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.

Question

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 = 28^o.

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 = I_rod + I_clay

[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 m_clay·L_rod·v_clay

, what was the clay's speed before striking the rod?

v =  m/s

Answer 1

Hi, Bri! I am ready to help you, but I would like to see the picture and need to know, when is your problem due, where this problem was published. Is it possible to use another platform, where the picture could be seen? Waiting for your reply in comments section.