Consider a gear wheel with 6 equally spaced teeth. Suppose below the wheel, ther

Question

Consider a gear wheel with 6 equally spaced teeth. Suppose below the wheel, there is a flat spring (see Fig.l) with a mass of 8 nt (about 1.8 lb) hanging at the end of the spring. The system has its static equilibrium 1 cm below horizontal line, and we let it start from this position with initial upward velocity 10 cm/sec. If the radius of the wheel at its largest value is 10 cm and the center of the wheel is to be placed vertically above the mass' position, how fast should the wheel be turning so the mass will almost touch each tooth of the wheel and how far should the center be from the horizontal line? (Assume the first rebound will almost touch a tooth.)

Explanation / Answer

We can find the spring constant by equating the weight of the mass and kx spring force.

Then conservation of energy will give the height of the mass.

and accordingly we can choose the height of the gear.

:)

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