P2110_Exam2_Practice.pdf - Problem#1(Show your work(25 pts A sand bag of mass m = 22.7 kg sits on a plank at position A which is at a distance of 10

# P2110_Exam2_Practice.pdf - Problem#1(Show your work(25 pts...

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Problem #1 (Show your work) (25 pts) A sand bag of mass m = 22.7 kg sits on a plank at position A which is at a distance of 10 meters from the bottom of the plank (position B). A worker slowly raises the top end of the plank without touching the bag. At the instant when the bag is just about to slide, the plank makes an angle ࠵? = 30° with the horizontal. A. (5) Draw a free body diagram for the system when the bag is just about to slide down. B. (5 pts) What is the coefficient of static friction ࠵? ࠵? of the plank? C. (5 pts) As soon as the bag starts sliding, the worker adjusts the angle to ࠵? = 40°. What is the acceleration of the bag of sand? Assume the coefficient of kinetic friction is ࠵? ࠵? = 0.40. D. (5 pts) For ࠵? = 40° , how much time elapses while the bag slides from position A to B? E. (5 pts) What should be the angle ࠵? in part C above, such that the bag slides down at a constant velocity?
Problem #2 (show your work) (25 pts.): A roller coaster car of mass m = 250 kg starts from rest from position A at a height of 60 m. It rolls down the track with a circular loop of radius 20 m. The track is assumed to be frictionless. A. (5 pts.) What is the speed of the car at position B? B. (5 pts) What is the speed of the car at position D? C. (5 pts) What is the normal force due to the track at position D? D. (5 pts.) Roller coaster cars are attached to the track via a coupling. Assume that the coupling fails when the car reaches position D. What minimum speed the car must have at position D that it does not fall down from the track?

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