Conservation of Energy 2

Conservation of energy only works for non-conservative forces! You could do E = Work_net = Work_conservative + Work_non-conservative, but going back to Newton's 2nd law should give an easier time.

 

well you're on the right track, and assume from your last calculation that you're rounding g to 10m/s^2.

TE at bottom=pe+ke where pe=0

however, there is energy lost in going from top to bottom in form of friction.

so TE at top=TE at bottom plus frictional energy. You are given a magnitude for friction and have computed the distance right, can you finish from here?

edit: this was more or less simultaneous post, I think its actually easier using energy eqn, but solveable from either approach.

 

closer. this is how I approached the problem, and always BTW much better to complete the algebra before posting numbers--both for purposes here and on an exam as a simple number mistake made early will cost dearly;

mgh=1/2mv^2+Ff*distance where Ff=frictional force

we know from problem, that frictional force = 1/4mg

so mgh-1/4*(mg)*8m= 1/2mv^2
(8m from your calculations involving length of slide)

 

The question said the frictional force was one quarter of the child's weight. Weight is m*g, expressed in newtons. So it should be (1/4)mg.

 

Where did the 1/2 from the kinetic energy go? You dropped it in the second last line.

 

I agree with that answer.