Question

Suppose you need to remove a nail from a board by using a claw hammer. What is the input distance for a claw hammer if the output distance is 2.0 cm and the mechanical advantage is 5.5?

Answer 1

`d_i = 11.0\ cm`

Step-by-step explanation:

It is given that,

Output distance of claw hammer is
`d_o=2.0 \ cm`

And mechanical advantage of claw hammer, m = 5.5

We need to find the input distance for a claw hammer.

The mechanical advantage of claw hammer is given by the ratio of input distance for a claw hammer to its output distance:

`m=(d_i)/(d_o)` ....equation 1.

Now, putting values of
`d_o` and m in equation 1.

`5.5=(d_i)/(2.0)`

`d_i = 5.5* 2.0 = 11.0\ cm`

Therefore value of input distance is 11.0 cm.Hence this is the required solution.

Answer 2

The system in the problem can be assimilated to a simple lever. The mechanical advantage (MA) of a lever is

`MA= (d_i)/(d_o)`
where
`d_i` is the distance of application of the input force with respect to the fulcrum, and
`d_o` the distance of the output force from the fulcrum.
In our problem, MA=5.5 and
`d_o = 2.0 cm`. So we can find the input distance:

`d_i = MA \cdot d_o = 5.5 \cdot 2.0 cm =11.0 cm`