Equilibrium and Elasticity

1
Equilibrium and Elasticity

• Ch 12 (all)

2
Equilibrium

• An object is in equilibrium when
• - The vector sum of all the external forces that
  act the body must be zero. Fnet 0
• - The vector sum of all the external torques that
  act on the body, measured about any possible
  point, must all be zero. Tnet 0
• Objects in Equilibrium
• 1) A book resting on a table
• 2) A hockey puck sliding with constant velocity
  across a frictionless surface
• 3) The rotating blades of a ceiling fan
• 4) The wheel of a bicycle that is traveling along
  a straight path at constant speed
• An object is in static equilibrium if it follows
  the rules of equilibrium, and the linear
  momentum of the body must be zero.
• Objects in Static Equilibrium
• 1) A book resting on a table

3
Center of Gravity

• The gravitational force Fg on a body effectively
  acts at a single point, called he center of
  gravity (cog) of the body.
• If g is the same for all elements of a body, then
  the bodys cog is coincident with the bodys
  center of mass (com).

4
Elasticity

• All real rigid bodies are to some extent
  elastic, which means that we can change their
  dimensions slightly by pulling, pushing,
  twisting, or compressing them.
• A body is placed under eithe stress or strain,
  which are proportional to each other because
  stressmodule x strain.

5
Tension and Compression

• For simple tension or compression, the stress on
  the object is defined as F/A, where F is the
  magnitude of the force applied perpendicularly to
  an area A on the object. The strain, or unit
  deformation, is then the dimensionless quantity
  ?L/L, the fractional change in a length of the
  specimen.
• The modulus for tensile and compressive stresses
  is called the Youngs modulus and is represented
  in engineering practice by the symbol E.
• F/A E ?L/L

6
Shearing

• In the case of shearing, the stress is also a
  force per unit area, but the force vector lies in
  the plane of the area rather than perpendicular
  to it. The corresponding modulus, which is given
  the symbol G in engineering practice, is called
  the shear modulus.
• F/A G ?x/L

7
Hydraulic Stress

• The stress is the fluid pressure p on the object,
  and pressure is a force per unit area. The strain
  is ?V/V where V is the orginial volume of the
  specimen and ?V is the absolute value of the
  change in the volume. The corresponding modulus,
  with symbol B, is called the bulk modulus of the
  material.
• p B ?V/V

8
20 Questions
9
Which of the following is not a requirement for
an object to be in equilibrium?A) linear
momentum is constantB) energy is conservedC)
angular momentum is constant

• B) energy is conserved

10

• Explain what each symbol in the formula p B
  ?V/V stands for and when this formula might be
  used

Used to determine the hydraulic stress
experienced by an object p pressure B the
bulk modulus of the object ?V the change in
volume from the force V the original volume
11

• Because forces are applied to the end points of a
  rod in opposite direction, the stress experienced
  is _______.

Tension
12

• A steel rod has a radius R of 9.5 mm and a length
  of 81 cm. A 62 kN force F stretches it along its
  length. What is the stress experienced by the rod?

stress F/A stress F/pR2 stress(6.2x104)/p(9.5
x10-3) stress 2.2 x 108
13

• To find the tension of
• T1,where would the
• best pivot point be?

C
T1
A
B
A
14

• Which disks are in equilibrium?

F
F
F
F
F
3F
2F
2F
2F
F
A
C
B
B only
15

• Which way will the seesaw tip?

5 kg
3kg
2 kg
1 m
1 m
2 m
A
B
Towards B
16

• Since the constant of proportionality is called a
  modulus of elasticity, stress equals

modulus x strain
17

• The bending of a wave as it enters a new medium
  is called______

Refraction
18

• Find the tension
• in T. The box has a
• mass of M and the
• bar has a mass of 3M.

2d
Ø
6d
tnet Fr Ty T (sinØ)
M1r1 M2r2 Tyr3 M2d 3M3d T(sinØ) 6d 11/6
M T(sinØ) T 11M/6(sinØ)
19

• A 50 kg man is on one side of a seesaw and is 2
  meters away from the pivot point, a 40 kg man
  wants to balance the force, how far from the
  pivot point should he stand?

t1 t2 x1m1g x2m2g (2)(50)(9.8)
(x2)(40)(9.8) X2 2.5
20

• Find the tension in
• T2.
• (blue beam is mass less)

T1
T2
Pivot Point
5kg
3m
4m
tnet RF tnet -(r1xmg)(Fxr2) r1 x mg F x
r2 3 x 5 x 9.8 F x 7 F 21N
21
2 kg

• Is the center of mass near
• A, B, or C?

5 kg
A
C
B
3kg
The center of gravity is closest to C.
22

• Which of the following are in equilibrium?
• A car accelerating
• B) A hockey puck at constant speed
• C) A book resting on a desk

Both B and C. A is not because it is not at
constant speed.
23

• If a 10 kg mass is placed on a rod 5 meters away
  its pivot point, when is the torque experienced?

t x Fg t x m g t (5) (10) (9.8) t 490 Nm
24

• When force is applied to a bridge, it results in
• Tension
• Compression
• Both

Both
25

• The stress with is force per unit area and the
  force vector lies in the plane is the case of
  _________.

Shearing
26

• Which equation is the modulus for tension and
  compression?

1. F/A G ?x/L
2. p B ?V/V
3. F/A E ?L/L

27

• Which equation is the modulus for shearing?

1. F/A G ?x/L
2. p B ?V/V
3. F/A E ?L/L

28

• Which equation is the modulus for hydraulic
  stress?

• F/A G ?x/L
• p B ?V/V
• F/A E ?L/L

29
10 Questions
30

• A book resting on a table is in _______
  equilibrium.

Static
31

• The single point in which gravity is effectively
  acting on for any object is called the
  __________.

Center of Gravity
32

• When an object is being pulled apart by two
  forces in opposite direction parallel to its
  plane, the object is under ______.

Tension
33

• An object being acted on by two opposite forces
  perpendicular to its plane is said to be under a
  _________ stress.

Shearing
34

• When a object being acting upon by a surrounding
  fluid is said be to under a ________________.

Hydraulic Compression
35

• If g is the same for all elements of a body, then
  the bodys center of gravity is coincident with
  the bodys ___________.

Center of Mass
36

• All real rigid bodies are to some extent
  _________.

Elastic
37

• For simple tension or compression, the stress on
  the object is defined as ____.

F/A (Force / Area)
38

• The translational motion of a body is governed by
  Newtons _______ law in its linear momentum form.

Second (Fnet dP/dt)
39

• Name the three elastic moduli used to describe
  the elastic behavior of an object.

• Tension and Compression
• Shearing
• Hydraulic Stress