Question

Question #32114

Answer 1

According to conservation of energy, the final velocity will be

`v_f=sqrt(v_i^2+2gh-(2fl)/m)`

Explanation:

This problem is best done using conservation of energy methods.

There will be three terms in the expression, as there are three different energy changes that occur - kinetic, potential and frictional heating (shown in that order in the equations below).

`DeltaK+DeltaU+DeltaE = 0`

Using the symbols given in the problem

`1/2mv_f^2-1/2mv_i^2-mgh+fl = 0`

where the middle term for the potential energy is subtracted because this will be an energy decrease.

We now rearrange the make `v_f` the subject of the expression

`1/2mv_f^2 = 1/2mv_i^2+mgh-fl`

Multiply each term by 2 and divide each by `m`

`v_f^2=v_i^2+2gh-(2fl)/m`

and finally

`v_f=sqrt(v_i^2+2gh-(2fl)/m)`