Question

@44 l 67% 12:39 Problem Two. An object of mass m starts from rest and slides a distance d down an incline of angle 6. While sliding, it contacts an uncompressed spring as shown in the figure. The object slides an additional distance x as it is brought momentarily to rest by the compression of the spring (with spring constant k). As the spring is being compressed, it scrapes on the ramp causing friction with a with a varying coefficient of kinetic friction given by ti = a r?, where a is a constant (with units of m%). Find the spring constant k. wiwand 4.) (A) k = 6mg(d + x)sin 0 + 2x'a mg cos 3x? (B) k = 2x'a mg cos 0 - 6mg(d + x )sin 3.x2 (C)k = 6mg(d - x)sin 0 - 2x'a mg cos 0 3.x2 (D) k = 2x'a mg cos 0 - 6mg(d – x)sin e 3.x2 III 6mg(d + x)sin 0 – 2x'a mg cos (E) k = 3.x2

Answer 1

Now. When the mass is at the top, the total solution: we consider this problem in 3D:- The Diagram of this 3D problem in given en by WOSO u= mg x Imousino a and momentarily Now, Free Body Diagram. Now, the object in initialy or read and starts to noll and compress the se Spring fully get still When the spring gert compressed, africtiona force acts with the friction coefficient, M= ax 2 f = MN [Normar em sonce acted by the Plane] Now, potential energy on the total energy of the system =3mg (d+x) sino

Now, when the mass in at the bottom, tue totar energy in given by [man in momentan nestendly Still, verocity o The Potential Energy Storea in tue spring - frictional lon, Now, frictional energy loss frictional force X distance comprened = fx Ili Na um my conox from energy mgcono conservation, 3ing Calax) sind = 3 K x 2 x² mg cano => 3 Kx²= 6mg Colt x) sino + 2ax + 2ax ² mg como 6 mg (+X) Sino + 2ax -> K " mg cond 3 x 2 I can Option (A