LON-CAPA Prob0766.probl... x Bb Assignments Phys 212 Search Textbook Solutions X
ID: 1450398 • Letter: L
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LON-CAPA Prob0766.probl... x Bb Assignments Phys 212 Search Textbook Solutions X physi uploaded%2fndsu%2f8A2361183b98e c a search New Messages Courses Help Logout Makenzie Reutter v Student section: 01 Physics 211 College Physics I Spring 2016 Main Menu Contents Grades syllabus Feeds Time Notes Evaluate Feedback Print Info Course Contents Homework 10 Prob0766 problem A cart of mass m 11 kg slides down a frictionless ramp and is ma oop of radius 0.4 m as shown in Figure P7.66 30 kg which then heads into a vertical to collide with a second cart of mass m2 (a) Determine the height h at which cart 1 w ould need to start from to make sure that cart #2 completes the loop w ithout leaving the track. Assume L an elastic collision. Submit Answer Tries 0/10 (b) Find the height needed if instead the more massive cart is allowed to slide down the ramp into the smaller cart Submit Answer Tries 0/10 Send Feedback Post Discussion 11:09 AM 3/31/2016Explanation / Answer
a)
let
u1 and u2 are velocities of m1 and m2 before the collision.
and v1 and v2 are velocities of m1 and m2 after the collision.
clearly, u1 = sqrt(2*g*h)
to complete the loop, v2 = sqrt(5*g*r)
but we know,
v2 = 2*m1*u1/(m1+m2)
sqrt(5*g*r) = 2*m1*sqrt(2*g*h)/(m1+m2)
5*g*r = 4*m1^2*2*g*h/(m1+m2)^2
==> h = 5*r*(m1+m2)^2/(8*m1^2)
= 5*0.4*(11+30)^2/(8*11^2)
= 3.47 m <<<<<<<<-------------------Answer
b)
in this case, Final speed of both cars must be, V = sqrt(5*g*r)
m1*u1 = (m1+m2)*V
m1*sqrt(2*g*h) = (m1+m2)*sqrt(5*g*r)
m1^2*2*g*h = (m1+m2)^2*5*g*r
h = 5*(m1+m2)^2*r/(2*m1^2)
= 5*(11+30)^2*0.4/(2*11^2)
= 13.9 m <<<<<<<<-------------------Answer
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