.Pump Jack Problem: An oil well pump jack is

Question

shown in Figure 3-9f. As the motor turns, the
walking beam rocks back and forth, pulling the
rod out of the well and letting it go back into
the well. The connection between the rod and
the walking beam is a steel cable that wraps
around the cathead. The distanced from the
ground to pointP, where the cable connects to
the rod, varies periodically with time.
a.As the walking beam rocks, the angleθ it
makes with the ground varies sinusoidally
with time. The angle goes from a minimum
ofD0.2 radian to a maximum of 0.2 radian.
How many degrees correspond to this range
of angle (θ)?
b.The radius of the circular arc on the cathead
is 8 ft. What arc length on the cathead
corresponds to the range of angles in part a?
c.The distance,d, between the cable-to-rod
connector and the ground varies
sinusoidally with time. What is the
amplitude of the sinusoid?
d. Suppose that the pump is started at time t= 0 s. One second later, Pis at its highest point above the ground.P is at its next low
point 2.5 safter that. When the walking
beam is horizontal, pointP is 7 ft above the
ground. Sketch the graph of this sinusoid.
e.Find a particular equation expressingd as a function oft.
f.How far above the ground isP att = 9?

Answer 1

Suppose that the pump is started at time t= 0 s. One second later, Pis at its highest point above the ground.P is at its next low
point 2.5 safter that. When the walking
beam is horizontal, pointP is 7 ft above the
ground. Sketch the graph of this sinusoid.