A cork gun contains a spring whose spring constant is 13.0 N/m. The spring is co

Question

A cork gun contains a spring whose spring constant is 13.0 N/m. The spring is compressed by a distance DeltaX = 9.2 cm and used to propel a cork of mass 3.14 g from the gun. Assuming the cork is released when the spring passes through its equilibrium position (Xeq), what is the speed of the cork as it is released from the spring? Suppose now that the cork temporarily sticks to the spring, causing the spring to extend 4.5 cm beyond its equilibrium position before separation occurs. What is the speed of the cork as it is released from the spring in this case?

A cork gun contains a spring whose spring constant is 13.0 N/m. The spring is compressed by a distance DeltaX = 9.2 cm and used to propel a cork of mass 3.14 g from the gun. Assuming the cork is released when the spring passes through its equilibrium position (Xeq), what is the speed of the cork as it is released from the spring? Suppose now that the cork temporarily sticks to the spring, causing the spring to extend 4.5 cm beyond its equilibrium position before separation occurs. What is the speed of the cork as it is released from the spring in this case?

Explanation / Answer

first case:
using work- energy theorem ,

mv^2 /2 = kx^2 /2

0.00314 * v^2 /2 = 13 * 0.092^2 /2

v = 5.92 m

second case :

mv^2 /2 = kx1^2 /2 - kx2^2 /2

0.00314v^2 = 13 * 0.092^2 - 13 x 0.045^2   

v =5.16 m/s

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