Question

An inclined plane is 5.00 m long and 3.00 m high. What is the ideal mechanical advantage of this machine?

1.00 , 2.00, 1.67 , or 2.50

? :/

Answer 1

here is my reasoning:

in order to lift the box, if I use the inclined plane, I apply the subsequent force:
\[F = mg\sin \theta \]

Answer 2

:) yes

Answer 3

whereas if I don't use the inclibed plane I apply this force:
\[R = mg\]
namely the weight of the box

Answer 4

so the advantage is given by the ratio R/F, namely:
\[\frac{R}{F} = \frac{{mg}}{{mg\sin \theta }} = \frac{1}{{\sin \theta }}\]

Answer 5

ok:)

Answer 6

now, what is sin(\theta) ?

Answer 7

it is simple, here is its value:
\[H = L\sin \theta ,\quad \sin \theta = \frac{H}{L}\]

Answer 8

where H is the height of the inclined plane, where L is its length

Answer 9

so, replacing that expression into the formula for R/F, we get:
\[\frac{R}{F} = \frac{{mg}}{{mg\sin \theta }} = \frac{1}{{\sin \theta }} = \frac{L}{H}\]

Answer 10

okay! so what do we plug in? :/

Answer 11

lenght and height

Answer 12

here is the next step:
\[\frac{R}{F} = \frac{L}{H} = \frac{5}{3}\]

Answer 13

ohh so we get 1.66666 so our solution is 1.67?

Answer 14

correct!

Answer 15

yay! thank you!

Answer 16

:)