The laboratory work № 6

Determination of curvature radius of a concave surface by method of a rolling ball.

Had done by the student gr.__220473я__ F.N.S. Pavlov F.E.

Checked by ______________________ date ____________

Purpose of work: to study motion laws of a ball rolling along the spherical concave surface.

Move of work:

1. Define the ball radius, using micrometer (5 times).

2. Measure a time (t) of 10 fluctuations of the ball, which was remove from the static state(5 times).

3. Evaluate fluctuation period (T) in the every experiment.

4. Evaluate average fluctuation period (DT_i) and

5. Evaluate <R`>:

6. Evaluate , where

We consider system acting in external forces free dimension. As an initial angle of the motion is very small, let the fluctuations be harmonic. An example of the ball motion is shown in the picture. The results of the experiments and all calculations are represented in the table.

The scheme of the ball motion.

Results of the measurements.

No	t	n	T	T	r	r	<R`>	R`	E
	s		s	s	m	m	m	m	%
1	27.02	10	2.702	0.0324	0.00769	0.00005	1,30352	0,0309	3,1704
2	27.41	10	2.741	0.0066	0.00769	0.00005	1,34124	0,0065	5,8976
3	27.28	10	2.728	0.0064	0.00769	0.00005	1,32858	0,0063	3,0038
4	27.44	10	2.744	0.0096	0.00769	0.00005	1,34412	0,0095	6,0465
5	27.57	10	2.757	0.0226	0.00769	0.00005	1,35677	0,0224	4,0157
A v e r a g e			2,7344	0,01552	0.00769	0.00005	1,32862	0,0151	4,4268

Conclusion:

So we have studied motion laws of a ball rolling along the spherical concave surface. And we have learned how to define curvature radius of a concave surface by method of a rolling ball.