A box of mass m is being pulled by a rope as shown. The force Fin the rope as a function of x can be calculated from the equations:

where N and μ are the normal force and friction coefficient between the box and surface, respectively. Consider the case where m = 18 kg, h = 10 m, μ = 0.55, and g = 9.81 m/s2.
(a) Use MATLAB to derive an expression for F, in terms of x, h, m, g, and μ·
(b) Use the subs command to substitute m = 18kg, h = 1 0 m, μ = 0.55, and g = 9.81 m/s2 into the expressions that were derived in part (a). This will 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 x starting at 5 and ending at 30 m.
(d) Determine the distance x where the force that is required to pull the box is the smallest, and determine the magnitude of that force.

r+h2