AMERICAN UNIVERSITY IN CAIRO
ENGR 214: Engineering Mechanics II (Dynamics)
Final Exam, 18 December, 2010
1. (25) To maintain a safe following distance x
between cars travelling on a highway at speed v,
drivers should abide by the “two-second rule”.
The rule states that a driver should stay at least
2 seconds behind the vehicle in front of him as
it passes a fixed mark such as a tree. Determine
the safe distance x for vehicles traveling at (a)
60 km/h, and (b) 100 km/h.
Ans. 33.3 m, 55.6 m
v
v
x
2. (25) A rock is thrown off a cliff with an initial velocity v0 = 20 m/s at
the angle shown. After 2.5 seconds,
(a) what will be the radius of curvature of the path of the rock, and
the rate of change of velocity of the rock?
(b) how far from the starting position is the rock at this point?
v0 = 20 m/s
5
3
Neglect air resistance and use a value of g = 10m/s2.
Ans. 28.125 m, 6 m/s2, 31.25 m
3. (25) The bowling ball is cast on the alley with
a backspin  = 10 rad/s while its center O has a
forward speed of vo = 8 m/s. Determine the
velocity of point A touching the alley.
Ans. 9.2 m/s
4
 = 10 rad/s
O
vO = 8 m/s
120 mm
A
4. (25) A 30 kg uniform thin panel is placed on a truck
with end A resting on a rough horizontal surface and end
B supported by a smooth vertical surface. Knowing that
the deceleration of the truck is 4 m/s2, determine the
reactions at ends A and B.
Ans. RyA = 294 N, RxA = 24.8 N, RB = 144.8 N
1.5 m
Bonus Problem
5. (20) A 73-kg gymnast is executing a series of full-circle swings
on the horizontal bar. In the position shown, he has a negligible
clockwise angular velocity and will maintain his body straight
and rigid as he swings downward. Assuming that during the
swing the centroidal radius of gyration of his body is 0.457 m,
determine his angular velocity and the force exerted on his hands
after he has rotated through (a) 90°, and (b) 180°.
Ans. 3.9 rad/s, Rx = 1221.3N, Ry = 105.1N
5.5 rad/s, Rx = 0, Ry = 3114.5N
Equation Sheet
v
dx
dt
a
dv d 2 x
dv
 2 v
dt dt
dx
Uniform rectilinear motion
x  x0  vt
Uniformly accelerated rectilinear motion
v  v0  at
x  x0  v0t  12 at 2
v 2  v02  2a  x  x0 
Acceleration components
dv
at 
dt
ar  r  r 2
Tangential & normal:
Radial and transverse:
T1  U12  T2
Conservation of energy: T1  V1  T2  V2
Work and energy:
t2
Impulse and momentum:
mv1   Fdt  mv2
t1
Coefficient of restitution:
vB  vA
vA  vB
e
vB  vA  vB / A  vA    rB / A
aB  aA  aB A  aA   aB A    aB A 
 a t  r
 F  ma
G
 a n  r
M  I 
2
G
G
n
t
an 
v2

a  r  2r