Experimental Investigations

1.  How does the acceleration of a steel ball down the track depend on the slope of the track?  Note that the screw-adjusted mechanism changes its length by 1/32 of an inch for every 360 degree turn of the screw.

2.  If a ball rolls from rest down one straight incline the directly onto and up another, its PE gain on the second incline will be less than the PE loss on the first.  The ratio of the PE gain on the second ramp to the PE loss on the first can be expressed as a percent. 

·         Can this percent be determined by the angle between the two inclines?

·         If not, what other factors need to be taken into consideration, and how do they affect the result?

3.  If a straight incline resting on a tabletop is given a small slope from left to right by means of an appropriately thin object (e.g., a coin or a washer, whose thickness can be measured) placed under the left end, a steel ball will accelerate along the incline from left to right.  If the same thin object is then moved so that it supports the right edge, then a steel ball will accelerate from right to left.

·         How does the difference between the two accelerations depend on the thickness of the object?

·         Theoretically, how should the difference depend on the thickness of the object?

·         In your experimental results, is there evidence of the effect of rolling friction?

4.  On a slope of about .05, does the steel ball roll down the track without slipping?  At what max slope does this continue to be the case?

5.  If a larger steel ball collides center-to-center with a smaller, what are the velocities before and after collision?  According to your results, assuming that momentum is conserved, what is the ratio of the masses of the two balls?

6.  As the respective altitudes of the two steel balls at collision change, in the neighborhood of equal altitudes, how do the ranges of the two balls after collision change?  Control to achieve uniform before-collision velocities for the first ball.

7.  What maximum horizontal range can be achieved for a 2-marble ‘diatomic’ system, initially at rest, in collision with a small steel ball with a given initial velocity, provided that the steel ball strikes one (and only one) of the two marbles in a horizontal trajectory with the centers of the two colliding objects at the same altitude?

8.  How can you measure the equilibrium-position velocity of a pendulum of given length L, released from a point at horizontal position x < < L away from equilibrium? 

·         How does the velocity at the equilibrium position depend on the distance x?

·         How does the kinetic energy of a pendulum at its equilibrium position compare with its loss of gravitational potential energy between its extreme position and its equilibrium position? 

9.  How does the horizontal range of a projectile which leaves the end of a straight ramp at a constant height above the floor, after accelerating from rest along the full length of the ramp, depend on the slope of the ramp?  Assuming acceleration along the ramp proportional to slope, how then would the horizontal range depend on the velocity at the end of the ramp?

10.  How much of the work required to stretch a rubber band chain can you get back when you release the chain?  That is, to what extent is the force exerted by the rubber band chain conservative?

11.  To what extent is the motion of a mass suspended from the end of a rubber band chain similar to that of a pendulum, in the sense that the period of a pendulum is pretty much independent of the amplitude of the motion?  To what extent is the decay of the amplitude of the same nature (even if of different magnitude) as that of a pendulum?

12.  To what extent is the motion of a mass suspended from the end of a steel spring similar to that of a mass suspended from a rubber band?

13.  If a ball rolls down one straight incline and then onto another, to maximum altitude on that incline, then down this incline, onto the first, etc., etc., it will pass the ‘transition point’ where the two inclines meet many times before coming to rest at this point.  In the same way a pendulum released from rest at a point away from its equilibrium position passes its equilibrium point many times before coming to rest at equilibrium.  Unlike the motion of a pendulum, each ‘cycle’ takes perceptibly less time than the preceding.  What is the essential difference, other than the clear fact that the pendulum will probably go through a lot more cycles than the ball, between the motion of the pendulum and that of a ball on two straight inclines?

14.  In reference to the preceding, is there a difference between nature of the motion of a pendulum and that of a ball rolling back and forth within a hemispherical bowl (or along a track which makes a semicircular loop)?  For what shape of bowl or track would the motion be of the same fundamental nature?

15.  Does the sliding friction of a block over a smooth homogenous surface depend on the velocity of the block?  Does the friction of an object rotating on wheel bearings depend on the velocity of the object?

16.  How and in what ways does the behavior of a rubber band chain depend on temperature?  How and in what ways does the temperature depend on the behavior of the chain?