Theory: Static friction (F_s) and kinetic friction (F_k) are equal to their coefficients times the normal force, all forces acting on an object are equal and opposite, the sum of forces acting on an object (the block) is equal to the mass of the object times its acceleration. In experiments:
1) This means the tension from cup suspended with a (assumed) massless pulley will create a tension equal the normal force times the coefficient of static friction.
2) A constant pull force will equal the coefficient of kinetic friction.
3) The coefficient of static fiction times the normal force can be determined from a motionless block on a sloped surface track.
4) The coefficient of kinetic fiction times the normal force can be determined from a sliding block on a sloped surface track.
5) The kinetic friction can be confirmed by a (assumed) massless pulley creating a tension that pulls the block, and a motion sensor records actual acceleration.
Procedure: In experiment
1)
*Get four blocks, string, a pulley, a Styrofoam cup, and some water
*Weigh each block to determine mass
*Tie string to one block, hang the other side of the string off from the pulley and attach the Styrofoam cup to the other side of the string.
*Add drops of water to the cup, until the block begins to slide
*Record mass of cup, place another block on top of the original, and repeat the process until you have used all four blocks
2)
*Get four blocks, string, force gage and logger pull.
*Weigh each block, and zero the force gage.
*Tie one end of the string to a block, and the other to the force, and at a constant speed pull on the force gage to drag the block.
*Add another block on top of the original, repeat, add the third block, repeat, add the fourth block, repeat.
3)
*Get a block and track.
*raise the block up slowly until it begins to slide, and determine the angle of the raised block.
4)
*Get a block, a track, a motion sensor, and logger pro.
*Place the block on an incline that it will slide on down the track, record angle and acceleration of block.
5)
*Get a block, a pulley, string, a hanging mass, a track, and a motion sensor.
*Attach the string to the block and hanging mass, hang mass over pulley, place block on track, and record acceleration with motion sensor.
Experiment 1
*We got the necessary supplies
*Multiplying the mass of the block by acceleration due to gravity (g=9.8 m/s^2), gives us the normal force, and the tension in the string (mass of cup times g) is equal to the friction force.
Results
|
Mass Blocks (kg)
|
Mass Cup (kg)
|
Normal force (N)
|
Friction force (N)
|
|
0.131
|
0.059
|
1.284
|
0.5782
|
|
0.252
|
0.093
|
2.47
|
0.9114
|
|
0.359
|
0.121
|
3.518
|
1.186
|
|
0.485
|
0.165
|
4.753
|
1.617
|
Graph Friction Force vs Normal
*The slope is the coefficient of static friction, and we get 0.3475 +/- 0.01287
*The reason: F_s*Normal force=Friction Force, solve for F_s
Experiment 2
*We set up equipment
*Zeroed the pull gage, pulled, recorded the run, and repeated four times with increasing mass
Results
|
Mass Blocks (kg)
|
Normal force (N)
|
Friction force (N)
|
|
0.121
|
1.186
|
0.3909
|
|
0.252
|
2.47
|
0.7374
|
|
0.378
|
3.704
|
1.01
|
|
0.485
|
4.753
|
1.232
|
Graph Friction Force vs Normal
*Same reasoning in determining F_s, the slope is F_k and that is 0.2712 +/- 0.0098
Experiment 3
*Set equipment up
*The track was raised to 20 degrees, before it started to slip, and the block(m) was 0.105kg
*Equation of net forces in the sloped direction (F_s*N=m*g*cos 20)
*Solving for F_s gives us 0.3640
Experiment 4
*The track was raised to 26 degrees, and set up the motion detector to record acceleration.
Graph
*We average the acceleration, and get 1.789 m/s^2
*Equation for acceleration (F_k*g*cos26 - g*sin26 = a)
*Solving for F_k we get 0.2846
Experiment 5
*We attached a .05kg mass to a string, hang it over a pulley, and the other end of the string to the block.
*Using the equation for acceleration, we determine the block should accelerate 1.877 m/s^2
*Actual was 2.613 m/s^2, 28% off from calculated.
Conclusion
*From my calculations the coefficient of static friction was larger than the kinetic friction, which was expected.
*As for the large error for acceleration in experiment in 5 and 4, I think the acceleration was effected by the track's ramp. As the block slid, it would turn askew and grind against the rallying, instead of being pulled straight.
*I'm satisfied with my models for calculating the coefficient of friction.
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