Two objects slide without friction on a circular ring of radius R oriented in a

Question

Two objects slide without friction on a circular ring of radius R oriented in a vertical plane. The heavier object (of mass 3m) is attached to a spring with an unstretched length of zero (admittedly an unphysical assumption) and spring constant k. The fixed end of the spring is attached to a point a horizontal distance 2 R from the center of the circle. The lighter object (of mass m) is initially at rest at the bottom of the ring. The heavier object is released from rest at the top of the ring, then collides with and sticks to the lighter object. Find the value for m that will allow the combined object (of mass 4m) to just reach the point A on the ring, but go no higher. Express your answer in terms of some or all of the quantities k, R and the acceleration of gravity g.

Explanation / Answer

Decrease in PE for mass 3m = increase in PE for spring + increase in PE for m x = 3 R - (4 R^2 + R^2)^1/2 = (3 - 5^1/2) R amount spring stretches Decrease in PE for 3 m = 3 m g R Increase PE for m = m g R 3 m g R = 1/2 k [(3 - 5^1/2) R]^2 + m g R m = k R [(3 - 5^1/2)^2/ (4 g) = .146 k R / g

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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