Question: Consider the accelerometer design shown in Figure P4.57, in which a small sphere sits in a hemispherical dish. Suppose the dish has an acceleration of

Consider the accelerometer design shown in Figure P4.57, in which a small sphere sits in a hemispherical dish. Suppose the dish has an acceleration of a_xalong the horizontal and a small amount of friction causes the sphere to reach a stable position relative to the dish as shown in the figure. Find the position of the sphere (i.e., find the angle Î¸) as a function of a_x.

Figure P4.57

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