# Homework Help: Question: "A child on a sled (m=47.0 kg) slides down a long hill "

1. Jul 24, 2014

### Jaimie

Hi,
I know this question has been posted before but could someone advise me if my answer for c) is accurate? I really want to make sure I understand how this works. The entire question is:

"A child on a sled (m=47.0 kg) slides down a long hill starting from a rest position at a point 10.0 m
higher in elevation than his finishing point.
a) What is the total mechanical energy present?
b) Assuming that there is no friction and no external pushes, determine the child's speed at the bottom of the hill.
c) The child's speed at the bottom of the hill is actually 5.0 m/s. Explain whether or not this defies the law of conservation of energy.

I've calculated both a) & b) as 4606 J and 14m/s respectively.
But I am having trouble with c). My answer is ...

"This does not defy the law of conservation of energy. The conservation of energy states that the total energy of an isolated system can be neither be created nor destroyed (remains constant) and must be converted into another form. It is defined by the equation Einitial = Efinal or ETOTAL = EG + EK, the latter of which refers to the total mechanical energy in the system in the absence of friction. In real life however, many situations including sliding along a surface, involve friction. Friction causes the conversion of the kinetic energy (EK) into thermal energy (ETH) or heat as opposed to it all being converted into kinetic energy. So the Efinal or ET would actually be equal the sum of Ek and ETH, where EG is equal to zero. This upholds the energy conservation law. As kinetic energy is directly proportional and depends on velocity (as per its equation Ek = 1/2mv2), by decreasing the velocity, we would be decreasing the amount of kinetic energy, where the loss of energy would be accounted for by thermal energy".

Thank you for your help.

2. Jul 24, 2014

### Simon Bridge

You are correct - but you have over-written your answer. You don;t need a lecture - just to show you understood what is going on.

"5m/s for the final speed is less than the 14m/s calculated; however, the calculation neglected friction and assumed all the initial energy was converted to kinetic, so this is expected. The result just means that some of the initial energy went elsewhere - probably via friction. (i.e. Heat, sound, etc)"

3. Jul 28, 2014

### Jaimie

Thank you Simon!

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