Conservation of Energy of a slide

In summary, the child slides without friction from a height h along a curved water slide. She is launched from a height h/5 into the pool. Her maximum airborne height is y in terms of h and η.
  • #1
hlha227
4
0

Homework Statement


A child slides without friction from a height h along a curved water slide (Fig. P5.44). She is launched from a height h/5 into the pool. Determine her maximum airborne height y in terms of h and η. (Use q for η and h as appropriate.)
p5_44.gif
(Fig. P5. 44)

Homework Equations


I know you use conservation of energy to solve the problem but I just am completely lost on where to start at right now...
which is: mgh = 1/2mv^2

The Attempt at a Solution


I don't know where to begin that's my problem... could I just get some help getting started possibly?
 
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  • #2
Here's a hint. This is a sequence to two separate problems.
Problem 1. She slides from a height h to a height h/5. What is her launch speed?
Problem 2. She is launched as a projectile with the speed determined in Problem 1 and at a launch angle theta. What is the maximum height of her trajectory?

Chet
 
  • #3
Problem 1.) The launch speed would just be 0, correct? Or am I just totally missing something here...
 
  • #4
hlha227 said:
Problem 1.) The launch speed would just be 0, correct? Or am I just totally missing something here...
You're missing something. If the girl's elevation decreases by a distance 4h/5, her potential energy decreases, so her kinetic energy (determined by her speed) must increase.

Have you ever been down a water slide? If so, was your speed zero when you shot out the bottom of the slide?

Chet
 
  • #5
Oh, the bottom... whoops, I was thinking from the start...
so h-h/5? Maybe?
 
  • #6
hlha227 said:
Oh, the bottom... whoops, I was thinking from the start...
so h-h/5? Maybe?
I don't understand what you're asking.
 
  • #7
Am I getting somewhere with (h-h/5)?
 
  • #8
That would depend on how you plan to use it ... It is the vertical distance between the top and end of the slide. What does this imply?
 
  • #9
Use the law of conservation of energy:
[itex] mgh_1 + \frac{1}{2} mv_1 ^ 2 = mgh_2 + \frac{1}{2} mv_2 ^ 2 [/itex]
At the top of the slide she has a velocity of zero, she starts at position 'h' and ends at position 'h/5', so solve for velocity and then apply the law of conservation of energy again, remembering that her horizontal velocity will be constant
 
  • #10
Phase 1, calculating the release velocity :
Even though the girl hits the bottom of the slide then rises again, the crucial dimension is the height difference between the top of the slide and the exit point from the slide ( 0.8 h)
 
  • #11
hlha227 said:
Am I getting somewhere with (h-h/5)?
You are getting warm. We're looking for the change in energy associated with that change in height.
 

What is the conservation of energy?

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

How does the conservation of energy apply to a slide?

In the context of a slide, the conservation of energy means that the total amount of energy at the top of the slide (potential energy) is equal to the total amount of energy at the bottom of the slide (kinetic energy). This is because energy is transferred from potential energy to kinetic energy as the person slides down.

What factors affect the conservation of energy on a slide?

The main factors that affect the conservation of energy on a slide are the height and angle of the slide, the weight and speed of the person sliding, and any friction or resistance on the slide. These factors can impact how much potential energy is converted into kinetic energy.

Why is understanding the conservation of energy important in regards to slides?

Understanding the conservation of energy on a slide is important because it allows us to predict and explain the behavior of objects on the slide. It also helps us design safer and more efficient slides by considering factors that can affect the conservation of energy, such as the slope and surface of the slide.

How is the conservation of energy related to other laws of physics?

The conservation of energy is closely related to other laws of physics, such as the laws of motion and the law of gravity. The transfer and transformation of energy are governed by these laws and understanding the conservation of energy helps us understand and apply these laws in various situations.

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