Lab 7: Modeling Friction Forces

Title:
Modeling Friction Forces

Purpose:
This lab's goal is to produce a model for friction based on measurements of mass and acceleration of an object moving on a uniform surface.

Theory:
The force of friction on an object is proportional to the normal force from the surface and a constant of either static or kinetic friction. Static friction of an object ranges from 0 to a maximum value where the object will remain at rest unless the applied force exceeds maximum static friction. The coefficient for static friction may be found if the mass of an object is known and the maximum force applied before the object moves is known. The coefficient for kinetic friction may be found if the mass of the object is known and the net force in the direction of motion is known. This is because kinetic friction remains a constant value as long as the object moves along the same surface. By making measurements to determine the maximum force of static friction and the acceleration of an object down a ramp of known incline, it is possible to find both constants and produce models predicting the behavior of an object with friction.

Apparatus:

• Block with linoleum tile surface (1)
• String
• Pulley (1)
• 5g hanging mass (1)
• Movable tabletop or board with flat plastic surface (1)
• Large quantity of 5g, 10g, 20g, and 50g masses
• 200g mass (3)
• Force sensor (1)
• Motion detector (1)
• LabPro (1)
• Computing device with Logger Pro software
• Angle measurement device (1)

Procedure:

Set the block on the flat plastic surface. Attach the hanging mass to the block using the string and place on the pulley. Slowly add mass to the hanging mass in 5g increments until the block begins to move. Subtract 5g from the total mass on the hanging mass and record as maximum static friction. Repeat these steps with 1, 2, and 3 added 200g masses on the block. Calibrate the force sensor and record the force as the block is dragged horizontally at a constant velocity across the plastic surface. Repeat this step with 1, 2, and 3 added 200g masses on the block. Place the block flat on the surface and slowly increase the incline of the surface and record the angle when the block begins to move. Attach a motion detector to the stop of the slanted surface and release the block again, recording its acceleration. Using calculated values of the coefficient of kinetic friction, predict the motion of the block as it is accelerated by a known mass. Use a motion sensor to measure the actual acceleration of the block.

Data and Graphs:

Photo of apparatus used in the experiment - Part 1

Photo of apparatus used in the experiment - Part 3

Velocity v time graph - Part 4

Velocity v time graph - Part 5

Calculations for uncertainties

Table of data

Part 1	Mblock (g±0.1)	Mhanging (g±5)	μs	±
	187	100	0,535	0,0264639
	387	255	0,659	0,01275128
	587	350	0,596	0,00841275
	787	410	0,521	0,00628746
		Average μs	0,578	0,05488515
Part 2	Mblock (g±0.1)	Avg Force (N±0.001)	μk	±
	187	0,492	0,268	0,0004014
	387	1,045	0,275	0,0001921
	587	1,638	0,284	0,000125
	787	2,204	0,285	9,3097E-05
		Average μk	0,278	0,00082374
Part 3	Angle (°±0.1)	μs	±
	29,8	0,573	0,001922819
Part 4	Accel (m/s^2)	μk	±
	1,818	0,359	0,00019747
Part 5	Mblock (g±0.1)	Mhanging (g±0.1)	Calc. accel (m/s^2)	±
	187	105	1,272175582	4,1553E-05
		Actual accel (m/s^2)	1,346

Equations used (circled)

Analysis:

Using Newton's equation F=ma and the equations of friction, a value for the coefficient of static or kinetic friction was found in parts 1-4 of the experiment. Uncertainties were calculated for each coefficient of friction. Other equations used are shown in photos.

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Conclusion:

Our predicted acceleration in part 5 using the coefficient of kinetic friction found in part 4 was 1.272+-0.0000416m/s^2 and our measured acceleration was 1.346 m/s^2. Based on these results, we can conclude that the models used will produce accurate coefficients of friction given the procedure and methods used for measurement. Part 1 of the experiment was likely the most error prone as the method used to determine maximum static friction had uncertainties of +- 5g of mass, a large value by comparison to other measurement methods. It was also observed that behavior of the block was not entirely consistent throughout the trials as some masses that produced motion of the block would later fail to overcome static friction.