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0593_C10_fm Page 349 Monday, May 6, 2002 2:57 PM

Introduction to Energy Methods 349

P10.6.10: Repeat Problems P10.6.5 and P10.6.6 if the simple pendulum of Figure P10.6.5
is replaced by a rod pendulum of length 3 ft and weight 5 lb as in Figure P10.6.10, with
P being the end point of the rod.

O

θ k
(3 ft)

B(m)
P

FIGURE P10.6.11
FIGURE P10.6.10 A vertical mass–spring
A rod pendulum. system.

P10.6.11: A block B with mass m is attached to a vertical linear spring with modulus k as
in Figure P10.6.11. Suppose B is held in a position where the spring is neither stretched
nor compressed and is then released from rest. Find:

a. The maximum downward displacement of B
b. The maximum force in the spring
c. The maximum speed of B
d. The position where the maximum speed of B occurs

P10.6.12: Solve Problem P10.6.11 for k = 7 lb/in. and m = 0.25 slug.
P10.6.13: Solve Problem P10.6.11 for k = 12 N/cm and m = 2 kg.
P10.6.14: A 5-lb block B sliding in a smooth vertical slot is attached to a linear spring with
modulus k of 4 lb/in. as in Figure P10.6.14. Let the natural length of the spring be 8 in.
Let the displacement y of B be measured downward from O, opposite the spring anchor
Q as shown. Find the speed of B when (a) y = 0, and (b) y = 5 in.

B (5 lb)

k = 4 lb/in.
6 in.

O Q

FIGURE P10.6.14 8 in.
A spring connected block in a smooth
vertical slot. y
P10.6.15: Solve Problem P10.6.14 if the natural length of the spring is 6 in.
P10.6.16: A 10-kg block B is placed at the top of an incline which has a smooth surface as
represented in Figure P10.6.16. If B is released from rest and slides down the incline, what
will its speed be when it reaches the bottom of the incline?