Class 091019

Set up an Atwood machine using dominoes and clips.

• Choose a positive direction and start adding paperclips to the appropriate side until you get positive acceleration.  Measure the minimum possible positive acceleration, and note the number of clips that have been added.  Then add two more clips and repeat. 
• Remove all added clips and start adding clips to the negative side until you get the smallest possible negative acceleration, which you should measure.  Note the number of clips that have been added.  Then add two more clips to the negative side and repeat.
• Keep track of every 'move', including every mass added to either side of the system.

`q001.  Report your data for the Atwood machine.  Report all the raw data you will use in the analysis, in which you will figure out the four accelerations and the total effect of the gravitational force in accelerating each system.

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`q002.  Figure out the acceleration for each system, and report below, with a brief synopsis of how you proceeded from your raw data to your conclusions.

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`q003.  Find the total effect of the gravitational force on each system, as a multiple of the weight of a paper clip.  Paper clips added on one side exert positive force, clips added on the other side exert negative force on the system.

For example if you have 9 clips on one side and 5 clips on the other, the net gravitational force is equal to the weight of 4 clips.

Give a table of acceleration vs. total gravitational force.

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3 rubber band chains

`q004.  Your table should include a fairly large 'gap' in the total gravitational force, where the acceleration is zero.  How wide is that 'gap'?  What does that 'gap' mean?

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Suspend some number of dominoes, between 3 and 7, from your rubber band chain and measure its length.  Don't let anyone know how many dominoes you suspended.  Measure the length of the chain.  Measure once more with the chain supporting a single domino.  Then proceed as follows:

• Get together with 2 other people in the class and hook all three chains to the same paper clip. 
• Choose one person to provide the equilibrant force. 
• The other two will pull their chains back until they are at their previously measured lengths, keeping them at a right angle, while the third provides the equilibrant. 
• When the system is in this state, the person providing the equilibrant will measure the length of his or her chain, and data will be taken to determine the angles between the first two rubber bands and the equilibrant. 
• The two people whose rubber bands are at right angles will share the numbers of dominoes that resulted in the given length. 
• The lengths of all three rubber bands for this trial will be shared.

Then the experiment will be repeated twice more, so that it has been repeated once with each person providing the equilibrant.

If one or more groups of four people are required, adjust the experiment so that each individual provides the equilibrant force one time.

`q005.  You will find the magnitude of the resultant of the two forces exerted at right angles, the angle made by the equilibrant with these two forces, and the estimated force exerted by the equilibrant, based a two-point graph of number of dominoes supported vs. chain length.

Report the raw data you will use to find these quantities.

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`q006.  Find the magnitudes of the two forces, the angle of the equilibrant and the force exerted by the equilibrant, as estimated from your data.  Briefly indicate how you found these quantities.

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`q007.  Sketch the first two forces on a set of coordinate axes, and find the magnitude and angle of their resultant.  Give your results and your explanation of the calculation below.

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`q008.  Sketch the equilibrant on the same set of coordinate axes, and find its x and y components.

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`q009.  Compare the observed equilibrant with the resultant:

• To what extent is the equilibrant obtained from your data equal and opposite to the resultant of the other two forces? 
• By how much does its magnitude differ from that of the resultant?   
• By how much does its angle differ from that of the resultant? 
• By how much do its components differ from those of the resultant?

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Ball down incline to floor: analysis using vectors, energy

`q010.  A ball rolls down an incline of length 30 cm with slope 0.1, and falls to the floor 1.05 meters below.

A slope of 0.1 can be associated with a rise of 0.1 and a run of 1.0.  A vector with a rise of 0.1 and a run of 1.0 has a y component of 0.1 and an x component of 1.0, so it makes angle

theta = arcTan(y comp / x comp) = arcTan (0.1 / 1.0) = 5.7 degrees

with the positive x axis, as measured in the counterclockwise direction.

A ramp slope of 0.1 can also be associated with a vector whose rise is either +0.1 or -0.1, and whose run is either +1.0 or -1.0.

• What possible angles might the vector therefore make with the positive x axis?

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`q011.  The ball comes off the bottom of the incline with its velocity in the direction of the ramp.  What therefore are the possible angles, in the coordinate plane, of the velocity vector with a horizontal x axis?

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`q012.  If the ball requires 1.1 seconds to roll the length of the ramp, what is the magnitude of its velocity vector as it comes off the end of the ramp?

What therefore are the x and y components of its velocity vector at this instant?

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`q013.  The initial vertical velocity of the ball is equal to the y component of its velocity as it comes off the ramp.  Its acceleration in the vertical direction is that of gravity. 

• Use this information and the distance of the fall to determine the time required for the ball to fall to the floor.

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`q014.  The ball's horizontal velocity is constant, and equal to the horizontal component of its velocity as it comes off the ramp.  Using this with the time interval determined previously, how far does it travel in the horizontal direction as it falls?

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`q015.  Assuming the ball to be a sphere of density 8 grams / cm^3 and diameter 2.5 cm, find its kinetic energy at each of the following instants:

• when it is released
• when it leaves the end of the ramp
• when it reaches the floor

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`q016.  Continuing the preceding, assuming that the ball descends 3 cm on the ramp:

• What is its PE change while on the ramp, and what is its PE change while falling to the floor?
• How much work is therefore done by the frictional force between the ball and the ramp?

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`q017.  Answer for your rubber band, for the number of dominoes you chose to suspend from it:

Assuming that each domino weighs .2 Newton, and making the approximation that the force vs. length curve for the rubber band chain is linear, what is the average force required to stretch the chain from its 1-domino length to the length corresponding to your chosen number of dominoes?

How much work is therefore required to stretch it between these two lengths?

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Homework:

Your label for this assignment: 

ic_class_091019

Copy and paste this label into the form.

Report your results from today's class using the Submit Work Form.  Answer the questions posed above.

Work through and submit q_A_15 and q_A_16.  These qa's are on impulse and momentum, and collisions.

URL's of qa's 10-19:

http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_10.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_11.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_12.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_13.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_14.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_15.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_16.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_17.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_18.htm
http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qa_19.htm