課程名稱︰動力學
課程性質︰必修
課程教師︰蕭浩明
開課學院：工學院
開課系所︰機械工程學系
考試日期（年月日）︰104/4/14
考試時限（分鐘）：180分鐘
試題 :
ENGINEERING MECHANICS: DYNAMICS
Midterm 1 (April 14, 2015)
Instructor: Hao-Ming Hsiao
1. The pilot of an airplane executes a vertical loop which in part follows the
path of a cardioid, r = 600(1 + cosθ) ft. If his speed at A(θ = 0) is a
constant V_p = 80 ft/s, determine the vertical force the seat belt must
exert on him to hold him to his seat when the plane is upside down at A.
He weighs 150 lb. (15%)
http://imgur.com/k9GRWsi
2. The driver of the car maintains a constant speed of 40 m/s. Determine the
。
angular velocity of the camera tracking the car when θ = 15. (20%)
http://imgur.com/M8q0CAx
3. Using a forked rod, a smooth cylinder P, having a mass of 0.4 kg, is forced
to move along the vertical slotted path r = (0.6θ) m, where θ is in
radians. If the cylinder has a constant speed of V_c = 2 m/s, determine the
force of the rod and the normal force of the slot on the cylinder atthe
instant θ= π rad. Assume the cylinder is contact with only one edge of
the rod and slot at any instant. (20%)
http://imgur.com/GtXxM6e
4. A curve in a speed track has a radius of 300 m and a rated speed of 190
km/h. The rated speed of a banked track curve is the speed at which a car
should travel if no lateral friction force is to be exerted on its wheels.
Knowing that a racing car starts skidding on the curve when traveling at a
speed of 290 km/h, determine (a) the banking angle θ, (b) the coefficient
of static friction between the tires and the track under the prevailing
conditions, (c) the minimum speed at which the same car could negotiate that
curve. Please consider the direction of the friction force carefully in (b)
and (c). (25%)
http://imgur.com/VhCkTGN
5. Airplanes A and B are flying at the same altitude and are tracking the eye
of typhoon C. The relative velocity of C with respect to A is V_(C/A) = 350
__ 。
km/h ↙ 75, and the relative velocity of C with respect to B is V_(C/B) =
__ 。
400 km/h ↘ 40. Determine (a) the relative velocity of B with respect to A,
(b) the velocity of A if ground-based radar indicates that the typhoon is
moving at a speed of 30 km/h due north. (20%)
http://imgur.com/q1q8jQQ