NEXT Chapter 07, Problem 38 GO A ball is attached to one end of a wire, the othe

Question

NEXT Chapter 07, Problem 38 GO A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.7 kg and 2.4 kg, and the length of the wire is 1.31 m. Find the velocity (magnitude and direction) of the ball (a) just before the collision, and (b) just after the collision. 24 (a) v (b) v 2000:20 All Rights Division of 2ohn Sons uos. Version 4.22.2.9

Explanation / Answer

using conservation of energy between Top and bottom for motion of ball before collision

Kinetic energy at Bottom = initial potential energy at Top

(0.5) m v2 = mgh

v = sqrt(2gh)
v = sqrt(2 g L) = sqrt(2 x 9.8 x 1.31) = 5.1 m/s

b)

m = mass of ball = 1.7 kg

M = mass of block = 2.4 kg

vi = initial velocity of ball before collison = 5.1 m/s

vf = final velocity of ball after collison

Vi = initial velocity of block before collison = 0 m/s

Vf = final velocity of block after collison

using conservation of momentum

m vi + M Vi = m vf + M Vf

1.7 x 5.1 + (2.4) (0) = 1.7 vf + 2.4 Vf

Vf = (8.67 - 1.7 vf )                      eq-1

using conservation of kinetic energy

m v2i + M V2i = m v2f + M V2f

1.7 x 5.12 + (2.4) (0)2 = 1.7 v2f + 2.4 ((8.67 - 1.7 vf ) )2

vf = 3.1 m/s

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