061009

• `pPrinciples of Physics

• Read text Chapter 6, Sections 1 - 5

• Ch. 6 Problems 1-6, 12, 13

• `gGeneral College Physics

• Read text Chapter 6, Sections 1 - 6

• Ch. 6 Problems 1-6,, 9, 11-14

Originally assigned 10/4/06:

• Familiarize yourself with Introductory Problem Set 3, Problems 1-12, concerning Newton's Second Law and the concept of kinetic energy.
• Familiarize yourself with Introductory Problem Set 5, Problems 1-5, concerning basic vector calculations.

Do and submit the experiment on hypothesis testing at http://www.vhcc.edu/dsmith/forms/ph1_2_testing_hypothesis_regarding_time_intervals.htm (access at the Physics homepage > Assts, scroll to Assignment 8, click on link entitled 'Hypothesis Testing and Time Intervals' ).  This experiment requires the TIMER program.  The typical reported time requirement for this experiment is about 30 minutes.

From the 061004 class:

For the following experiments, work in groups of no more than 3, preferably in groups of 2.  If you have a group of 4, split into groups of 2.  If you have a group of 5, split into a group of 2 and a group of 3.  If you have a group of 6, split into three groups of 2.

Both experiments can be running at the same time.  If you don't have access to the rubber bands, grab a computer.  If you don't have access to a computer, observe the rubber bands.

Rotation Experiment 2:

As accurately as possible, using the TIMER program, obtain rotational position vs. clock time data for a person spinning in a chair.

Use your data to obtain ave. angular velocity vs. midpoint clock time for each interval.

Graph average velocity vs. midpoint clock time, and using this graph everything you can about the angular acceleration of the system, including:

• Is angular acceleration constant?
• Is angular acceleration related to angular velocity?

Sketch graphs of the following:

• angular acceleration vs. clock time
• angular acceleration vs. angular velocity

Continuation of Force Experiment 1:

Repeat your observations of your rubber band system.  Make no reference to the data you obtained previously.

Analysis of Data for Energy Conservation Experiment 1:

You should have data for the experiment in which you observed a ball descending one ramp from rest starting as point A, rolling directly at point B to a second ascending ramp then rolling to rest at point C on the second ramp.  In this experiment you will have measured the vertical and horizontal positions of the ball, information from which you can determine the slope of each ramp, and will have information from which you can determine the clock times at points A, B and C.

You are given the following information:

• The mass of the ball may be assumed to be .050 kg.  This is not accurate but it will be very easy to modify the analysis for the accurate mass, in those calculations where the mass matters.  The mass won't matter in some of the calculations.
• The acceleration of an object of mass m subject to net force F_net is a = F_net / m.  This can also be expressed as F_net = m a.  Another expression for F_net is sum(F), where 'sum' is often written as a summation sign.  When we multiply m * a the MKS units are therefore units of mass multiplied by units of acceleration, or kg * m/s^2.  The unit kg * m/s^2 is called a Newton.
• The force gravity exerts on an object will, in the absence of other forces, accelerate that object at 9.8 m/s^2.  This force is called the 'weight' of the object.  Therefore weight = m * g, where g is the acceleration of gravity.
• The work done by a force F acting through displacement `ds parallel to F is `dW = F * `ds.  The boldface indicates that F and `ds are vector quantities, meaning that you have to be careful about signs.  (In particular note that when the force and the displacement are parallel and in the same direction, F and `ds will have the same sign and will therefore give us a positive product; but when the directions are opposite, F and `ds have opposite signs so that the product is negative).
• The unit of work is therefore equal to the unit of force multiplied by the unit of distance, i.e., Newtons * meters.  The unit N * m is called a Joule.  Since the unit N is also expressed as kg m/s^2, the unit of work is Joule = N * m = kg m / s^2 * m = kg m^2 / s^2.  The unit 'Joule' is abbreviated 'J'.
• When gravity does work on an object, the gravitational potential energy of the object changes by an amount equal and opposite to that work.  (So, for example, when gravity does negative work on an object its potential energy increases, and when gravity does positive work the potential energy decreaes).
• It follows that, provided the gravitational acceleration remains constant (which will be the case if the percent change in the distance from the center of the Earth is negligible), the change in gravitational potential energy when an object of mass m changes its vertical position by amount `dy is m g `dy.  Note that the units of this calculation are kg * m/s^2 * m = kg m^2 / s^2, or Joules.
• The kinetic energy of a mass m moving with speed v is KE = 1/2 m v^2.  (This is equal to the work required to accelerate the mass from rest to speed v).
• The angle of the incline is arcTan(incline slope).  The arcTan function is typically found on your calculator as 2d fn   Tan .

Using this information for one run of the experiment:

• Analyze the motion from A to B.
• Analyze the motion from B to C.
• Calculate the slope of each incline.
• Calculate the angle of each incline.
• Calculate the weight of the ball.
• Sketch the ball on each incline using conventions covered during the last week, sketching and estimating the x and y components of the weight of the ball.
• Using the weight and the angle of each incline, calculate the x and y components of the weight of the ball.
• Using the x component of the weight, and the mass of the ball, calculate the acceleration of the ball on each incline.  Assume that the frictional force acting on the ball is negligible.
• Compare with the accelerations you calculated when you analyzed the motion of the ball.
• Calculate the work done by gravity on the ball from A to B, and from B to C, based on the displacement along each incline.  Remember that if you use the displacement along the incline, you can use only the component of the force which runs parallel to the incline.  This is because F and `ds must be in parallel directions.  Be sure to consider the signs of F and `ds.
• Using the velocity at B, as determined from your analysis, find the kinetic energy of the ball at point B.
• Using m g `dy, find the change in potential energy from A to B, and from B to C.  Be careful of the sign of `dy.  Remember that `dy is the change in vertical position.

Be sure you have included units at every step of every calculation, and be sure you have actually done the algebra of the units.

How negligible is the percent change in the distance of the ball from the center of the Earth during this experiment?

Spreadsheet Exercise

Put the interval between observations into cell C3.

Put the numbers 0 and 1 into cells C5 and C6, the highlight these cells and use the 'fill handle' to drag the pattern down about 15 rows.

Put your clock times for a run of the rotation experiment into a column starting at D5.

In E5, type ''= ", click on cell C5, the type ' * $c$3'.

With E5 highlighted, use the 'fill handle' to drag this calculation down to the end of your clock times.

In G5, type "=", click on cell D6, type "-", click on D5 and enter.  This should give you the time interval between your first two clicks.

In cell H5, use a similar procedure to get the difference between E5 and E6.

In cell K5, type '=', click on cell H5, type '/', click on cell G5 and enter.  What does this give you?

Highlight cells F5 thru H5 and 'drag' the calculations down to the appropriate point.

Column F is still empty.  Figure out how to get your midpoint clock time for the first interval into this F5, then use the fill handle to fill the rest of this column.