Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

A 20.00 kg lead sphere is hanging from a hook by a thin, massless wire 2.80 m long and is free to swing in a complete circle. Treat the sphere as a point mass. Suddenly it is struck horizontally by a 5.00 kg steel dart that embeds itself in the lead sphere. What must be the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision

Sagot :

onyebuchinnaji

The minimum initial speed of the dart so that the combination makes a complete circular loop after the collision is 58.5 m/s.

Minimum speed for the object not fall out of the circle

The minimum speed if given by tension in the wire;

T + mg = ma

T + mg = m(v²)/R

tension must be zero for the object not fall

0 + mg = mv²/R

v = √(Rg)

Final speed of the two mass after collision

Use the principle of conservation of energy

K.Ef  = K.Ei + P.E

¹/₂mvf² = ¹/₂mv² + mg(2R)

¹/₂vf² = ¹/₂v² + g(2R)

¹/₂vf² = ¹/₂(Rg) + g(2R)

vf² = Rg + 4Rg

vf² = 5Rg

vf = √(5Rg)

vf = √(5 x 2.8 x 9.8)

vf = 11.7 m/s

Initial speed of the dart

Apply principle of conservation of linear momentum for inelastic collision;

5v = vf(20 + 5)

5v = 11.7(25)

5v = 292.5

v = 58.5 m/s

Learn  more about linear momentum here: https://brainly.com/question/7538238

#SPJ1

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.