Energy Conversion Problem

In summary, the problem involves a 100 kg acrobat falling from a 10 m high platform and encountering a 1 m long spring after falling 9 m. The spring constant is solved for by setting the gravitational potential energy equal to the spring potential energy and solving for k, which results in 1.96 * 10^4 N/m. The acrobat will reach the same height above the ground after being launched by the rebounding spring due to energy conservation. However, there may be a loss of energy due to friction or the spring not fully extending, which could cause the acrobat to have a longer fall.
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Homework Statement



A very short 100 kg acrobat steps off a 10 m high platform and
starts falling. The acrobat falls 9 m, then encounters a 1 m long
spring connected at one end to the ground below. (a) What’s the
spring constant so the acrobat just touches the ground (that is, so the
spring contracts 1 meter)? The spring-with-acrobat system rebounds
and launches the acrobat back into the air. (b) How high off the
ground does the acrobat go above the ground before falling back?


Homework Equations



(1/2)k(x-x0)^2
mgΔh

The Attempt at a Solution



To solve this, wouldn't one set the gravitational potential energy (mgh) to the spring potential energy (1/2kx^2) because the energy converts to one another, then solve for k? 1.96 * 10^4 N/m is the answer I got.

For the second part of the problem, the acrobat will be the same exact height above the ground because the energy is conserved, right?

Am I missing something in this problem? This was unexpectedly simple.
 
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  • #2
You are on the right track, but be careful: you wrote Δh in the second formula, not h. What is the difference in this case?

Part two seems to be that simple, unless I'm also missing something :)
Let's hope for the acrobat that there is some loss due to friction (or the spring won't fully extend after having been crushed to length 0) otherwise it may be a long evening for him!
 
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1. How is energy converted from one form to another?

Energy conversion involves transforming one type of energy into another. This can be done through various processes such as mechanical, thermal, chemical, or electrical conversions. For example, a wind turbine converts kinetic energy from the wind into electrical energy.

2. What are the different types of energy conversion?

There are several types of energy conversion, including mechanical, thermal, chemical, and electrical. Mechanical energy conversion involves converting kinetic energy to potential energy or vice versa. Thermal energy conversion involves converting heat energy to mechanical or electrical energy. Chemical energy conversion involves converting chemical energy to thermal or electrical energy. Electrical energy conversion involves converting electrical energy to other forms of energy or vice versa.

3. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but it can be converted from one form to another. This means that the total amount of energy in a closed system remains constant. In other words, energy can be transformed, but the total amount of energy in the system remains the same.

4. How is energy efficiency calculated?

Energy efficiency is calculated by dividing the useful energy output by the total energy input. This gives a percentage that represents how much of the input energy is converted into useful output energy. For example, if a device requires 100 Joules of energy input and produces 80 Joules of useful output energy, the efficiency would be 80%. The higher the efficiency, the more energy is converted into useful work.

5. What are some real-life examples of energy conversion?

Energy conversion is a fundamental process that occurs in our daily lives. Some common examples include a car engine converting chemical energy from gasoline into mechanical energy, a light bulb converting electrical energy into light and heat energy, and a power plant converting thermal energy from burning fossil fuels into electrical energy. Other examples include solar panels converting light energy into electrical energy and our bodies converting chemical energy from food into mechanical energy to move our muscles.

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