A simple accelerometer is constructed inside a car by suspending an object of massm from a string of length L that is tied to the cars ceiling. As the car accelerates thestringobject system makes a constant angle of 0 with the vertical. (a) Assuming thatthe string mass is negligible compared with m, derive an expression for the carsacceleration in terms of u and show that it is independent of the mass m and thelength L. (b) Determine the acceleration of the car when 0 = 23.0°.

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B 4. Consider a scenario where a ball with a mass of 10 kg is hung on a frictionless inclined plane at a = 30°. The inclined plane itself moves along the direction indicated in the right figure with an acceleration a = g/3. Find: (a) the tension in the rope. (b) the normal force of the ball on the inclined plane. (c) the acceleration of the inclined plane at which the normal force of the ball on the inclined plane becomes zero.
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