1.3 Solutions
13
1.62 A cube rests on a rough horizontal plane. A tension parallel to the plane
is applied by a thread attached to the upper surface. Show that the cube
will slide or topple according to the coefficient of friction is less or greater
than 0.5.
1.63 A ladder leaning against a smooth wall makes an angle α with the horizontal
when in a position of limiting equilibrium. Show that the coefficient of friction
between the ladder and the ground is
1
2 cot α.
1.3 Solutions
1.3.1 Motion in One Dimension
1.1 (a) Equation of motion for the truck: s = ut
(1)
Equation of motion for the car: s =
1
2
at
2
(2)
The graphs for (1) and (2) are shown in Fig. 1.13. Eliminating t between
the two equations
s
1 −
1
2
as
u 2
= 0
( 3 )
Fig. 1.13
Either s = 0 or 1 −
1
2
as
u 2 = 0. The first solution corresponds to the result
that the truck overtakes the car at s = 0 and therefore at t = 0.
The second solution gives s =
2u 2
a
=
2 × 10 2
2
= 100 m
(b) t =
s
u
=
100
10
= 10 s
(c) v = at = 2 × 10 = 20 m/s
13
1.62 A cube rests on a rough horizontal plane. A tension parallel to the plane
is applied by a thread attached to the upper surface. Show that the cube
will slide or topple according to the coefficient of friction is less or greater
than 0.5.
1.63 A ladder leaning against a smooth wall makes an angle α with the horizontal
when in a position of limiting equilibrium. Show that the coefficient of friction
between the ladder and the ground is
1
2 cot α.
1.3 Solutions
1.3.1 Motion in One Dimension
1.1 (a) Equation of motion for the truck: s = ut
(1)
Equation of motion for the car: s =
1
2
at
2
(2)
The graphs for (1) and (2) are shown in Fig. 1.13. Eliminating t between
the two equations
s
1 −
1
2
as
u 2
= 0
( 3 )
Fig. 1.13
Either s = 0 or 1 −
1
2
as
u 2 = 0. The first solution corresponds to the result
that the truck overtakes the car at s = 0 and therefore at t = 0.
The second solution gives s =
2u 2
a
=
2 × 10 2
2
= 100 m
(b) t =
s
u
=
100
10
= 10 s
(c) v = at = 2 × 10 = 20 m/s