251 Fundamentals of Classical Mechanics .
Exercise 8
1. Two identical cylindrical vessels with their bases at the same level contain a liquid of
density p. The area of either base is A, but in one vessel the liquid height is h, and
in the other is hg wher

251 Fundamentals of Classical Mechanics
Exercise 2
l. A 28.0kg block is connected to an empty 1.35kg bucket by a cord running over a
frictionless pulley (Fig. 1). The coefcient of static friction between the table and the
block is 0.450 and the coefcient

251 Fundamentals of Classical Mechanics
Exercise 2
,_ Suggested sclution
1. (a) Consider the free-body diagrams for both objects, initially stationary (see Fig. 1).
As sand is added, the tension will increase, and the force of static friction on the
block

251 Fundamentals of Classical Mechanics
Exercise 4
Suggested solution
1. (a) From the freebody diagram (Fig. 1) for the load being lifted, write
Newtons 2nd law for the vertical direction, with up being positive.
FT - mg 2 ma 2 0.160mg
=> FT = 1.16mg : 1.

251 Fundamentals of Classical Mechanics
Exercise 3
suggeSted Solution
1. Note that A moves while B remains at rest until the string has been rotated clockwise
by 90. After that, B starts to move and the string become taut again. Fig. 2 shows
the motion of

1. (a)
251 Fundamentals of Classical Mechanics .
Exercise 7
Suggested solution
Let the mass of the head and feet of the astronaut to be mh and mf, respec
tively. Since the astronaut of height h, oats feet down, his head and feet are
respectively at a di

251 Fundamentals of Classical Mechanics
Exercise 1
1. Use dimensional analysis to determine which of the following equations must be wrong:
/F
A: at, E : mart, v : 29h7 F: TU, 7) = i
t m
where g is the acceleration due to gravity, A and h are lengths. The

251 Fundamentals of Classical Mechanics
Exercise 4
l. A 285kg load is lifted 22.0 In vertically with an acceleration a, = 0.160g by a single
cable. Determine
(
(
a the tension in the cable,
b
)
) the net work done on the load7
(c) the work done by the cab

251 Fundamentals of Classical Mechanics
Exercise 5
1. An elastic string of unstrctched length l extends by half its length when a mass m
hangs from it. The mass and string are now placed on a smooth horizontal table with
one end of the string xed. The str

251 Fundamentals of Classical Mechanics r
Exercise 6
1. A thin uniform wire is bent to form the two equal sides AB and AC of a triangle,
where AB 2 AC : 5cm (see Fig. 1). The third side B0, of length 6cm7 is made of
uniform wire of twice the density of th

251 Fundamentals of Classical Mechanics .
Exercise 7
Useful data:
Gravitational constant G = 6.67 X 1011 N . 1112/ng
Mass of Earth M E = 5.98 x 1024 kg
Radius of Earth RE 2 6.37 X 106mm
1. An astronaut whose height is 1.70 rn oats feet down in an orbiting

251 Fundamentals of Classical Mechanics
Exercise 3
1. Two particles A, and B, of equal mass are at rest on a smooth horizontal table? joined
by a string which is just taut. A is projected with velocity u at 45 to AB as shown
in Fig. 1. Find the velocities

251 Fundamentals of Classical Mechanics
Exercise 5
Suggested solution
1. The string of unstretched length l extends by half its length When a mass m hangs
from it. By Hookes lavv,
l
k (E) = mg
When the extension of the string is l, the restoring force is

251 Fundamentals of Classical Mechanics .
Exercise 8
suggested solution
1. After the two vessels are connected, the equilibrium height of the liquid is:
h = (hl +h2)
2
In equalizing the levels of the two vessels, a liquid column of height (hl it) falls b

251 Fundamentals of Classical Mechanics
Exercise 6
Suggested solution
1. We set up the coordinate system as shown in Fig. 1. Let the linear mass density of
edges AB and AC be A. (So the linear mass density of edge BC is 2A.)
Fig. 1
The cc coordinates of