incline as usual. Repeat, with the paper a little closer to the path of the ball. Keep repeating until the ball just barely brushes the paper as it passes. Mark the position of the corner of the paper.
Do this with near the edge, 5 cm back from the edge, 10 cm back from the edge, and also just after the ball has rolled off the first book and onto the second.
Sketch the straight line or smooth curve you believe best indicates the path of extreme 'edge' the ball along the second book, in the absence of the magnet (the word 'edge' isn't quite right because round objects don't have edges, but any other term would involve bigger and potentially more confusing phrases).
Sketch on the 'target paper' a single line representing, as best you can, the path of the undeflected ball. Mark on this line the point you believe best indicates the average position of the 'straight-drop' trials. Then measure the distance from this point to each of the 5 marks made by the undeflected ball. Orienting yourself in the direction of the ball's motion, measure also the displacement of each of these 5 marks from the line representing the path of the ball, with marks lying to the right being positive and marks to the left negative.
In the space below report the 5 distances in the first comma-delimited line, and the 5 displacements from your straight line in the second. In the third line indicate the mean of the distances, your best estimate of how far you think the 5 distances deviate, on the average, from their mean, and your best estimate of how far right or left the path of the ball deviates from the straight line, on the average. In the following line or lines, explain the meaning of your data:
#$&* 5 distances, 5 displacements from straight line, mean of distances, estimate of deviation from mean, ave dist from straight line
Now, based on the path of the extreme 'edge' of the ball and the indicated positions of the magnet, measure the distance of the magnet from the closest part of the ball. Do this for the trail in which the magnet was closest. Then for each of the 5 corresponding marks on the target paper, measure the distance of the mark from the straight-drop landing point, and also the distance of the mark from the straight line you have drawn on the target paper.
In the first line report the distance of the magnet from the closest part of the ball and the distance of the magnet from the edge. In the second line give your 5 distance measurements, and in the third give your 5 distances from the straight line. Use comma delimitation in each line. Starting in the fourth line explain how you measured the distance of the magnet from the closest part of the ball.
#$&*
Give the same information for subsequent trials, using 3 lines for each trial and reporting in the same format as above.
The vertical motion of the falling ball is in each case indistinguishable from the vertical motion of a ball dropped from rest from the edge. Using the equations of uniform acceleration, determine how long it therefore takes the ball to fall. Report the time in seconds in the first line below, and starting in the second line explain what your result means and how you got it.
The speed of the ball in the horizontal direction will be very nearly constant, so the horizontal range and time of fall will very accurately determine how fast the ball was moving in this direction.
Based on the average distance measured for the trial in which the magnet was absent, how fast was the ball moving at the instant it left the edge? Report your result, in cm/sec, in the first line below and in the second line explain what your result means and how you obtained it.
Based on the time of fall and average distance measured from the straight-drop point, you can determine the speed of the ball for each magnet distance. Report these speeds, in the order of your trials, in the first line, using commas to delimit your numbers. Starting in the second line explain the meaning of your rsults and how you got them.
Based on the time of fall and the distances of the landing points from the straight-line path, you can use the same procedures to determine the velocities of the ball perpendicular to the original path. Report using the same format as in the preceding, and include your explanation starting in the second line:
Based on the results obtained here, do you believe that the presence of the magnet affected the kinetic energy of the ball? State your conclusion and give the evidence for or against it. Be sure to consider experimental uncertainties.
Determine the average magnetic forces for the various trials:
Report ball volume and mass in the first line, momentum perpendicular to path for each trial in comma-delimited second line, time required for the ball to pass the magnet in the third line and force in Newtons for each trial in comma-delimited fourth line. In the fifth line explain the meaning of your results and give an explanation of how you calculated each:
In the figure above the ball is depicted as traveling along a straight-line path, then suddenly changing to another straight-line path. What is wrong with this? How do we know it doesn't happen here?
The field of the magnet is as shown in the next figure. Note that the field drops rapidly as we move away from the magnet, and that the field is strongest near the center of the largest face of the magnet. To the right and left of the magnet, as drawn below, the field is pretty weak and rapidly becomes insignificant as we move away from the magnet.
Given these characteristics of the force field:
Answer these questions in the space below:
Which of the paths shown in the figure below is more consistent with your previous answers? Why?
Which of the paths shown in the figure below is more consistent with your previous answers?
The figure below shows a hypothetical circular disk magnet, which attracts steel objects equally around its entire circumference, and always toward its center. It is not clearly indicated in the figure but again this field is to be regarded as decreasing rapidly as we move away from the disk.
[ Note: This is example depicts a magnetic monopole, a magnet with just a 'north' or just a 'south' pole without the opposite pole. No magnetic monopole has ever been observed in nature (why a monopole has never been observed is unknown, and is one of the great mysteries of physics). So nobody has ever created such an object and we are now in the realm of imagination. ]
Three paths are shown below for a steel ball rolled past this hypothetical circular magnet, from left to right..
Give your answers and your reasoning in the space below:
Your instructor is trying to gauge the typical time spent by students on these experiments. Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades:
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