Question

Tarzan who weighs 688N,swings from a cliff at the end of a vine 18m long . From the top of the cliff to the bottom of the swing, he descends by 3.2m and should not exceed 950N. If the vine breaks,what is the greatest force on it during the swing?

Answer 1

The greatest force is 244.6 N at the bottom of the swing. The question doe not make sense. If the vine breaks then it must exceed 950 N.

Check the answer by @AO8. I have not added the weight of Tarzan at the bottom of the swing.

Explanation:

The weight of Tarzan = 688 N

To get his mass:

`sf(mg=688" "N)`

`:.` `sf(m=688/g=688/9.81=70.13color(white)(x)"kg")`

The change in his potential energy will appear as kinetic energy at the bottom of the swing.

`:.` `sf(cancel(m)gDeltah=1/2cancel(m)v^2)`

`:.` `sf(v^2=2gDeltah)`

`sf(v=sqrt(2gDeltah)`

`sf(v=sqrt(2xx9.81xx3.2)=sqrt(62.78)=7.923color(white)(x)"m/s")`

The centripetal force is given by:

`sf(F=(mv^2)/(r))`

`:.` `sf(F=(70.13xx7.923^2)/(18)=244.6color(white)(x)N)`

Check the answer by @A08. I have neglected to add the weight of Tarzan to the centripetal force.

This is an oddly worded question as the vine should not break.

Answer 2

Vine does not break,
greatest force`=932.6N`

Explanation:

We know that for an object of mass `m`, moving with a linear velocity `v` in a circle of radius `r`
Centripetal force`=(mv^2)/r` .....(1)

As shown in the figure above, change in potential energy `=mgDeltah`
has been converted in the kinetic energy of Tarzan.
Kinetic energy `1/2mv^2=mgDeltah`
`=>v^2=2gDeltah` ....(2)
We see that velocity is maximum at the bottom of swing.

Also due to movement in a circle there must be a net
force pointing towards the center of the circle to provide the centripetal force. If `T` is tension in the vine at the bottom of swing then
`T-"Weight of Tarzan "W="Centripetal force"` ....(3)

From (1)
`T=mg+(mv^2)/r`
Using (2)
`T=688+(mxx2gDeltah)/r`
Inserting given values
`T=688+(2xx688xx3.2)/18`
`=>T=932.6N`
We see that this tension is less than the breaking capacity of vine given as `950N`

Hence vine does not snap.