A box of mass m is being pulled by a ropeas shown. The force Fin the rope as a

Chapter 11, Problem 12

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A box of mass m is being pulled by a ropeas shown. The force Fin the rope as a functionof x can be calculated from the equations:-F Jx2X+ h2 +JlN=O-mg+N+F h = Jx2+ h2 0where N and Jl are the normal force and friction coefficient between the box and surface, respectively. Consider the case where m = 18 kg, h = 10 m,11 = 0.55, and g = 9.81 mJsz.(a) Use MATLAB to derive an expression for F, in terms of x, h, m, g, and ll(b) Use the subs command to substitute m = 18kg, h = 1 0 m, ll = 0.55,and g = 9.81 m/s2 into the expressions that were derived in part (a). Thiswill give the force as a function of the distance x.(c) Use the ezplot command to plot the force F as a function of x, for xstarting at 5 and ending at 30 m.(d) Determine the distance x where the force that is required to pull the box isthe smallest, and determine the magnitude of that force.