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`

Step-by-step 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 (\sin 15^(\circ))/(\cos 45^(\circ))\\\\\Rightarrow F=40* 0.366\\\Rightarrow F=14.64\ N`