Conservation of Energy of a sled

[chubbyorphan]

Homework Statement

A kid on a sled slides down a hill from a rest position.
m=47.0kg
vertical displacement is 10.0m

Homework Equations

a)For total mechanical energy I calculated (Egravity=mgh) to equal 46 x 10^2 J

b)*mentions we assume there is no friction or external pushes*
and for speed at the bottom of the hill I used (W = Ekf - Eki) to get 14m/s
I'm pretty confident these answers ^ are right but if someone wanted to double check them that'd be really cool, but what I'm really trying to check is what's next:

The Attempt at a Solution

The final question asks..
'the child's actual speed at the bottom of the hill is 5.0m/s. explain whether or not this defies the conservation of energy'

my thoughts are yes.. because assuming there is no friction or external pushes.. for the speed at the bottom of the hill to be 5.0m/s we've lost energy we can't account for.
Can someone please tell me if I'm right?

also.. an example question in the book mentions 'a 55.0kg cyclist rides off the edge of a 5.0m high cliff with a speed of 15m/s'
.. then the sample answer says that 'the cyclist's gravitational potential energy is 2700 J and his kinetic energy is 6188 J'

does this mean that his total mechanical energy is the addition of these two figures? I'm thinking yes.. is that right?

Thanks in advance for any help!

 

[PhanthomJay]

Homework Statement

A kid on a sled slides down a hill from a rest position.
m=47.0kg
vertical displacement is 10.0m

Homework Equations

a)For total mechanical energy I calculated (Egravity=mgh) to equal 46 x 10^2 J

b)*mentions we assume there is no friction or external pushes*
and for speed at the bottom of the hill I used (W = Ekf - Eki) to get 14m/s
I'm pretty confident these answers ^ are right but if someone wanted to double check them that'd be really cool, but what I'm really trying to check is what's next

looks good

The final question asks..
'the child's actual speed at the bottom of the hill is 5.0m/s. explain whether or not this defies the conservation of energy'

my thoughts are yes.. because assuming there is no friction or external pushes.. for the speed at the bottom of the hill to be 5.0m/s we've lost energy we can't account for.
Can someone please tell me if I'm right?

since total (not mechanical) energy is always conserved, apparently this part of the problem assumes that friction and air resistance IS present...

also.. an example question in the book mentions 'a 55.0kg cyclist rides off the edge of a 5.0m high cliff with a speed of 15m/s'
.. then the sample answer says that 'the cyclist's gravitational potential energy is 2700 J and his kinetic energy is 6188 J'

does this mean that his total mechanical energy is the addition of these two figures? I'm thinking yes.. is that right?

yes, you are correct that his initial mechanical energy is the sum of those 2 numbers.

 

[chubbyorphan]

shweet, thanks PhantomJay!
back to when you said:

since total (not mechanical) energy is always conserved, apparently this part of the problem assumes that friction and air resistance IS present...

..okay makes sense.. But.. if friction and air resistance was NOT present for this part of the problem, then it would be defying the law of conservation of energy.. right?

 

[chubbyorphan]

also, could you clarify the difference between total and mechanical energy? Total energy is all energy within a system. Mechanical energy is energy that is.. still useable for an object in focus within a scenario?
thats just my rough guess.. if you could elaborate a little more or correct me if I'm wrong that'd be great!

 

[cepheid]

Total energy is all energy within a system.

Yes

Mechanical energy is energy that is.. still useable for an object in focus within a scenario?
thats just my rough guess.. if you could elaborate a little more or correct me if I'm wrong that'd be great!

Mechanical energy is specifically defined as the sum of kinetic energy and potential energy.

 

[PhanthomJay]

shweet, thanks PhantomJay!
back to when you said:

since total (not mechanical) energy is always conserved, apparently this part of the problem assumes that friction and air resistance IS present...

..okay makes sense.. But.. if friction and air resistance was NOT present for this part of the problem, then it would be defying the law of conservation of energy.. right?

Well, mechanical energy does not have to be conserved, which means that friction and air resistance or some other force which does work MUST be present to account for the mechanical energy loss. Total energy (including especially heat energy) is always conserved . So the question doesn't make much sense if you assume there are no other forces present which do work.

 

[chubbyorphan]

Cepheid, Phantom Jay, can't thank you two enough! I'm understanding this stuff way more now :D