A spring with spring constant k is positioned vertically and then compressed fro

Question

A spring with spring constant k is positioned vertically and then compressed from its equilibrium length by a distance ?y (Figure 1) . A ball of mass m is placed on top of the spring, and is launched into the air when the spring is released (this setup is similar to the projectile launcher seen earlier in the semester). The ball travels to a maximum height hmax.

Figure 1:

http://session.masteringphysics.com/problemAsset/1000231061/8/spring2.jpg

1) Using the Work-Kinetic Energy theorem, determine hmax  in terms of the given variables and any other constants you deem necessary.

2) Using the Work-Kinetic Energy theorem, write an expression for the speed of the ball v at y = 0 in terms of the given variables and any other constants you deem necessary.

3) Using constant acceleration kinematics, write an expression for hmax as a function of v and g.

A spring with spring constant k is positioned vertically and then compressed from its equilibrium length by a distance (Figure 1) . A ball of mass m is placed on top of the spring, and is launched into the air when the spring is released (this setup is similar to the projectile launcher seen earlier in the semester). The ball travels to a maximum height hmax.

Explanation / Answer

1) 1/2 k dy^2 - m g dy = m g h

h = k dy^2/( 2 mg) - dy

2) 1/2 k dy^2 - m g dy = 1/2 mv^2

k/m dy^2 - 2 mg dy = v^2

v = sqrt( k/m dy^2 - 2 m g dy)

3) v^2 = v0^2 - 2 gy

h = v^2/2g

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