Question

Problem 2. On a horizontal, frictionless table, an open-topped 5.50 kg box is attached to an ideal horizontal spring having force constant 350 N/m. Inside the box is a 3.20 kg stone. The system is oscillating with an amplitude of 7.50 cm. When the spring has reached its maximum extension, the stone is suddenly plucked vertically out of the box without touching the box. (a) What is the period of the motion of the box before and after the stone is removed? (b) What is the amplitude of the motion of the box before and after the stone is removed? (c) What is the maximum speed of the box before and after the stone is removed?

Answer 1

boksione Ans] Combined mass of (box + block) = M = (5.5+3.20) Kg mboxt monk M=8.7kg. spring constant = K = 3500 initial amplitude = A;= 7.50cm= 7.5810 m. I . Initial totod mechanical Energy = E= 1 KA² spring potential as Snergy at extreme 2 position. @ Torfore= 25 m = 2T 8.7 -0.gg seconds. V 350 A nswer Tapter = 2 9 Mbox =2T 15.5 = 0.787 seconds 1 350 Answer 6 Before the amplitude was A.=7.5cm, so after removal of stone also the amplitude remains the same, as the total mechanical Energy at extreme position is also conserved.le. I KA = 1 KAR Ai = A = 7.5cm Ars (c) The total mechanical Energy is conserved hence at mean position when the spring is extended nothing, then total mechanical

Energy is Kinetic, which is equal to total I potential Energy at extreme position Kinetic Energy Before the stone is removed is - M max = 1 KA² = 1 x 250 x (7.5x102) - 2 350x 75 x 10-4 8.7 Inox Vimax - 9. 030172 Q. 2 2 637 - Umax = 0.475 m/s Answer. After the stone is removed, Kinetic Energy is KE max = 1 m box Vimax = 1 KA² =) Vrax = / 350x 7.5² x 10" > Vnes (03579) = 0.598 m/s 2 T 5.5 X Answer.