# Adolf and Ed are wearing harnesses and are hanging...

Adolf and Ed are wearing harnesses and are hanging from theceiling by means of ropes atached to them. They are face toface and push off against one another. Adolf has a mass of120 kg, and Ed has a mass of 78 kg. Following the push, Adolfswings upward to a height of 0.65 m above his starting point. To what height above his starting point does Ed rise?

## Answers ( 1 )

1. The picture is somewhat crude, but the idea isthis: Initially Adolf (m1) and Ed (m2) are at the bottom ofthe arc. with initial momentum = 0.
After they push off,   m1 moves left withv1

p1=m1 v1

and m2 moves right with v2

p2 = m2 v2

but from conservation of momentum p1 = p2 =>

m1 v1 = m2v2                          (1)

m1 rises up to height h1 where his potential energy is givenby

m1 g h1

which is equal to the kinetic energy he had when he left thebottom, i.e.

m1 g h1 = (1/2) m1v12                 (2)

Similarly for m2

m2 g h2 = (1/2) m2v22                (3)

From (1)

v2 = ( m1/m2)v1                      (4)

From (3)
h2 = (1/2g)v22                                (5)

substitue v2 from (4) to get

h2 = (1/2g) (m1/m2)2v12           (6)
Now take v12 from (2) to get

h2 = (1/2g) (m1/m2)2 2g h1  or
h2 = (m1/m2)2 h1
= ( 120/78)2(.065m) ~ .154 m