i. Derive a relationship between time t and the velocity V (6 marks)
ii. Derive a relationship between time t and the displacement D (8 marks)
iii. Draw V Versus D for 0<t< 500 s ( 6 marks)
Figure Q2 shows a jet aircraft cruising at an altitude of 10 km at constant speed V = 1100 km/hr
(approx. parallel to the ground level) which was tracked by ground radar station at A, as shown in
Figure Q2.
i. Calculate 𝑟̇ and 𝜃
̇
when θ = 50
0
(8 Marks)
ii. Calculate 𝑟̈ and 𝜃
̈
when θ = 50
0
(6 Marks)
iii. Calculate the horizontal distance S travelled and time taken by the jet to cruise from θ =
90
0
to θ = 55
0
(5 Marks)
iv. At θ = 55
0
the jet aircraft drops a “dummy bomb”. Calculate the horizontal distance from
the radar station A to the “dummy bomb” when it hit the ground level. (6 Marks)
MEC2401 – Dynamics 1 S2, 2015
3
Q3. (Marks 35/100)
Y=2(X)
0.5
x
y
40 m
θ
B (x,y)
A
O (0,0)
Figure Q3, shows a steel ball of mass M= 1.5 kg on a smooth parabolic path (in vertical plane) which can be represented as Y= 2 (X) 0.5 with respected to the coordinate system shown in the figure Q3. The ball accelerates along the path when it releases from the rest at point A which was located at horizontal distance of 40m from the origin O. (You can assume the ball as a particle)
I. Determine expressions for the tangent (tan(θ), radius of curvature (ρ)), tangential velocity (V), acceleration (a) and Normal reaction of ball to the parabolic surface (N), when the ball reaches point B which is located at coordinates (x, y) using general notations i.e. θ, ρ, x, y and g(gravitational acceleration) (15 Marks)
II. Draw graphs for tangential velocity (V), acceleration (a), Normal reaction of ball to the parabolic surface (N) for the range 5 m <x < 40 m (You may use MS Excel or similar program. However you need to submit your program file with your assignment). (15 marks)
Leave a Comment