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0593_C10_fm Page 347 Monday, May 6, 2002 2:57 PM

Introduction to Energy Methods 347

Section 10.5 Kinetic Energy
P10.5.1: An 2800-lb automobile starting from a stop accelerates at the rate of 3 mph per
second. Find the kinetic energy of the vehicle after it has traveled 100 yards.
P10.5.2: A double pendulum consists of two particles P and P having masses m and m 2
1
1
2
supported by light cables with lengths and , making angles θ and θ with the vertical
1
2
2
1
as in Figure P10.5.2. Find an expression for the kinetic energy of this system. Express the
results in terms of m , m , , , θ , θ , θ ˙ 1 , and θ ˙ 2 .
1
2
1
2
1
2
θ
1 1
P (m )
1 1
θ
2 2
FIGURE P10.5.2 P (m )
2 2
A double pendulum.
P10.5.3: Determine the kinetic energy of the rod pendulum of Figure P10.5.3. Let the rod
have length and mass m. Express the result in terms of m, , θ, and .θ ˙

θ

G

FIGURE P10.5.3
A rod pendulum.
P10.5.4: See Problem 10.5.3. Consider the double rod pendulum as in Figure 10.5.4. Let
each rod have length and mass m. Determine the kinetic energy of the system. Express
the results in terms of m, , θ , θ , θ ˙ 1 , and θ ˙ 2 .
1
2

θ
1

θ
2
FIGURE P10.5.4
Double-rod pendulum.
P10.5.5: See Problems P10.5.3 and P10.5.4. Extend the results of Problems P10.5.3 and
P10.5.4 to the triple-rod pendulum of Figure P10.5.5.
P10.5.6: An automobile with 25-in.-diameter wheels is traveling at 30 mph when the
operator suddenly swerves to the left, causing the vehicle to spin out and rotate at the
rate of 180°/sec. If the wheels each weigh 62 lb and if their axial and diametral radii of