Question

A cart weighing 40 pounds is placed on a ramp incline 15 degrees to the horizon. The cart is held in place by a rope inclined 60 degrees to the horizontal. find the force that the rope must exert on the cart to keep it from rolling down the ramp.

Answer 1

Answer: $14.64\ N$

Explanation:

Given

Inclination of ramp is $\theta=15^{\circ}$

Rope is inclined $\phi=60^{\circ}$ to the horizontal

Weight of cart $W=40\ lb$

from the diagram, rope is at angle of $45^{\circ}$ w.r.t ramp

Sine component of weight pulls down the cart Cosine component of force applied through rope held it at the position

$\Rightarrow 40\sin 15^{\circ}=F\cos 45^{\circ}\\\\\Rightarrow F=40\cdot \dfrac{\sin 15^{\circ}}{\cos 45^{\circ}}\\\\\Rightarrow F=40\times 0.366\\\Rightarrow F=14.64\ N$