Problem Involving The Conservation Of Energy

In summary, a 51.1 kg child slides down a water slide with a velocity of 0.9 m/sec at the top. At the bottom of the slide, she is moving horizontally, y=2.5 meters above the water. She splashes into the water d=3 meters to the left of the bottom of the slide. The potential energy of the child is zero at the water's surface, so that's where her mechanical energy is at. When she found that her mechanical energy was 1704J, she realized that she was solving for the height of the slide rather than for the total height.
  • #1
Pat2666
33
0
I have another problem I need some help with.

Here's the problem :

A 51.1 kg child slides down a water slide with a velocity of 0.9 m/sec at the top. At the bottom of the slide, she is moving horizontally, y=2.5 meters above the water. She splashes into the water d=3 meters to the left of the bottom of the slide.
--------------------------------------------------------------------------------
a) Assuming potential energy to be zero at the water level, what is the mechanical energy of the child at the top of the slide?
MEo= J
1704 J
--------------------------------------------------------------------------------
b) How high is the top of the slide above the bottom of the slide?

As shown I was able to find out the mechanical energy of the child at the top of the slide (1704J) but I can't seem to figure out how to solve for the height of the slide.

I would have thought that you just set KE + PE = 1704 and solve for h, which I did and got 3.36m, but it isn't the right answer :(

So I did .5(51.1kg)(.9m/s)^2 + 51.1kg(9.81m/s^2)h = 1704J

I'm stumped as I don't see any other way of solved for the height. Any help would be appriciated. :)
 
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  • #2
Hi Pat2666,

The potential energy is zero at the water's surface, so that's where h=0 at. So when you found that h=3.36m, that means the slide is that far above the water's surface.

However, although that will help to answer part b, that's not quite what part b was asking for.
 
  • #3
Well it's not really asking for the total height is it? Just the height of the top of the slide to the end of it no? I tried adding 3.36m to the 2.5m above water just to see if I misread the question, but it was still wrong.
 
  • #4
The top of the slide is 3.36 m above the water, the bottom of the slide is 2.5 meters above the water. The question is asking for how far the top of the slide is above the bottom of the slide. What would that be?
 
  • #5
OMG I'm so dumb! Thank you lol

I kept thinking that what I was solving for was h, rather than h + the additional height.

Thanks so much! I've been working on this problem forever!
 
  • #6
Sure, glad to help!
 

1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another.

2. Why is the conservation of energy important?

The conservation of energy is important because it is a fundamental principle of physics that helps us understand and predict the behavior of energy in various systems. It also helps us make practical decisions about how we use and conserve energy in our daily lives.

3. What are some real-life examples of the conservation of energy?

Some real-life examples of the conservation of energy include a pendulum swinging back and forth, a roller coaster moving from a high point to a low point, and a light bulb producing light and heat from electrical energy.

4. How does the conservation of energy relate to the first law of thermodynamics?

The first law of thermodynamics is a specific application of the law of conservation of energy, stating that the total energy of a closed system remains constant. This means that in any process, the total energy of the system before and after the process must be the same.

5. Are there any exceptions to the law of conservation of energy?

There are no known exceptions to the law of conservation of energy. However, in some cases, it may seem like energy is being created or destroyed, but it is actually being converted into a different form that is not easily measured or observed.

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