A cork gun contains a spring whose spring constant is 11.0 N/m. The spring is co

Question

A cork gun contains a spring whose spring constant is 11.0 N/m. The spring is compressed by a distance delta-X = 9.5 cm and used to propel a cork of mass 7.66 g from the gun.

a.) 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?

b.) 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

Here

Loss in Potnteial Enrgy of Spring = Increase in kinetic energy

Therefore

0.5*k*x^2 = 0.5*m*v^2

0.5*11*(9.5*10^-2)^2 = 0.5*(7.66*10^-3)*v^2

v = 3.6 m/sec

==================================

Here

0.5*k*(x2^2 - x1^2) = 0.5*m*v^2

0.5*11*(0.095^2 - 0.045^2) = 0.5*(7.66*10^-3)*v^2

v = 3.17 m/sec

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