Inner ear. A student constructs a model of the utricle of the ear by attaching wooden balls (m = 0.080 kg) by strings to the bottom of a fish tank and then submerging them in water so that they float with the strings in a vertical direction. She finds that the wooden balls float with a buoyant force that exerts a tension of 0.20 N on each string as shown in Figure P4.74 (left). She then has her mother take her (and the model) on a drive. She notes that as her mother applies the gas pedal, the strings make an angle θ = 16° with respect to the vertical as shown in Figure P4.74 (right). 

(a) What was the acceleration of the car?

(b) If the car started from rest, how long would it take to get to freeway speed of 30 m/s (about 65 mi/h)? During the acceleration, the water also makes an angle with the horizontal. Are the wooden balls even needed? Explain. Ignore any forces due to the pressure in the water.

Figure P4.74