Question

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A 4.5kg instrument is conditioned in an insulating packaging that has a keq = 9000N/m. The packaging is dropped from a height of 90cm. Determine: (i) the maximum deformation of the insulating material, (ii) the maximum acceler- ation of the instrument and in the maximum force transmitted to the base of the package upon collision with the ground. Consider that the mass of the package is negligible compared to the mass of the instrument. (2.5 points) Data: va = v. = 12.9.h; g = 9,8m/s2 m } ww PERREXNEW Answer: (i) Xmár = 9,39 x 10-2m (ii) Čmáx = 187,82m/s2 (ii) Fmáx = 845,1N

Answer 1

0 Given : Mass of object = 4.5kg Keg = 9000 N/m Height = 90cm = 0.9m Vo = Sogn g = 9.8 In this question a 4.5kg instrument is kept inside the insulating packiging. The mass of package is negligible. When this instrument is dropped from height 90 cm their potential energy is converted into Kinetic energy when this instrument Strike the ground their kE is get converted into de formation energy of insulating materia de Strain energy or potential energy. MW www A point object is at rest So their initial velocity is zero. [4=07 At point 2 juht above the ground. V = Vagn = 2x9,2x0,9 = 4.2 m

(1) Now, Formula of in deformed energy stored Strain object = Ik x? equating kinetic energy of object just above the ground to potential energy oy Strain energy of Deformed body Imv2 = Į kx² KE = SE mom va x = 14.5 x 4.2 = 0.09391 m - 9.391 x 102m.

(1) To find the mawimum acceleration Here, we will treat the package as an spring on which mass 4.5kg is kept Spring stiguess isigiven = 9000 N/m Force acting on spring F = KX = mxa. a= K2 - 9000 x 0.09391 4.5 a = 187.82 m/s2 to (111) Maximum force transmitted the base = m.a - 4.5 X 187.82 IF = 845.19 N