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Example: A constant force, P, acts up the incline on a cylinder
of mass, M, and radius, r. Friction
is sufficient to prevent sliding. A spring with spring constant, K,
attaches to the center of the cylinder,
C. The cylinder is initially at rest and the
spring is at its natural length. Once
the force, P, is applied
the
center of the cylinder moves up the plane a distance, d. Apply the principle of Work and Energy
to
determine the velocity of the center of the cylinder after moving up the
plane the distance, d.
The
data is: M = 1 slug, r = 1 ft, P =
100 lb, K = 10 lb/ft, g = 30 ft/sec2,
μ = 0.3, d = 10 ft.
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The
key steps in applying the
Principle of Work and Energy in plane motion are as follows:
Step 1: Draw a free body diagram to show external
forces and moments doing work.
Step 2: Calculate the work done.
Step 3: Calculate the kinetic energy and set work
done equal to the change in kinetic energy.
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Recall work done by a
spring W1-2 = ½ k ( di2
– df2) (ft
lb or N m)
where k = spring constant, (lb/ft, N/m) di
= the initial extension of the spring, (ft, m) and
df = the final extension of the
spring (ft, m)
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