Problems with Solutions - Mechanics II: Dynamics | ME 206, Assignments of Dynamics

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Problem 14.57 The crate is drawn across the floor by a winch that retracts the cable at a constant rate of 0.2 m/s. The crate’s mass is 120 kg, and the coefficient of kinetic friction between the crate and the floor is jz, = 0.24. (a) At the instant shown, what is the tension in the cable? (b) Obtain a “quasi-static” solution for the tension in the cable by ignoring the crate’s acceleration. Compare this solution with your result in (a). Solution: dt? Nowe tha? +07? = 22, ao” = 22% wna oth fay’ (a) Note that b- + (2 = L*, so a ey ands fC #L fdLy 153+ (7) Setting b=4m, dL/dt =—0.2 ms and d?L/dt? =0, we obtain d2b/d!2 = —0.0025 nv/s?, The crate's acceleration toward the right is @ = 0.0025 mis, From the free-body diagram, Tsing+N—mg=0, (1) where @& obtain F arctan(2/4) = 26.6°. Solving Egs (1) and (2), we 82.3.N. (b) Solving Egs (1) and (2) with « = 0, we oblain [= 282.0 N. ly Problem 14.58 If y = 100 mm, = = 600 mm/s, and a ary = = —200 mnvs*, what horizontal force is exerted on dt* the 0.4 kg slider A by the smooth circular slot? Solution: The horizontal displacement is x? = R? — y*. Differen- alte twice with respect to time: a_i (4) +e c fdy\2 @y “dt dt’ \de dee -(2) “ (S): from which. ax Ly fpxy2 dy py dy See (=) (2741S 2) = ar ( :) () \F ) () de? d*Xx 2 Substitute: = = —1.3612 m/s” dr 4m 2 my | 300 mm FBD ME 206 - Prater Problem Set 4 Solutions Page 1/4