1.2 Problems
3
Equation of motion of a body in air whose resistance varies as the velocity of the
body (see prob. 1.22).
Centre of mass is defined as
r cm =
m i r i
m i
=
1
M
m i r i
(1.8)
Centre of mass velocity is defined as
V c =
1
M
m i ˙
r i
(1.9)
The centre of mass moves as if the mass of various particles is concentrated at
the location of the centre of mass.
Equilibrium
A system will be in translational equilibrium if F = 0. In terms of potential
∂ V
∂ x
= 0, where V is the potential. The equilibrium will be stable if
∂ 2 V
∂ x 2 < 0.
A system will be in rotational equilibrium if the sum of the external torques is zero,
i.e. τ i = 0
1.2 Problems
1.2.1 Motion in One Dimension
1.1 A car starts from rest at constant acceleration of 2.0 m/s 2 . At the same instant
a truck travelling with a constant speed of 10 m/s overtakes and passes the car.
(a) How far beyond the starting point will the car overtake the truck?
(b) After what time will this happen?
(c) At that instant what will be the speed of the car?
1.2 From an elevated point A, a stone is projected vertically upward. When the
stone reaches a distance h below A, its velocity is double of what it was at a
height h above A. Show that the greatest height obtained by the stone above A
is 5h/3.
[Adelaide University]
1.3 A stone is dropped from a height of 19.6 m, above the ground while a second
stone is simultaneously projected from the ground with sufficient velocity to
enable it to ascend 19.6 m. When and where the stones would meet.
1.4 A particle moves according to the law x = A sin π t, where x is the displacement and t is time. Find the distance traversed by the particle in 3.0 s.
3
Equation of motion of a body in air whose resistance varies as the velocity of the
body (see prob. 1.22).
Centre of mass is defined as
r cm =
m i r i
m i
=
1
M
m i r i
(1.8)
Centre of mass velocity is defined as
V c =
1
M
m i ˙
r i
(1.9)
The centre of mass moves as if the mass of various particles is concentrated at
the location of the centre of mass.
Equilibrium
A system will be in translational equilibrium if F = 0. In terms of potential
∂ V
∂ x
= 0, where V is the potential. The equilibrium will be stable if
∂ 2 V
∂ x 2 < 0.
A system will be in rotational equilibrium if the sum of the external torques is zero,
i.e. τ i = 0
1.2 Problems
1.2.1 Motion in One Dimension
1.1 A car starts from rest at constant acceleration of 2.0 m/s 2 . At the same instant
a truck travelling with a constant speed of 10 m/s overtakes and passes the car.
(a) How far beyond the starting point will the car overtake the truck?
(b) After what time will this happen?
(c) At that instant what will be the speed of the car?
1.2 From an elevated point A, a stone is projected vertically upward. When the
stone reaches a distance h below A, its velocity is double of what it was at a
height h above A. Show that the greatest height obtained by the stone above A
is 5h/3.
[Adelaide University]
1.3 A stone is dropped from a height of 19.6 m, above the ground while a second
stone is simultaneously projected from the ground with sufficient velocity to
enable it to ascend 19.6 m. When and where the stones would meet.
1.4 A particle moves according to the law x = A sin π t, where x is the displacement and t is time. Find the distance traversed by the particle in 3.0 s.