A long wooden rod is supported in the vertical position by a hinge/pivot at its upper end so that it is free to swing like a pendulum.
A long wooden rod is supported in the vertical position by a hinge/pivot at its upper end so that it is free to swing like a pendulum. The length of the rod is 2.70 m and its mass is 2.10 kg. The rod is struck by a lump of clay, whose mass is 500 g, moving horizontally and which sticks to the bottom end of the rod. This makes the rod swing out to a maximum angle of 𝜃 = 28o.
A. How far, h0, from the top of the rod is the center of mass of the rod-clay system just before the rod leaves the vertical position with the clay attached?
h0 = m
B. When the system has swung to o, how high, Δh,has the center of mass moved from its original position?
[Suggestion: Draw a before and after diagram of the rod and used trigonometry.]
Δh = m
C. What is the system's increase in potential energy?
[Hint: Would knowing about the center of mass's motion help?]
ΔU = J
D. What is the moment of inertia of the rod-clay system? The rod is pivoting about its upper end and the clay is a point mass. I = Irod + Iclay
[Suggestion: Look up the expression for the moment of inertia of the rod pivoting at one end.]
I = kg m2
E. Using conservation of mechanical energy, what is the initial kinetic energy, angular speed and angular momentum of the rod-clay system (before it leaves the vertical position)?
K0 = J
𝜔 = rad/s
L0 = kg m2/s
F. If the clay's initial angular momentum before striking the rod was mclay·Lrod·vclay
, what was the clay's speed before striking the rod?
v = m/s