How much work is done by friction in this process?

[Jayhawk1]

Really not understanding this problem... A 32.4 kg child descends a slide 5.63 m high and reaches the bottom with a speed of 3.54 m/s. How much work is done by friction in this process?

 

[Pseudo Statistic]

I guess it's something like 32.4(9.81) and you get the downward force.. and then do (3.54)^2 = 0^2 + 2a(5.63) and see what the acceleration was, in reality, and then multiply the acceleration you get there by the mass and then subtract the second force you got from the first one..
I think that's it, but I might be wrong.. try it out.
It would also help to draw an FBD... though I have no clue how it helps.
Good luck.

 

[Jayhawk1]

..Hmmm that doesn't seem to work, maybe I just don't understand what you are trying to tell me about the subtraction part?

 

[cepheid]

Okay...let's do this step by step. I'm assuming you know what is meant by friction on the slide. First look at a simpler case. If there were no friction, what forces would be acting on the child?

P.S. Always draw a free body diagram. It's extremely useful, I would even say essential, because it allows you to account for exactly what forces (all of them) that are acting on the body in question (the child in this case), so that you can determine its motion.

 

[HallsofIvy]

PseudoStatistic: don't just throw numbers at it!

jayhawk1: what he did was calculate the child's potential energy at the top of the slide- mass times height- then calculate the child's kinetic energy at the bottom- 1/2 mass time speed squared. Since the potential energy is 0 at the bottom, if there were no friction, the kinetic energy there would be exactly the same as the potential energy at the top.
But because of friction, the kinetic energy at the bottom is less than the potential energy at the top- the difference is the work done by friction.

 

[dextercioby]

After identifying the forces acting on the child,you need to know one equation.The one stated in the the theorem of variation of KE.

\Delta KE=W

,where W is the work done by all forces acting on the body.Since normal reaction from the incline & normal component of gravity produce 0 displacement,the work done by them is 0.You're lef just with the work done by friction and by the tangential component of gravity.

Daniel.