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PROBLEM 13.55
A force P is slowly applied to a plate that is attached to two springs and causes a deflection
0
.x
In each of the
two cases shown, derive an expression for the constant
,
e
k
in terms of
1
k
and
2
,k
of the single spring
equivalent to the given system, that is, of the single spring which will undergo the same deflection
0
x
when
subjected to the same force P.
PROBLEM 13.56
A loaded railroad car of mass m is rolling at a
constant velocity v0 when it couples with a
massless bumper system. Determine the
maximum deflection of the bumper assuming the
two springs are (a) in series (as shown), (b) in
parallel.
PROBLEM 13.56 (Continued)
PROBLEM 13.57
A 750-g collar can slide along the horizontal rod shown. It is
attached to an elastic cord with an undeformed length of 300 mm
and a spring constant of 150 N/m. Knowing that the collar is
released from rest at A and neglecting friction, determine the
speed of the collar (a) at B, (b) at E.
PROBLEM 13.58
A 4-lb collar can slide without friction along a horizontal rod and is
in equilibrium at A when it is pushed 1 in. to the right and released
from rest. The springs are undeformed when the collar is at A and
the constant of each spring is 2800 lb/in. Determine the maximum
velocity of the collar.
PROBLEM 13.59
A 4-lb collar can slide without friction along a horizontal rod and is
released from rest at A. The undeformed lengths of springs BA and
CA are 10 in. and 9 in., respectively, and the constant of each spring
is 2800 lb/in. Determine the velocity of the collar when it has moved
1 in. to the right.
PROBLEM 13.60
A 500-g collar can slide without friction on the curved rod BC in a horizontal
plane. Knowing that the undeformed length of the spring is 80 mm and that
400
k=
kN/m, determine (a) the velocity that the collar should be given at A
to reach B with zero velocity, (b) the velocity of the collar when it eventually
reaches C.
PROBLEM 13.60 (Continued)
PROBLEM 13.61
For the adapted shuffleboard device in Prob 13.28, you decide to utilize an elastic
cord instead of a compression spring to propel the puck forward. When the cord is
stretched directly between points A and B, the tension is 20 N. The 425 gram puck
is placed in the center and pulled back through a distance of 400 mm; a force of
100 N is required to hold it at this location. Knowing that the coefficient of friction
is 0.3, determine how far the puck will travel.
PROBLEM 13.61 (Continued)
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