Page 182 - Standard Handbook Of Petroleum & Natural Gas Engineering

Dynamics 167

The constant k, called the spring constant, represents the ratio of the force exerted
by the spring to X, its net compression or extension from the rest length.

Example 2-11
A 1-lb sphere is dropped from a height of 20 ft to strike a 2-ft long relaxed vertical
spring with a constant of 100 lb/ft (see Figure 2-17). What will be the velocity of the
sphere at a height of 2 ft when it strikes the spring? What will be the maximum
compression of the spring?
The sphere and the spring may be considered as a system in which no outside
forces or moments are acting. Thus the work term in Equation 2-39 is zero. Before
the collision with the spring, AVe = 0 also, and Equation 2-39 reduces to
AT + AVp = 0

AVp = W(h, - hi)

which can be solved for the impact velocity.

Vf = 34 ft/s

At full compression the velocity of the sphere is zero. Thus Equation 2-39 reduces to
AV? + AVg = 0

I8 ft

Figure 2-17. Diagram for Example 2-11.