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An engine uses compression springs to open and close valves, using cams. Given a spring stiffness of 30,000 N/m, and a spring mass of 0.08 kg, what is the maximum engine speed to avoid “floating the valves”? During the engine cycle the spring is compressed between 0.5 cm (valve fully closed) and 1.5 cm (valve fully open). Assume the camshaft rotates at the same speed as the engine. Floating the valves occurs when the engine speed is high enough so that the spring begins to lose contact with the cam when the valve closes. In other words, the spring doesn’t extend quickly enough to maintain contact with the cam, when the valve closes. For simplicity, you may assume that Hooke’s Law applies to the spring, where the force acting on the spring is proportional to its amount of compression (regardless of dynamic effects). You may ignore gravity in the calculations.

An engine uses compression springs to open and close valves, using cams. Given a spring stiffness of 30,000 N/m, and a spring mass of 0.08 kg, what is the maximum engine speed to avoid “floating the valves”?

During the engine cycle the spring is compressed between 0.5 cm (valve fully closed) and 1.5 cm (valve fully open). Assume the camshaft rotates at the same speed as the engine.

Floating the valves occurs when the engine speed is high enough so that the spring begins to lose contact with the cam when the valve closes. In other words, the spring doesn’t extend quickly enough to maintain contact with the cam, when the valve closes.

For simplicity, you may assume that Hooke’s Law applies to the spring, where the force acting on the spring is proportional to its amount of compression (regardless of dynamic effects).

You may ignore gravity in the calculations.

Grade:12

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