The entrance of a science museum features a funnel into which marbles are rolled

Question

The entrance of a science museum features a funnel into which marbles are rolled one at a time. The marbles circle around the wall of the funnel, eventually spiraling down into the neck of the funnel. The internal radius of the funnel at the top is 0.52 m. At the bottom, the funnel’s neck narrows to an internal radius of 0.042 m. A 1.8 × 102 kg marble begins rolling in a large circular orbit around the funnel’s rim at 0.34 rev/s. If it continues moving in a roughly circular path, what will the marble’s angular speed be as it passes through the neck of the funnel? (Consider only the effects of conservation of angular momentum.) Answer in units of rad/s.

Explanation / Answer

angular momentum = mw^2*r where m is mass ,w is angular velocity and r is radius

conserving angular momentum

r1=0.52 m

w1=0.34 rev/s=2.136 rad/sec

r2=0.042 m

m(w1)^2*r1=m(w2)^2*r2

(w2)^2=(w1)^2*r1/r2=56.503

w2=7.52 rad/s=>answer

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.