Question

L
2.5. Rope on a plane *
A
rope with length L and mass density per unit length p lies on a plane
inclined at an angle (see Fig. 2.11). The top end is nailed to the plane,
and the coefficient of friction between the rope and the plane is u. What
are the possible values for the tension at the top of the rope?
pl
e
Fig. 2.11
2.6. Supporting a disk **
(a) A disk of mass M and radius R is held up by a massless string, as
shown in Fig. 2.12. The surface of the disk is frictionless. What is
the tension in the string? What is the normal force per unit length
that the string applies to the disk?
(b) Let there now be friction between the disk and the string, with
coefficient pe. What is the smallest possible tension in the string
at its lowest point?
M
1
1​

Answer 1

Answer:

weight of over hanging part=

g

m

l

1

g

weight of rope lying on the table=

l

m

(l−l

1

)g

normal reactionR=

l

m

(l−l

1

)g ,F=μR⟹F=μ

l

m

(l−l

1

)g

the rope will not slide down when

l

ml

1

g

<F

l

ml

1

g

<μ

l

m

(l−l

1

)g⟹l

1

<μ(l−l

1

)

for maximum value ofl

1

⟹l

1

=μ(l−l

1

)⟹l

1

=

1+μ

μl