Question

A small branch is wedged under a 200 kg rock and rests on a smaller object. The smaller object is 2.0 m from the large rock and the branch is 12.0 m long.

(a) If the mass of the branch is negligible, what force must be exerted on the free end to just barely lift the rock?
(b) What is the mechanical advantage of this lever system?

Answer 1

a

`F =326.7 \ N`

b

`M = 6`

Step-by-step explanation:

From the question we are told that

The mass of the rock is
`m_r = 200 \ kg`

The length of the small object from the rock is
`d = 2 \ m`

The length of the small object from the branch
`l = 12 \ m`

An image representing this lever set-up is shown on the first uploaded image

Here the small object acts as a fulcrum

The force exerted by the weight of the rock is mathematically evaluated as

`W = m_r * g`

substituting values

`W = 200 * 9.8`

`W = 1960 \ N`

So at equilibrium the sum of the moment about the fulcrum is mathematically represented as

`\sum M_f = F * cos \theta * l - W cos\theta * d = 0`

Here
`\theta` is very small so
`cos\theta * l = l`

and
`cos\theta * d = d`

Hence

`F * l - W * d = 0`

=>
`F = (W * d)/(l)`

substituting values

`F = (1960 * 2)/(12)`

`F =326.7 \ N`

The mechanical advantage is mathematically evaluated as

`M = (W)/(F)`

substituting values

`M = (1960)/(326.7)`

`M = 6`