Help with elastic potential energy

AI Thread Summary
To find the speed of the dart as it leaves the toy, use the principle that elastic potential energy (Ee) equals kinetic energy (Ek). The formula for Ee is 1/2 k x^2, where k is the spring constant and x is the compression distance. The kinetic energy formula is 1/2 mv^2, where m is the mass of the dart. By equating these two energies and solving for v, you can determine the dart's speed using the provided values. This approach effectively utilizes the relationship between potential and kinetic energy in the context of the problem.
jbjohnybaker
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Homework Statement



A child's toy shoots a rubber dart of mass 7.8g, using a compressed spring with a force constant of 3.5 x 10^2 N/m. The spring is initially compressed 4.5cm. All the elastic potential energy is converted into kinetic energy of the dart.
What is the speed of the dart as it leaves the toy?


Homework Equations


Ee = Ek
Ee = 1/2 k x^2
Ek = 1/2 mv^2

The Attempt at a Solution


Ee = Ek
1/2 (3.5 x10^2)(?) = 1/2 (.0078)v^2 ??]
 
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jbjohnybaker said:

Homework Statement



A child's toy shoots a rubber dart of mass 7.8g, using a compressed spring with a force constant of 3.5 x 10^2 N/m. The spring is initially compressed 4.5cm. All the elastic potential energy is converted into kinetic energy of the dart.
What is the speed of the dart as it leaves the toy?


Homework Equations


Ee = Ek
Ee = 1/2 k x^2
Ek = 1/2 mv^2

The Attempt at a Solution


Ee = Ek
1/2 (3.5 x10^2)(?) = 1/2 (.0078)v^2 ??]
How much is the spring compressed?

http://www.physics247.com/physics-tutorial/spring-potential-energy.shtml"
 
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equating Ee to Ek is indeed the right way to go. I suggest writing that equation in symbols (not yet plugging in the numbers) and then solving for v.
You'll get an expression for v in terms of k (spring constant), m (mass of the dart) and x (initial compression of the spring), all of which are given.
Then you simply plug in the given values and compute the value for v.

Alex
 
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