Question

Consider a pendulum rod (length 30.6 cm) with mass 10g, with the cage (250 g) and ball (64 g) as a point mass at the end of the rod. θ = 43 °

M + m

i. Find the initial height of the center of mass (as a height above the bottom cage/ball position).

ii. Find the final height of the center of mass.

iii. Find the change in potential energy.

iv. Set the final potential energy equal to the initial linear kinetic energy, and find the initial velocity.

v. Convert this initial linear velocity directly to an initial angular velocity.

vi. Find the moment of inertia of this system (about the pivot).

vii. Set final potential energy equal to initial rotational kinetic energy, and find the initial angular velocity. viii. Are the answers to (v) and (vi) the same?

ix. Which answer is correct (if either), and why?

Answer 1

the first method is correct because we can't apply energy conservation for whole process energy will be conserved after collision

because there will be energy loss in heat as bullet penetrated into mass M so method 2nd gives worng answer

Los h = L-L Case Li-Cose COM com H = L -Cose AND APE momg L- Cose = m+mW V = mv mth ( m+ m). Invey) = (mtm]ge (1-Coso) M 292 -toso imtm). 291 (1-6050) 1. = 6.227 ms

ME Li + mv. L = (mi? + m2) We ml Lh2 energy conservation PEF - Rotational energy intial (m+m), 4(1- Coso) = f I wk (m+ m) JL (1– Coso) = (ML2+ m2) (Chantal (m + m)JL (1-6050) = 1 m 32 ma Me'y m2]x2+m) gL (I- Cose)