An aluminum block of mass m 1 = 4.45 kg and a copper block of mass m 2 = 6.90 kg

Question

An aluminum block of mass

m1 = 4.45 kg

and a copper block of mass

m2 = 6.90 kg

are connected by a light string over a frictionless pulley. They sit on a steel surface as shown in the figure below, where

= 31.0°.

(See this table for the appropriate coefficients of friction).

(a) When they are released from rest, will they start to move?

Yes or No    

(b) If the blocks move, determine the magnitude of their acceleration. (If the blocks do not move, enter 0.)
           m/s2

(c) If the blocks move, determine the magnitude of the tension in the string. (If the blocks do not move, enter 0.)
            N

(d) If the blocks do not move, determine the sum of the magnitudes of the forces of friction acting on the blocks. (If the blocks move, enter 0.)
             N

Explanation / Answer

(a) motive force F = m2*g*sin
F = 6.9kg * 9.8m/s² * sin31º =34.83 N

coefficient of friction of aluminium=.61

coefficient of friction of copper=.53

total maximum static friction force f = µ*m*g*cos
f = (0.61 * 4.45kg * cos0º + 0.53 * 6.9kg * cos31º) * 9.8m/s² = 5.849 N

So "No," when they are "released" they will remain in place.

(b) 0

(c) 0

(d) I think you found the difference F - f (although I get 28.981 N). But the sum of the static frictions is equal to the motive force F = 34.83
That's what keeps the blocks stationary (in equilibrium).

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