# Conservation of Energy 2

## Homework Equations

Total Energy = Kinetic Energy + Potential Energy
T.E = 1/2mv^2 + m(g)(h)

## The Attempt at a Solution

Distance Child travels
Sin 30 = 4/ x
x = 8m

T.E at top
= 1/2mv^2 + m(9.8)(h)
= 40m

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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.

40m = 1/2mv^2 + 1/4m
v = 12.6 - m

is this correct?

And I dont know how to calculate the mass.

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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)

This is what I got:
40m-1/4*(m)*8m= 1/2mv^2
40m - 2m = 1/2mv^2
76m / m = v^2
v = 8.7 m/s

Question stated that friction is 1/4m not 1/4mg. Or is it suppose to be 1/4mg?

hage567
Homework Helper
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.

This is what I got now:
40m-1/4*(m)*8m= 1/2mv^2
40m - 20m = 1/2mv^2
20m / m = v^2
v = 4.47 m/s

hage567
Homework Helper
Where did the 1/2 from the kinetic energy go? You dropped it in the second last line.

O ya thanks I forget to multiply by 2.

This is what I got now:
40m-1/4*(m*g)*8m= 1/2mv^2
40m - 20m = 1/2mv^2
40m / m = v^2
v = 6.3 m/s

hage567
Homework Helper