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Spring Gun. A hydraulic press is used to compress a spring that will then be used to project a 21.0-kg steel ball. The system is similar,
at smaller in scale, to the car jack illustrated in Figure 11.14. In this case, the smaller cylinder has a diameter of d₁ -0.75 cm and has a
anually operated plunger. The larger cylinder has a diameter of d₂=9.5 cm, and its piston compresses the spring. The idea is that the
n operator pulls a lever that pushes the plunger on the small cylinder, which transmits a pressure to the larger piston that, in turn,
erts a force on the spring and compresses it. Once the spring is compressed, the steel ball is loaded and the spring is released,
ecting the ball.
If a force of 950 N is exerted on the primary (smaller) piston to compress the spring 1.15 m from its equilibrium (uncompressed)
sition, what is the spring constant k of the spring?
What is the velocity of the steel ball just after it is ejected?
Neglecting air resistance, what is the maximum range of this "spring gun"?

Sagot :

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