Statics of a Particle

1
Lecture 8

• Statics of a Particle

2
Equilibrium

• Definition of Equilibrium

For two-dimensional problems This is satisfied
only if
Equations of equilibrium
3
Equilibrium
For three-dimensional problems Hence,
Equations of equilibrium
4
Example 1
y

• Problem
• Determine F1 and F2 from the information given in
  the free body diagram.

FBD
F2
F1
60º
30º
x
10.8 N
5
Example 1
y

• Solution
• 1. Re-draw the FBD as previously shown.

FBD
F2
F1
60º
30º
x
10.8 N
6
Example 1

• 2. Determine Fx1, Fy1, Fx2, and Fy2.

7
Example 1

• 3. Apply the equations of equilibrium.

Ans.
Ans.
8
Example 2
B
A

• Problem
• Cables (chords, ropes, chains) have little or no
  bending stiffness. They behave as two-force
  members acting in tension.
• Determine the forces in cables A, B, C, and D.

40º
30º
1
C
60º
D
2
250 kg
Note F mg (250 kg)(9.806) 2450 N
9
Example 2

• Solution
• 1. Draw the Free Body Diagrams for joints 1 and 2.

10
Example 2

• 2. Determine the rectangular components of FD and
  FC and apply the equations of equilibrium.

11
Example 2

• 3. Determine the rectangular components of FA and
  FB and apply the equations of equilibrium.

(1)
(2)
Simplifying equations (1) and (2) becomes
(3)
(4)
12
Example 2

• Solving the two equations with two unknowns

(5)
From (4)
Substitute into (3)
Ans.
Ans.
13
Example 3

• Problem
• For rigid bodies in contact on a frictionless
  surface, the action of one body on the other is
  directed normal to the surface of contact.
• Determine the forces exerted by the supports at
  A, B, and C on the pipes.

Pipe 1
Pipe 2
Note Each pipe has a mass of 200 kg.
14
Example 3

• Solution
• 1. Draw FBDs of pipe 1 and 2.

y
y
FD
45º
45º
FB
FD
FC
1960 N
1960 N
x
FA
x
Pipe 1
Pipe 2
15
Example 3

• 2. Determine the rectangular components of the
  force 1960 N along the line of action of forces
  FC and FD, and apply the equations of equilibrium.

Ans.
Ans.
16
Example 3

• 3. Determine the rectangular components of the
  force 1960 N and FB, and apply the equations of
  equilibrium.

Ans.
Ans.
17
Additional Material

• Read Sections 3.1-3.3
• Problems 3-2, 6, 15, 31, 32, 39