University of Rhode Island
Department of Mechanical, Industrial and Systems Engineering
MCE 263 Dynamics Final Exam May 7, 2012
CLOSED-BOOK EXAM
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Problem #2 (100 points): A flat-bed truck is transporting a large crate. The truck is accelerating up a steep hill but at the top of the hill the speed is constant at 60 mph (88 ft/s) The crate weighs 2500-lb. At the top of the hill, the radius of curvature is a constant 300-ft. The static coefficient of friction between the truck flat-bed and the crate is μs = 0.4.
In answering the following questions, show all your equations before substituting the numbers and include correct units and directions of all velocities and accelerations.
(a) Draw a free-body diagram of the crate and a sketch showing the acceleration(s) at position A. (15 points)
(b) What is the maximum acceleration of the flat-bed truck to prevent the crate from sliding when the truck is at position A? (25 points)
(c) Draw a free-body diagram of the crate and a sketch showing the acceleration(s) on the top of the hill (position B). (15 points)
(d) What is the normal force acting on the crate at the top of the hill (position B)? (25 points)
(e) What is the maximum speed of the truck to prevent the crate from lifting off the flat-bed at the top of the hill (position B)? (20 points)
CONTINUE TO NEXT PAGE FOR SOLUTION
a) ΣFt = mat Wccos75o – Ff = -mat Ff = μsN = μsWc/g
at = g(μscos150 – cos750) =32.2(0.4cos15o– cos750) at = 4.11 ft/s2
b)
c) ΣFn = man N - Wc = -man an = v2/r
N = Wc[1 – v2/(gr)] N = 2500[1 – 882/(32.2•300)] N = 496-lb
d) v2/(gr) = 1 v = (gr)1/2 v = 98.28-ft/s vt = 67 mph