Question

R The left box in the figure is released and slides down a frictionless bowl with a radius of curvature R. Both boxes have the same mass m. Please show your work clearly and express all answers in terms of the given variables, m and R. If the two boxes stick together at the bottom of the bowl, a. find their speed immediately after they collide; and b.find how far up the side of the bowl the two will rise. (Hint: use conservation of energy.) If instead of sticking together, the left box collides elastically with the right one, c. describe in words the behavior of each box after the collision; and d. find how far up the side of the bowl the right box will rise. how far up the side of the bowl will the right mass rise?

Answer 1

Answer

Potential energy of left box. mgh mgr. R. when it reaches the bottom of the bowl PE will be conversted to KE, mg R įmve J2gr Bottom box is at dest, before collision, het & bene combined velocity after collision. Using laus of reoweovation of momentum. momentum before collision a momentum after collearan MNi+mXo = - mx 2gr = 2 m v. l va 129R42. b) het hbe the height to enleich both the both the book is otsed. KE at boottom a PE at height h. 2mxv 2 +246 x 2g R amxgxb. ib c) If the collisina is elastic, then the borces will not strok together, and both of them move with their interesanal velocities, so that momentum and kinetic cuege are

conserved. d) In an elaine collision of two bodies with the same, nass, of the second body is at rest before collision, then the frisst body comes to rest and, second body begins to move with the velocity of the first. So in this case, sight box move with the velwuty of the left box and left box conses to rest. for the right box, het bo be the height through which it is soused after collision. Žm ve = mgh - 2 x mp x 2 g R a magh h = R. sise up to the Right box will rise the bowl. up to opening edge of