An aluminum block of mass 2kg is at rest (held still) on a flat horizontal steel

Question

An aluminum block of mass 2kg is at rest (held still) on a flat horizontal steel surface and attached by a light string over a frictionless pulley to a copper block of mass 6kg (also at rest) that is downward from the aluminum block on an inclined steel surface of 30 degrees to the horizontal. Calculate the system's acceleration, string tension, and the sum of the magnitudes of the forces of friction acting on the blocks to "DETERMINE WHETHER OR NOT THE BLOCKS WILL MOVE WHEN RELEASED FROM REST".

Explanation / Answer

Frictional coefficients obtained from the following site: http://www.engineeringtoolbox.com/friction-coefficients-d_778.html

Al to steel sa=.61 and Co to steel sc=.53

mco=6kg and mal=2kg

(a) finding acceleration 1st sum the forces on each particle: Fal=mala: T-samalg=mala, Fco=mcoa: mcogcos()-T-scmcog=mcoa :now add the equations together:

T-samalg+mcogcos()-T-scmcog=(mco+mal)a :Tension cancels out:

mcogcos()-samalg-scmcog=(mco+mal)a => ((g)(mcocos()-samal-scmco))/(mco+mal)=a

((9.8)(6cos(30)-.61(2)-.53(6)))/(6+2)=a, a=.975(m/s2)

(b) Use either equation to calculate Tension, I sugges the one for the aluminum block.

T-samalg=mala => T=samalg+mala, T=(.61)(2)(9.8)+(2)(.975)=13.906 or T=13.9N

(c) total frictional force acting on the system : (scmco+samal)(g)= ((.53)(6)+(.61)(2))(9.8)= 43.12N

Yes the system will move since it has acceleration

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