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7.85 The belt is placed between two rollers, which are free to rotate aboutA and B. Determine the smallest coefficient of static friction between the belt andthe rollers for which the device is self-locking; that is, the belt cannot be pulleddown for any value of P1.5R-+Belt-0.5RR350BFig. P7.85

Question
7.85 The belt is placed between two rollers, which are free to rotate about
A and B. Determine the smallest coefficient of static friction between the belt and
the rollers for which the device is self-locking; that is, the belt cannot be pulled
down for any value of P
1.5R-+
Belt
-0.5R
R
350
B
Fig. P7.85
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7.85 The belt is placed between two rollers, which are free to rotate about A and B. Determine the smallest coefficient of static friction between the belt and the rollers for which the device is self-locking; that is, the belt cannot be pulled down for any value of P 1.5R-+ Belt -0.5R R 350 B Fig. P7.85

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Step 1

Show the free body diagram of the roller B as in Figure (1).

Ву
В - 35°
R
В,
0.5R
В
F N
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Ву В - 35° R В, 0.5R В F N

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Step 2

Consider impending slipping of the belt.

Consider counter clockwise moment is positive and clockwise moment is negative.

Take moment about point B.

Determine the smallest coefficient of static friction between the belt and...

ΣΜ,-0
μV (R+ 1) - N() -0
μN(R+ 0.5Rcos β) - N(0.5R in β) =0
μ1+0.5 (1) cs35) -(0.5 (1) sin 35*) =0
0.287
μ.
1.409
μ=0.204
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ΣΜ,-0 μV (R+ 1) - N() -0 μN(R+ 0.5Rcos β) - N(0.5R in β) =0 μ1+0.5 (1) cs35) -(0.5 (1) sin 35*) =0 0.287 μ. 1.409 μ=0.204

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