Question

Total mass (block plus masses)	0.1029 kg	0.1529 kg	0.2529 kg	0.302.9 kg	0.3529 kg	0.402.9 kg
Normal Force	1.01 N	1.50 N	2.48 N	2.97 N	3.46 N	3.95 N
fsmax	0.06 * 9.8 = 0.588 N	0.13 * 9.8= 1.27 N	0.225 * 9.8 = 2.21 N	0.305 * 9.8 = 2.99 N	0.31 * 9.8 = 3.04 N	0.38 * 9.8 = 3.72 N
Mass of hanger plus masses	0.06 kg	0.13 kg	0.225 kg	0.305 kg	0.31 kg	0.38 kg

From your measurements and analysis, and your understanding of the maximum static frictional force, can you come up with an equation that describes how f_smax depends on the normal force? Hint: Is f_smax proportional to the normal force? Is f_smax proportional to the normal force squared? etc.

What is the proportionality constant?   

What are its units?

Does the proportionality constant make sense in terms of the materials of the block and horizontal surface? Explain.

Answer 1

f_{s max} = μ_s N , this is the relation between maximum static frictional force and normal force. And μs is the coefficient of static friction.

An easy way to measure the coefficient of static friction is to place two objects together and then tilt them until the top one slides. The angle at which one object starts to slip on the other is directly related to the coefficient.

When the two objects are horizontal there is no frictional force. As the objects are slowly tilted, the force of static friction must increase from zero to counteract the component of the force of gravity that acts along the interface.

Eventually, as the angle increases, that component of the force of gravity exceeds the maximum value of the force of static friction, and the top object slides off.

Use a coordinate system with +x down the slope and +y perpendicular to the slope.

Split the force of gravity into x and y components.

Apply Newton's second law twice on each coordinate:

ΣFx = m ax = 0	|	ΣFy = m ay = 0
mg sin(θ) - fs = 0	|	N - mg cos(θ) = 0
mg sin(θ) = μs N	|	N = mg cos(θ)

Substitute the second expression into the first:

mg sin(θ) = μ_s mg cos(θ)

The factors of mg cancel. Re-arranging gives:

sin(θ) cos(θ)

=

tan(θ)

=

μs

So you can see that the coefficient is unit less. And this is depends on nature of surface and object material.

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