Energy Conservation and Spring Compression

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To launch a marble horizontally at 150 cm/s, the spring must be compressed more than the initial 10 cm used for 75 cm/s. The relationship between speed and energy indicates that kinetic energy increases with the square of the speed, suggesting that the spring's compression must be increased significantly. Doubling the speed requires four times the kinetic energy, which relates to the potential energy stored in the spring. The discussion emphasizes the importance of understanding energy conservation principles rather than simply guessing relationships between speed and height. Proper calculations involving energy are essential for solving the problem accurately.
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Homework Statement


If a particular spring is compressed 10 cm, it can launch a marble horizontally at 75 cm/s. How much must it be compressed to launch the marble horizontally at 150 cm/s?

Homework Equations

The Attempt at a Solution


My guess is that the spring force needs to be doubled in order for the marble to reach double the height. Is this right? I feel like this is way too simple for my physics professor to put on an exam. I feel like there has to be something else like equations to try and solve this.
 
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It's always simple to guess an answer. What about trying to work it out?
 
There are several different ways to work this out. For example, if you know the force applied by the spring at each amount of compression, x, you can calculate the acceleration and so the speed as it leaves the spring. Or, if you know the potential energy of a spring at a given compression then you can calculate the kinetic energy when all that energy is converted from potential to kinetic energy and so get the speed.
 
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NkaujHelp said:

Homework Statement


If a particular spring is compressed 10 cm, it can launch a marble horizontally at 75 cm/s. How much must it be compressed to launch the marble horizontally at 150 cm/s?

Homework Equations

The Attempt at a Solution


My guess is that the spring force needs to be doubled in order for the marble to reach double the height. Is this right? I feel like this is way too simple for my physics professor to put on an exam. I feel like there has to be something else like equations to try and solve this.
The question asks about doubling the speed, but in your 'attempt' you mention doubling the height. If you think one implies the other then you are wrong. Also, it does say horizontally, so I'm not sure how height would come into it.
As Halls suggests, think about energy. How do doubled compression, doubled speed and doubled height relate to energy?
 

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