fisica1-youn-e-freedman-exercicios-resolvidos

8.111: a) The tension in the rope at the point where it is suspended from the table is
T = ( λx)g
, where x is the length of rope over the edge, hanging vertically. In raising the
rope a distance − dx , the work done is ( λ g) x ( − dx)( dx is negative).
The total work done
is then
− ∫
0
l / 4
2
x
2
λgl
32
l / 4
( λ g) x dx = ( λg) = .
b) The center of mass of the hanging piece is initially a distance l/8 below the top of the
λ g l / 4 , so the work required to raise the rope is
table, and the hanging weight is ( )( )
2
( λ g) ( l / 4) ( l /8) = λgl
/32,
as before.
0
2
8.112: a) For constant acceleration a, the downward velocity is v = at and the distance x
2
that the drop has fallen is x = 1
at . Substitution into the differential equation gives
1
2
g
the non-zero solution of which is a = .
2
1 ⎛ 9.80 m/s ⎞
2 2
⎜
3
⎟
⎝ ⎠
2 .00 g/m 14.7 m = 29.4 g
2
1
2 3 2 2
= ( at) a t ,
2
2
2
2
at g at a + =
1 2
2
b) at =
( 3.00 s) = 14.7 m.
c) kx = ( ) ( ) .
3