Conservation of Energy of a sled

In summary, a kid on a sled slides down a hill with a mass of 47.0kg and a vertical displacement of 10.0m. The total mechanical energy is calculated to be 46 x 10^2 J using the equation Egravity=mgh and assuming no friction or external pushes. The speed at the bottom of the hill is determined to be 14m/s using the equation W = Ekf - Eki. However, if the child's actual speed at the bottom of the hill is 5.0m/s, this would defy the conservation of energy as it would indicate a loss of energy that cannot be accounted for. The example of a 55.0kg cyclist riding off the edge of a
  • #1
chubbyorphan
45
0

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!
 
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  • #2
chubbyorphan said:

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.
 
  • #3
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?
 
  • #4
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!
 
  • #5
chubbyorphan said:
Total energy is all energy within a system.

Yes

chubbyorphan said:
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.
 
  • #6
chubbyorphan said:
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.
 
  • #7
Cepheid, Phantom Jay, can't thank you two enough! I'm understanding this stuff way more now :D
 

Related to Conservation of Energy of a sled

1. What is the conservation of energy principle?

The conservation of energy principle states that energy cannot be created or destroyed, only transferred or converted from one form to another. This means that the total amount of energy in a closed system remains constant.

2. How does the conservation of energy apply to a sled?

When a sled is in motion, it possesses both kinetic energy (energy of motion) and potential energy (energy due to its position). As the sled moves, this energy is transferred and converted between these two forms, but the total amount of energy remains the same.

3. What factors affect the conservation of energy of a sled?

The conservation of energy of a sled is affected by its mass, speed, and height. The greater the mass and speed of the sled, the more kinetic energy it possesses. The higher the sled is on a slope, the more potential energy it has.

4. How can friction affect the conservation of energy of a sled?

Friction is a force that opposes motion and can cause energy to be converted into other forms, such as heat. When a sled experiences friction, some of its kinetic energy is converted into heat, reducing the total amount of energy in the system. This can cause the sled to slow down or come to a stop.

5. Can the conservation of energy be violated?

No, the conservation of energy is a fundamental law of physics that has been observed and tested in countless experiments. While energy can be transferred and converted, it cannot be created or destroyed. Any apparent violations of this principle are due to incomplete understanding or measurement errors.

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