Spring Constant Force ????

Question

A pinball machine launches a 125 g ball with a spring-driven plunger. The game board is inclined at 7 degrees above the horizontal. Assume the plungers mass and frictional effects are negligible. The acceleration of gravity is 9.8 m/s2.

Find the force constant k of the spring that will give the ball a speed of 93 cm/s when the spring compressed 2 cm from its relaxed position. Answer in units of N/m

Answer 1

Using conservation of energy:

The spring potential energy will be released:
1/2*k*x^2
=.5*k*.02*.02
The ball will gain potential energy up the incline over the distance:
m*g*h
=.125*9.8*.02*sin(7)
The ball will also have kinetic energy
=1/2*m*v^2
=.5*.125*9.8^2
Setting up the conservatin of energy
.5*k*.02*.02=
.5*.125*9.8^2+.125*9.8*.02*sin(7)
k=6*2/(.02*.02)
=30,027N/m

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