Elastic potential energy question

AI Thread Summary
The discussion revolves around calculating the potential energy stored in a slingshot's rubber band when launching a 10-g pebble to a height of 22.0 meters. It confirms that the elastic potential energy of the slingshot is equal to the gravitational potential energy of the pebble at its peak height, assuming no energy loss. The conversation also touches on the relationship between elastic potential energy and kinetic energy, noting that the pebble's speed on descent matches the speed imparted by the slingshot's energy. Participants clarify that knowing the stretch distance and the spring constant (k) would allow for calculating elastic potential energy directly. Overall, the thread concludes with a clear understanding of the energy transfer involved in the slingshot mechanism.
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A slingshot will shoot a 10-g pebble 22.0 straight up. How much potential energy is stored in the slingshot's rubber band?

the solution is U = mgy = (10 g)(9.8 m/s^2)(22.0 m) according to the book.

does this mean the potential energy of the slingshot's rubber band is equal to the gravitational potential energy of the pebble? does it also mean the speed of the ball as it comes down is equal to its speed driven by the elastic potential energy of the slingshot's rubber band given air resistance is negligible? i don't get the solution since getting the "U sub el" requires distance from point where the rubber is stretched to the point where it is relaxed times the "k" constant and 1/2. i don't know how to get "k" and "how far it is stretched". yet the solution suggests otherwise. please enlighten me with this problem...
 
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Assuming there is no dissipation (i.e. the rubber band doesn't heat up, no air resistance, etc), then you are correct. The elastic energy is equal to the amount of kinetic energy imparted to the pebble, enabling it to rise 22.0 (units?).
 
Andy Resnick said:
Assuming there is no dissipation (i.e. the rubber band doesn't heat up, no air resistance, etc), then you are correct. The elastic energy is equal to the amount of kinetic energy imparted to the pebble, enabling it to rise 22.0 (units?).

what if we can get the distance from the stretched point to the relaxed point of the slingshot and the k constant is given, can we get the same answer? also, could you please answer the 2nd question in my first post? thanks
 
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never mind..it's crystal clear now. thanks a lot!
 
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