Chapter 06, Problem 027 Body A in the figure weighs 93 N, and body B weighs 66 N

Question

Chapter 06, Problem 027 Body A in the figure weighs 93 N, and body B weighs 66 N. The coefficients of friction between A and the incline are ,- 0.57 and 0.23. Angle is 49°. Let the positive direction of an x axis be up the incline. What is the acceleration of A if A is initially (a) at rest, (b) moving up the incline, and (c) moving down the incline? Frictionless massless pulley (a) Number (b) Number (c) Number Click if you would like to Show Work for this question: Units Units Units Open Show Work

Explanation / Answer

a] Suppose A moves up the incline m2g - T = m2a

T - m1 g sin theta - um1 g cos theta = m1a

a*(m1+m2) = m2g - m1g sin theta - um1g cos theta

a = [66 - 93 sin 49 degree - 0.57*93*cos 49 degree]/[93/9.8 +66/9.8]

= -2.44 m/s^2, this contadicts our supposition

If blocks move downward, a= [-66 + 93 sin 49 degree - 0.57*93*cos 49 degree]/[93/9.8 +66/9.8] = -1.88 m/s^2

which is still negative. So block A will be at rest.

a = 0 m/s^2

b] Here kinetic friction will act downward

a = [66 - 93 sin 49 degree - 0.23*93*cos 49 degree]/[93/9.8 +66/9.8]

= -1.123 m/s^2

c] Here kinetic friction will act upward

a =  [66 - 93 sin 49 degree + 0.23*93*cos 49 degree]/[93/9.8 +66/9.8]

= 0.607 m/s^2

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