Elastic Potential Energy- finding spring constant

AI Thread Summary
To find the spring constant in the given physics experiment, the elastic potential energy of the spring must be calculated using the formula Us = 0.5kx^2, where x is the compression distance. The ball, when released, converts this potential energy into kinetic energy as it travels horizontally. To determine the velocity of the ball, the equations of motion for vertical and horizontal displacement can be used, specifically y = y_0 + v_{0,y}t - 0.5gt^2 and x = v_{0,x}t. The time of flight can be derived from the vertical motion, allowing for the calculation of the horizontal velocity. Understanding these relationships is crucial for solving the problem effectively.
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Homework Statement



In a physics lab experiment, a spring clamped to the table shoots a 22 g ball horizontally. When the spring is compressed 18 cm, the ball travels horizontally 5.2 m and lands on the floor 1.5 m below the point at which it left the spring.

Homework Equations



Us= .5kx^2

The Attempt at a Solution



I tried to find the elastic potential energy and then i got stuck.
 
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Use energy conservation. When the spring is compressed the ball is stationary so all its energy is elastic potential energy. When the spring is released the ball loses potential energy and gains kinetic energy.
 
how would i find the velocity?
 
With y=y_0+v_{0,y}t-\frac{1}{2}gt^2 and x=v_{0,x} t.
 

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