fisica1-youn-e-freedman-exercicios-resolvidos

5.59: Consider a point a distance x from the top of the rope. The forces acting in this
point are T up and ( M
m ( L−
x
+ )
)g downwards. Newton’s Second Law becomes
T
m(
L−
x)
m(
L−
x)
( M + ) g = ( M + ) a.
L
L
F −(
M m)
g
m(
L x)
F
− Since , ( +
−
T = M + )( ).
L
= . At
a
M + m
L M + m
MF
M m
= M ( a +
x = 0 , T = F , and at x = L, T =
+
g)
as expected.
5.60: a) The tension in the cord must be m2g in order that the hanging block move at
constant speed. This tension must overcome friction and the component of the
gravitational force along the incline, so m2g
= ( m1
g sin α + µ
k
m1
g cosα)
and
m (sin
2
= m1 α + µ
k
cosα)
.
b) In this case, the friction force acts in the same direction as the tension on the block
of mass m
1
, so m2 g = ( m1
g sin α − µ
km1g
cosα)
, or m (sin 2
= m1 α − µ
k
cosα)
.
c) Similar to the analysis of parts (a) and (b), the largest m
2
could be is
m1 (sinα + µ
s
cos α)
and the smallest m
2
could be is m1 (sinα − µ
s
cos α)
.
5.61: For an angle of 45 .0°
, the tensions in the horizontal and vertical wires will be the
same. a) The tension in the vertical wire will be equal to the weight w = 12.0 N ; this must
be the tension in the horizontal wire, and hence the friction force on block A is also 12.0
N . b) The maximum frictional force is µ
s
w A
= (0.25)(60.0 N) = 15 N ; this will be the
tension in both the horizontal and vertical parts of the wire, so the maximum weight is 15
N.
5.62: a) The most direct way to do part (a) is to consider the blocks as a unit, with total
weight 4.80 N. Then the normal force between block B and the lower surface is 4.80 N,
and the friction force that must be overcome by the force F is
µ
k
n = (0.30)(4.80 N) = 1.440 N, or 1.44 N, to three figures. b) The normal force
between block B and the lower surface is still 4.80 N, but since block A is moving
relative to block B, there is a friction force between the blocks, of magnitude
( 0.30)(1.20 N) = 0.360 N, so the total friction force that the force F must overcome is
1 .440 N + 0.360 N = 1.80 N . (An extra figure was kept in these calculations for clarity.)