HOMEWORK 2
EQUILIBRIUM OF PARTICLES
Homework 2
1. Determine the
force P required to
maintain the 200-kg
engine in the position
for which q = 30
o
.
The diameter of the
pulley at B is
negligible.
Homework 2
2. The collar A of mass m may slide freely on the
horizontal frictionless rod. The spring attached to
the collar has a stiffness of 10 N/cm and it is
undeformed when the collar is directly below
support B. Determine the magnitude of the force P
required to maintain equilibrium.
9 cm
12 cm
B
A
P
m
Homework 2
3. A scale is constructed using the 10 kg mass A, the 2 kg
pan P and the pulley and cord arrangement. Cord BCA is 2 m
long. If s = 0.75 m, determine the mass D in the pan. Neglect
the size of the pulley.
Homework 2
4. The hoist shown is used
to position heavy workpieces
in a lathe. If the cable
between pulleys A and B can
support a maximum force of
1.2 kN, all other cables can
support a maximum force of
2.2 kN, and bar CE can
support a maximum
compressive force of 2.6 kN,
determine the largest
weight W that may be lifted.
Note that bar CE is a two
force member which can
support a force along its
longitudinal axis.
Homework 2
5. The pipe is held in
place by the vice. If
the bolt exerts a
force of 250 N on the
pipe in the direction
shown, determine the
forces F
A
and F
B
that
the smooth contacts
at A and B exert on
the pipe.
Homework 2
Homework 2
6. Determine the mass of each of the two cylinders
if they cause a sag of s = 0.5 m when supported from
the rings at A and B. Note that s = 0 when the
cylinders are removed.
Homework 2
7. Two particles weighing 800 N and 200 N are held in
equilibrium on frictionless perpendicular surfaces by a cable
which makes an angle q with the horizontal.
a) Determine the normal forces acting from the surfaces on
the particles,
b) Tension in the cable,
c) Angle q .
2 m
A
B
C
y
10 m
8. The pail and its contents have mass of 60 kg. If cable
BAC is 15 m long, determine the distance y of the pulley
for equilibrium. Neglect the mass of the pulley. Also find
the tension in the cable.
Homework 2
9. A small peg P rests on a spring that is contained inside the
smooth pipe. When the spring is compressed so that s = 0.15
m, the spring exerts an upward force of 60 N on the peg.
B
A
x
0.3 m
y
x
z
y
s
C
P
0.2 m
0.4 m
Homework 2
Determine the
point of
attachment A (x,
y, 0) of cord PA
so that the
tension in cords
PB and PC equals
30 N and 50 N,
respectively.
10. Straight bar AB is fixed in space. Spring CD has a stiffness
of 3 N/mm and its unstretched length is 200 mm. If there is no
friction between collar C and bar AB,
Homework 2
determine the weight W
of the collar that
produces the equilibrium
condition shown and the
reaction between the
collar and bar AB.
x
y
z
11. Determine the tensions in cables AB, AC, and AD
for equilibrium.
Homework 2
12. Determine the stretch in each of the two springs
required to hold the 20 kg crate in the equilibrium position
shown. Each spring has an unstretched length of 2 m and a
stiffness of k = 300 N/m.
Homework 2
13. Determine the
force in each
cable used to lift
the 9.50 Mg surge
arrester at
constant velocity.
Homework 2
14. If the maximum allowable tension in cables
AB and AC is 2000 N, determine the maximum
height z to which the 800 N crate can be lifted.
W=800 N
y x
1.5 m
2 m
2 m
z
A
B
C
z
3 m
F
Homework 2
What horizontal
force must be
applied?
