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Belt Friction Example (continued)

Now for sliding

F_A = μN_A, F_B = μ N_B, and β = π/2

Substitute into the equations of equilibrium. The result is:

N_A + μN_B = W ----------- (1)

μN_A ˗ N_B + P e ^μπ^/2 = 0 ----------- (2)

μN_A + μ N_B = P e ^μπ^/2 ----------- (3)

Here we have three equations with unknowns P, N_A, and N_B

Multiply (2) by μ and add to (3) (eliminating N_B). The result is N_A = (1/μ) P e ^μπ^/2

Put this result into (1). The result is: N_B = (1/μ) W ˗ (1/μ²) P e ^μπ^/2

Put the values of N_A and N_B into (2) and solve for P.

The result is: P = μ W e ^{˗ μπ/2} Note this result checks dimensionally.