The studio exploration has two parts: pulling a block on a flat surface with a f

Question

                    The studio exploration has two parts: pulling a block on a flat surface with a force measuring device at constant speed to determine the static and kinetic                     coefficients of friction, and determining the static coefficient of friction from the angle of slip on an inclined plane. The free body diagram for the block                     used in the first exploration is shown below (Figure 1) .                 

                

                    
                    Figure 1:
                    http://session.masteringphysics.com/problemAsset/1000230178/4/forcediagram.jpg                 

                

                    
                

                

                    Figure 2:                 

                

                    http://session.masteringphysics.com/problemAsset/1000230178/4/q.jpg
                

                

                    
                

                                     Express the static coefficient of friction in terms of the value of the tension at which the block first slips                     (Tslip), and the variables m and g.

                    Express the kinetic coefficient of friction in terms of the value of the tension at which the block moves at constant speed (T), and the variables m and                     g.
                    
                    

The studio exploration has two parts: pulling a block on a flat surface with a force measuring device at constant speed to determine the static and kinetic coefficients of friction, and determining the static coefficient of friction from the angle of slip on an inclined plane. The free body diagram for the block used in the first exploration is shown below (Figure 1) . Express the static coefficient of friction in terms of the value of the tension at which the block first slips (Tslip), and the variables m and g. Express the kinetic coefficient of friction in terms of the value of the tension at which the block moves at constant speed (T), and the variables m and g. In the second figure to the left (Figure 2) , the incline is raised until the block begins to slip. Express the static coefficient of friction in terms of the angle at which the block first begins to slip (?slip).

Explanation / Answer

T=f=u(static)*mg

u(static)=T/(m*g)

at constant speed still the net force =0

T=f=u(kinetic)*mg

u(kinetic)=T/(m*g)

f=m*g sin(theta)=u*m*g*cos(theta)

u=tan(theta)

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