Loster190idn
Answered

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you absentmindedly leave your bookbag on top of your car. Estimate the safe acceleration of the car needed for the bag to stay on the roof. Describe the assumptions you made.

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Sqdancefanidn

Answer:

  less than a number of g's equal to the coefficient of friction (assuming level roof and no air drag)

Step-by-step explanation:

We assume the top of the car is parallel to the ground when the car is accelerating. (We also assume that air drag does not come into play.) If k is the coefficient of static friction, the force required to move the book bag is kmg, where m is the mass of the book bag. That force will be applied if the acceleration of the car is kg.

The bag will stay in place if the car's acceleration is less than the product of the coefficient of static friction and the acceleration due to gravity.

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Additional comment

This changes if the car is on a slope or the acceleration causes it to pitch up. At higher speeds, air pressure will introduce significant force, so probably cannot be neglected. If the coefficient of friction is about 0.2, then the acceleration needs to be less than about 4.38 miles per hour per second. (0 to 43.8 mph in 10 seconds)

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