Question #32114

1 Answer
Dec 25, 2016

Answer:

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)#