Question

Pablem 2Conider a collar with mass m adached tv a sprina with stiff and unstretched length, The cellar is at rest in periton When the ' spnny is at a horirontn porition and t ength (.. A force F is apphed to the rollar and t siarls t» move upnards , makes an armle ompared thi verical rvd. The vertical rod s smoot h Determene the speed of the collar when it passes poin te at husht above B. k. Remember to list any assumpthan What abont frchen behveer collar anel od s you meke

Answer 1

As rod is smooth, we neglect eny force o friction between rod and collar. There are three forces acting on collar.

1) External force F1 as shown.

2) Gravitational force, mg in the downward direction, where m is mass of collar.

3) Spring force k(delta l), along line of spring towards fixed point A. k is spring stiffness and delta l is , l-lo, where l is instant length of spring and lo is it's unstretched length.

As collar moves under effect of these forces, sum of work done by these forces is equal to change on it's kinetic energy.

Initial kinetic energy of spring is zero. Kinetic energy at point C is mv^2/2 , where v is it's speed at C.