Gas station without pumps

2012 March 15

Friction lab writeup

Filed under: home school — gasstationwithoutpumps @ 22:16
Tags: , , , ,

For the past two meetings, I’ve had the students design and carry out their own lab on dry friction.  In the first meeting, they decided what variables they wanted to vary and how they would vary them, built the equipment and did preliminary tests of the procedure.  For the second, they made measurements and plotted them.

They started by deciding to look at the friction between a cardboard surface and the wood floor, with two different areas of cardboard and with different weight pressing the cardboard against the floor.  They were expecting (based on the models from the book), that the area should not matter and that the frictional force should be proportional to the normal force.  They also decided to measure both static and dynamic friction, but not to try different speeds.

They glued cardboard onto two sides of a block of wood to keep the cardboard flat and screwed a hook into the end of the block to provide a good place to pull with a force gauge.  The first day when they made measurements, they had some trouble with the smaller area cardboard, because some spray glue had gotten on the face of the cardboard for the smaller area and was making that side quite sticky.  A week later the glue had dried and did not disrupt measurements.

The measurements were typed directly into the computer as they were made, using RDB format (data at bottom of this post).  The data were plotted with gnuplot, and simple single-variable fits were done:

The dynamic coefficient of friction is about 0.258 and the static coefficient of friction about 0.353.

The static measurements are much noisier, because it was very difficult to read the peak value on the handheld gauge just before the block slipped.  A computerized force gauge with continuous recording would have been handy to have. The different areas were initially plotted in different colors and fits done separately for each of the 4 conditions (small/large area × static/moving), but the area did indeed seem to make little difference (as expected), so only the static/moving distinction was kept for the final plots.

Here is the gnuplot script for creating the plot:

# function to convert "grams force" to Newtons
Newton(gram_f) = 9.80665E-3 *gram_f

# set logscale xy
# set yrange[:]
# set xrange[2:60]

set xrange[0:]
set yrange[0:]

set ylabel "Frictional force (N)"
set xlabel "Normal force (N)"
set key top left

fit c_static*x '< row MOVING == 0 < frictionres-rdb.txt | column MASS FORCE | rdb2gnuplot' \
	using (Newton($1)):(Newton($2)) via c_static

fit c_dynamic*x '< row MOVING == 1 < frictionres-rdb.txt | column MASS FORCE | rdb2gnuplot' \
	using (Newton($1)):(Newton($2)) via c_dynamic

plot '< row AREA eq 128.8 and MOVING == 0 < frictionres-rdb.txt | column MASS FORCE | rdb2gnuplot' \
	using (Newton($1)):(Newton($2)) lt 1 pt 1 title "small static" , \
     '< row AREA eq 128.8 and MOVING == 1 < frictionres-rdb.txt | column MASS FORCE | rdb2gnuplot' \
	using (Newton($1)):(Newton($2)) lt 2 pt 1 title "small moving" , \
     '< row AREA ">=" 200 and MOVING == 0 < frictionres-rdb.txt | column MASS FORCE | rdb2gnuplot' \
	using (Newton($1)):(Newton($2)) lt 1 pt 2 title "large static" , \
     '< row AREA ">=" 200 and MOVING == 1 < frictionres-rdb.txt | column MASS FORCE | rdb2gnuplot' \
	using (Newton($1)):(Newton($2)) lt 2 pt 2 title "large moving" , \
	c_static*x title 'static model' lt 1, \
	c_dynamic*x title 'dynamic model' lt 2

Here is the raw data—the commented-out data were from the glue-sticky cardboard and were not used in the final plots.

