Answer
$14.6$ lb.
Work Step by Step
Step 1. Identify the given quantities: cart weight $W=40$ lb, incline angle $\theta=15^{\circ}$, angle of the rope $\alpha=60^{\circ}$ to the horizontal.
Step 2. Calculate the force components along the incline: by the cart $W_1=Wsin\theta=40sin15^{\circ}\approx10.35$ lb.
Step 3. Assume the force exert on the cart by the rope is $F$, its component along the incline is then given by $F_1=Fcos(60-15)^{\circ}\approx 0.707F$
Step 4. As the system is balanced, the above two forces need to be equal, which gives $0.707F=10.35$ and $F\approx14.6$ lb.
