Chapter 11, Problem 12P

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

$\begin{array}{l}-F\frac{x}{\sqrt{x^2+h^2}}+\mu N=0\\ -mg+N+F\frac{h}{\sqrt{x^2+h^2}}=0\end{array}$

where N and µ are the normal force and friction coefficient between the box and surface, respectively. Consider the case where m = 18kg, 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 = 18 kg, h = 10 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.