# Friction Measurement
# 2 Mar 2012 - 9 Mar 2012
# note: small area got some glue on it, may impact results
# area in cm^2, mass in grams, force in grams-force
AREA	SURFACE	MASS	MOVING	FORCE
N	S	N	N	N
256.7	Wood floor	745	0	200
256.7	Wood floor	745	1	175
#128.8	Wood floor	745	0	700
#128.8	Wood floor	745	1	350
256.7	Wood floor	1165	0	340
256.7	Wood floor	1165	1	275
#128.8	Wood floor	1165	0	500
#128.8	Wood floor	1165	0	500
#128.8	Wood floor	1165	0	530
#128.8	Wood floor	1165	0	535
128.8	Wood floor	1165	1	335
128.8	Wood floor	1165	1	375
128.8	Wood floor	1165	1	345
128.8	Wood floor	1165	1	330
128.8	Wood floor	1165	1	305
128.8	Wood floor	1165	1	300
128.8	Wood floor	1165	1	265
128.8	Wood floor	1165	1	300
256.7	Wood floor	1165	1	325
256.7	Wood floor	1165	1	345
256.7	Wood floor	1165	1	320
256.7	Wood floor	1165	1	320
256.7	Wood floor	1165	1	320
256.7	Wood floor	1165	1	305
256.7	Wood floor	1165	0	360
256.7	Wood floor	1165	0	305
256.7	Wood floor	1165	0	410
256.7	Wood floor	1165	0	360
256.7	Wood floor	1165	0	470
256.7	Wood floor	1165	0	380
256.7	Wood floor	1165	0	525
256.7	Wood floor	1165	0	530
256.7	Wood floor	1165	0	470
256.7	Wood floor	1165	1	310
256.7	Wood floor	1165	1	330
256.7	Wood floor	1165	1	320
256.7	Wood floor	1165	1	320
256.7	Wood floor	745	0	270
256.7	Wood floor	745	0	250
256.7	Wood floor	745	0	180
256.7	Wood floor	745	0	230
256.7	Wood floor	745	0	250
256.7	Wood floor	745	1	205
256.7	Wood floor	745	1	215
256.7	Wood floor	745	1	205
256.7	Wood floor	745	1	190
256.7	Wood floor	745	1	210
256.7	Wood floor	745	1	195
256.7	Wood floor	745	1	205
128.8	Wood floor	745	0	195
128.8	Wood floor	745	0	240
128.8	Wood floor	745	0	250
128.8	Wood floor	745	0	230
128.8	Wood floor	745	1	205
128.8	Wood floor	745	1	220
128.8	Wood floor	745	1	205
128.8	Wood floor	745	1	205
256.7	Wood floor	1080	0	240
256.7	Wood floor	1080	0	310
256.7	Wood floor	1080	0	280
256.7	Wood floor	1080	0	350
256.7	Wood floor	1080	1	285
256.7	Wood floor	1080	1	270
256.7	Wood floor	1080	1	295
256.7	Wood floor	1080	1	280
128.8	Wood floor	1080	0	240
128.8	Wood floor	1080	0	350
128.8	Wood floor	1080	0	350
128.8	Wood floor	1080	0	330
128.8	Wood floor	1080	1	280
128.8	Wood floor	1080	1	290
128.8	Wood floor	1080	1	280
128.8	Wood floor	1080	1	290
256.7	Wood floor	1080	0	275
256.7	Wood floor	1080	0	290
256.7	Wood floor	1080	0	280
256.7	Wood floor	1080	0	230
256.7	Wood floor	1080	1	275
256.7	Wood floor	1080	1	285
256.7	Wood floor	1080	1	285
256.7	Wood floor	1080	1	280
128.8	Wood floor	1080	0	355
128.8	Wood floor	1080	0	360
128.8	Wood floor	1080	0	330
128.8	Wood floor	1080	0	350
128.8	Wood floor	1080	1	315
128.8	Wood floor	1080	1	295
128.8	Wood floor	1080	1	295
128.8	Wood floor	1080	1	300
256.7	Wood floor	2160	0	600
256.7	Wood floor	2160	0	600
256.7	Wood floor	2160	0	650
256.7	Wood floor	2160	0	550
256.7	Wood floor	2160	1	530
256.7	Wood floor	2160	1	500
256.7	Wood floor	2160	1	500
256.7	Wood floor	2160	1	500
128.8	Wood floor	2160	0	400
128.8	Wood floor	2160	0	580
128.8	Wood floor	2160	0	760
128.8	Wood floor	2160	0	600
128.8	Wood floor	2160	1	520
128.8	Wood floor	2160	1	550
128.8	Wood floor	2160	1	505
128.8	Wood floor	2160	1	530
256.7	Wood floor	2160	0	645
256.7	Wood floor	2160	0	780
256.7	Wood floor	2160	0	810
256.7	Wood floor	2160	0	810
256.7	Wood floor	2160	1	520
256.7	Wood floor	2160	1	535
256.7	Wood floor	2160	1	545
256.7	Wood floor	2160	1	520
128.8	Wood floor	2160	0	670
128.8	Wood floor	2160	0	765
128.8	Wood floor	2160	0	700
128.8	Wood floor	2160	0	750
128.8	Wood floor	2160	1	585
128.8	Wood floor	2160	1	625
128.8	Wood floor	2160	1	595
128.8	Wood floor	2160	1	605
256.7	Wood floor	5040	0	2000
256.7	Wood floor	5040	0	2020
256.7	Wood floor	5040	0	1900
256.7	Wood floor	5040	0	2115
256.7	Wood floor	5040	1	1200
256.7	Wood floor	5040	1	1200
256.7	Wood floor	5040	1	1200
256.7	Wood floor	5040	1	1200
128.8	Wood floor	5040	0	2100
128.8	Wood floor	5040	0	1700
128.8	Wood floor	5040	0	2100
128.8	Wood floor	5040	0	1500
128.8	Wood floor	5040	1	1330
128.8	Wood floor	5040	1	1300
128.8	Wood floor	5040	1	1320
128.8	Wood floor	5040	1	1230
256.7	Wood floor	5040	0	1600
256.7	Wood floor	5040	0	2000
256.7	Wood floor	5040	0	1700
256.7	Wood floor	5040	0	2100
256.7	Wood floor	5040	1	1355
256.7	Wood floor	5040	1	1315
256.7	Wood floor	5040	1	1300
256.7	Wood floor	5040	1	1320
128.8	Wood floor	5040	0	1400
128.8	Wood floor	5040	0	1700
128.8	Wood floor	5040	0	1700
128.8	Wood floor	5040	0	1650
128.8	Wood floor	5040	1	1400
128.8	Wood floor	5040	1	1300
128.8	Wood floor	5040	1	1450
128.8	Wood floor	5040	1	1335

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