Model the leg of the T. rex in the example 13.10 (section 13.6) in the textbook

Question

Model the leg of the T. rex in the example 13.10 (section 13.6) in the textbook as two uniform rods, each 1.55 m long, joined rigidly end to end. Let the lower rod have mass M and the upper rod mass 2Af. The composite object is pivoted about the top of the upper rod. Compute the oscillation period of this object for small-amplitude oscillations. Computer the oscillation period of this for small-amplitude oscillations. Compare your result to that of the example 13.10 in the textbook (Texample = 2.9s) Express your answer using two significant figures.

Explanation / Answer

A)

Let L = 1.55 m

Moment of Inertia of the system of rod about picot, I = I_upper_rod + I_lower_rod

= M*L^2/3 + (2*M*L^2/12 + 2*M*(L + L/2)^2)

= M*L^2*(1/3 + 1/6 + 9/2)

= 5*M*L^2

Lcm = (M*(L/2) + 2*M*(3*L/2))/(M + 2*M)

= (7/6)*L

time perode of physical pendulum, T = 2*pi*sqrt(I/(m*g*Lcm))

= 2*pi*sqrt( 5*M*L^2/(M*g*(7/6)*L))

= 2*pi*sqrt(30*L/(7*g))

= 2*pi*sqrt(30*1.55/(7*9.8))

= 5.173 s <<<<<-----Answer

B) T/T_example = 5.173/2.9

= 1.784

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