A physics student decides he wants to see how fast his dad A physics student dec

Question

A physics student decides he wants to see how fast his dad

A physics student decides he wants to see how fast his dad??s new sports car will accelerate, so he fashions a clinometer (angle indicator shown in the figure) that he attaches to the passenger-side window of the car in the orientation shown, so that the plumb bob hangs straight down when the car is not accelerating. He gets his girlfriend to ride along with him to the local drag strip. While he??s accelerating down the strip, she records the angle the plumb bob makes with respect to vertical. Draw a free-body diagram of the bob (i.e. the nut on the end of the string) as it appears while the car is accelerating. Derive an expression for the acceleration of the car in terms of an angle q between the string and a vertical axis. If theta = 35 degrees, and the acceleration is constant, how fast (in mi/hr) is the car going at the end of the quarter-mile strip? (assume he starts from rest, and 1 mile = 1609 m) How many seconds does the ¼-mile trip take? If the mass of the car is 1500 kg, what are the net work and the average power output in horsepower (1 hp = 746 W) of the engine?

Explanation / Answer

a)Let magnitude of centripetal acceleration = a
In car's frame, the bob experiences a pseudo force of magnitude ma, where m = mass of the bob.
Forces on the bob are
1. Tension T in the string from which the bob is hanging
2. Weight mg downward
3. Pseudo force ma

Net force in vertical direction = 0

Therefore, T cos q- mg = 0
Or T = mg/cos q --------------------------(1)

Net force in horizontal direction = 0
Therefore, ma = T sin q
Using the value of T from equation (1) in the above equation,
ma = (mg/cos q

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