Conservation of energy

In summary, the problem involves a bungee jumper of mass 64.5 kg standing on a platform 48.0 m above a river. The unstretched bungee cord is 10.1 m long with a force constant of 65.5 N/m. The jumper falls from rest and just touches the water at a speed of zero, with the cord acting like an ideal spring. Using conservation of energy, the jumper's speed at a height of 12.5 m above the water on the first fall can be determined. The equation used is mgh = 1/2mv^2 + 1/2kx^2, with the substitution of incorrect values possibly leading to an incorrect answer. The
  • #1
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Homework Statement


A bungee jumper of mass 64.5 kg (including safety gear) is
standing on a platform 48.0 m above a river. The length of
the unstretched bungee cord is 10.1 m. The force constant
of the cord is 65.5 N/m. The jumper falls from rest and just
touches the water at a speed of zero. The cord acts like an
ideal spring. Use conservation of energy to determine the
jumper’s speed at a height of 12.5 m above the water on
the first fall.

Homework Equations


Ek=1/2mv^2
Ep=mgh
Ee=1/2kx^2

The Attempt at a Solution


so i did mgh = 1/2mv^2 + 1/2kx^2 and solve for v but somehow i am not getting the answer 6.3m/s
 
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  • #2
jasonbans said:

Homework Statement


A bungee jumper of mass 64.5 kg (including safety gear) is
standing on a platform 48.0 m above a river. The length of
the unstretched bungee cord is 10.1 m. The force constant
of the cord is 65.5 N/m. The jumper falls from rest and just
touches the water at a speed of zero. The cord acts like an
ideal spring. Use conservation of energy to determine the
jumper’s speed at a height of 12.5 m above the water on
the first fall.

Homework Equations


Ek=1/2mv^2
Ep=mgh
Ee=1/2kx^2

The Attempt at a Solution


so i did mgh = 1/2mv^2 + 1/2kx^2 and solve for v but somehow i am not getting the answer 6.3m/s

You may have substituted in some incorrect values, or you may have "mis-used" you calculator.

Show us your substitution / simplifications so we can see what went wrong.
 
  • #3
this is what i did
 

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  • #4
jasonbans said:
this is what i did

Two problems:

When 12.5 m above the water, the jumper has not descended 48m, so you h value is not appropriate, and the bungee has not been stretched 12.5 m, so your x value is not appropriate.
 
  • #5
12.5 above the water meaning 48 subtract 12.5 = 35.5m for the height?
i don't know how much it stretched by am i suppose to calculate it?
 
  • #6
thx got the answer now
 
Last edited:
  • #7
jasonbans said:
is the height 35.5 m and it stretched 25.5m right?

if it was 10.0 m long to start with it will have stretched 25.5m

edie: the h value is 35.5, yes. best called the change in height.
 

What is conservation of energy?

Conservation of energy is a fundamental law of physics that states that energy cannot be created or destroyed, but can only be transformed from one form to another.

Why is conservation of energy important?

Conservation of energy is important because it allows us to understand and predict how energy behaves in different systems. It also helps us to make more efficient use of energy and minimize waste.

How is energy conserved?

Energy is conserved through various processes such as friction, heat transfer, and energy conversion. In any closed system, the total amount of energy remains constant.

What are some examples of conservation of energy in everyday life?

Examples of conservation of energy in everyday life include the use of renewable energy sources, such as solar panels and wind turbines, to generate electricity, as well as the use of energy-efficient appliances and vehicles.

What are the implications of violating the law of conservation of energy?

The violation of the law of conservation of energy would lead to a breakdown of the fundamental laws of physics and cause the universe to behave in unpredictable ways. It would also have significant consequences on our daily lives, as energy would no longer be a reliable and consistent resource.

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