SE 101B/MAE 130B Dynamics Mock Midterm Examination WI08
SOLUTIONS
PROBLEM 1
. A 3 lbf ball is given an initial
velocity
v
A
of 8 ft/s at an angle of 45
O
from the
horizontal at position A, where the two
attached springs are unstretched with free
lengths of 12 in. The ball follows the dashed
path in space and at some point in the future
crosses point B, which is 5 in directly beneath
point A. Calculate the velocity v
B
of the ball at
B. Each spring has a stiffness of 10 lbf/in.
SOLUTION
: This problem should be solved by energy methods, since all forces acting are
conservative. Thus, energy is conserved. This also means that the path that the ball takes
through space doesn’t matter: the only important information is contained at the endpoints! If
we take the lower point (B) to be a gravitational potential energy reference, the ball only has
potential and kinetic energy at A (springs are unstretched at A), and this is translated into elastic
potential and kinetic energy at B. By using right triangle geometry, the springs stretch to 13 in at
B (12
2
+ 5
2
= 13
2
). So, we have
T
1
+
V
g
,1
+
V
e
,1
=
T
2
+
V
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 Winter '08
 Todd
 Energy, Force, Kinetic Energy, Potential Energy, Velocity

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