A hydraulic press is used to compress a spring that will then be used to project a 25.0-kg steel ball. The system is similar, but 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 manually operated plunger. The larger cylinder has a diameter of d₂ = 10.0 cm, and its piston compresses the spring. The idea is that the gun operator pulls a lever that pushes the plunger on the small cylinder, which transmits a pressure to the larger piston that, in turn, exerts a force on the spring and compresses it. Once the spring is compressed, the steel ball is loaded and the spring is released, ejecting the ball.

(a) If a force of 950 N is exerted on the primary (smaller) piston to compress the spring 1.25 m from its equilibrium (uncompressed) position, what is the spring constant k of the spring?

(b) What is the velocity of the steel ball just after it is ejected?

(c) Neglecting air resistance, what is the maximum range of this “spring gun”?