060908

1.  Give the definition of average acceleration.

Give the equation that expresses the definition of average acceleration in terms of `dv and `dt.

Show how this equation is solved for `dt.  Include the details of the algebra, justifying each step.

Sketch the ‘triangle’ diagram which depicts how to obtain `dt from `dv and aAve.

2.  The velocity of an object changes from 4 m/s to 22 m/s in 6 seconds. 

Sketch a possible graph of v vs. t and label the axes.

Find the average acceleration for this interval.  Does your answer depend on whether the v vs. t graph is or is not linear?

Assuming the v vs. t graph to be linear, find the displacement of the object during this time interval.  Does the answer to this question depend on whether the graph is linear?

Sketch the ‘triangle’ diagram for this problem (there will be more than one ‘triangle’ in your diagram).

3.  An object accelerates uniformly for 4 seconds at 5 m/s^2, starting with velocity 10 m/s.

Sketch a possible graph of v vs. t and label the axes.

Find the displacement of the object corresponding to this interval.  Does your answer depend on whether the v vs. t graph is or is not linear?

Sketch the ‘triangle’ diagram for this problem (there will be more than one ‘triangle’ in your diagram).

(sketch velocity vectors for unif accel and for nonunif accel)…

Experiment 4

Orient and/or shim the 'bead pendulum' so that it after release strikes the bracket at least 10 times with a uniform rhythm.

Using the TIMER program determine as accurately as you can the following for a 10 cm bead pendulum:

• The time from release of the 'bead pendulum' until it strikes the bracket the second time.
• The time from release of the 'bead pendulum' until it strikes the bracket the fourth time.
• The time from release of the 'bead pendulum' until it strikes the bracket the sixth time.
• The time from release of the 'bead pendulum' until it strikes the bracket the eighth time.
• The time from release of the 'bead pendulum' until it strikes the bracket the tenth time.

If you can't handle the rhythm of every other 'strike', as instructed above, use every third strike, or even every fourth strike.

See how well the 10 cm 'bead pendulum' synchronizes with a hand-held pendulum of the same length.

Repeat for a 4 cm 'bead pendulum'.

Submit your results as requested.

Experiment 4

Set up two grooved tracks, one supported by 3 dominoes at one end and by 1 domino at the other end, the second also supported  by the 1 domino, in such a way that the ball will roll freely from the first ramp onto the second, and with the other end of the second ramp right at the edge of the table so that when the ball rolls off that ramp it falls freely to the floor.

Set a marble on the first track so that it will roll 5 cm before rolling onto the second.  Release the marble from rest.

Using a meter stick observe both the vertical and horizontal position of the center of the ball as it starts from rest at this position, as it rolls from the first track onto the second, as its center reaches the end of the second track, and when it reaches the floor.

Using a 'bead pendulum' take data which will determine the clock times at which the ball starts, reaches the end of the first ramp, the end of the second ramp, and the floor.

You will have the information which allows you to analyze the motion of the ball during each of 3 phases, during which we will assume constant acceleration.  The first phase corresponds to the motion on the first ramp, the second phase corresponds to motion on the second ramp, the third corresponds to the motion of the ball as it falls to the floor.

From your data determine the following:

• The average horizontal velocity of the ball during each phase.
• The initial and final horizontal velocity of the ball during each phase.
• The horizontal acceleration of the ball during each phase.
• The average vertical velocity of the ball during each phase.
• The initial and final vertical velocity of the ball during each phase.
• The vertical acceleration of the ball during each phase.