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PPT – Torque and static equilibrium PowerPoint presentation | free to view - id: 10416-YmE2Y

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Chapter 8 Equilibrium and Elasticity

Topics

- Torque and static equilibrium
- The spring force
- Hookes law
- Elastic materials
- The elastic limit

Sample question

How does a dancer balance so gracefully en

pointe? And how does her foot withstand the great

stresses concentrated on her toes?

Slide 8-1

Torque and Static Equilibrium

For an extended object to be in equilibrium, the

net force and the net torque must be zero.

Slide 8-8

Choosing the Pivot Point

Slide 8-9

Solving Static Equilibrium Problems

Slide 8-10

Checking Understanding

- What does the scale read?
- 500 N
- 1000 N
- 2000 N
- 4000 N

Slide 8-11

Answer

- What does the scale read?
- 2000 N

Slide 8-12

Example

A 2-m-long board weighing 50 N extends out over

the edge of a table, with 40 of the boards

length off the table. How far beyond the table

edge can a 25 N cat walk before the board begins

to tilt?

0.8 m

Slide 8-13

Example

A 2-m-long board weighing 50 N extends out over

the edge of a table, with 40 of the boards

length off the table. How far beyond the table

edge can a 25 N cat walk before the board begins

to tilt?

pivot

0.8 m

Slide 8-13

Example

A 2-m-long board weighing 50 N extends out over

the edge of a table, with 40 of the boards

length off the table. How far beyond the table

edge can a 25 N cat walk before the board begins

to tilt?

n

Wcat 25 N

Wboard 50 N

What is the magnitude of n?

Example

A 2-m-long board weighing 50 N extends out over

the edge of a table, with 40 of the boards

length off the table. How far beyond the table

edge can a 25 N cat walk before the board begins

to tilt?

0.8 m

n

X

0.2 m

Wcat 25 N

Wboard 50 N

What is the magnitude of n? n 75 N.

What is n when the cat is right over the center

of the board?

0.8 m

0.2 m

Wcat 25 N

Wboard 50 N

What is n when the cat is right over the center

of the board? n 50 N (board) 25 N (cat) 75

N.

0.8 m

0.2 m

Wcat 25 N

Wboard 50 N

What is n when the cat is between the boards

center and the table edge?

0.8 m

0.2 m

Wcat 25 N

Wboard 50 N

What is n when the cat is between the boards

center and the table edge? The (board cat) CM

moves to a point between the center and the table

edge, and the joint 75 N weight is balanced by a

75 N normal force.

0.8 m

n 75 N

0.2 m

Wcat 25 N

Wboard 50 N

As the cat walks past the table edge, there is a

critical distance (x) when the board just begins

to tip. At this point the normal force (n) is

still 75 Nit has moved to the pivot point at the

edge of the table.

0.8 m

n 75 N

X

0.2 m

Wcat 25 N

Wboard 50 N

Lets find the non-zero torques about ( ) just

at the point of the board about to start tipping

0.8 m

n 75 N

X

0.2 m

Wcat 25 N

Wboard 50 N

Lets find the non-zero torques about ( ) just

at the point of the board about to start tipping

define CCW as -

0.8 m

n 75 N

X

0.2 m

Wcat 25 N

Wboard 50 N

Lets find the non-zero torques about ( ) just

at the point of the board about to start tipping

define CCW as -

0.8 m

n 75 N

X

0.2 m

Wcat 25 N

Wboard 50 N

Equilibrium condition

So, (-10 Nm) (25 N) x 0 N, or x (10

Nm)/(25 N) 0.4 m. The cat is in the middle of

the board section past the edge of the table. A

mm farther and the board suddenly tips!

0.2 m

.41 m

Wcat 25 N

Conceptual Question 3 p 256. Could a ladder on

a level floor lean against a wall in static

equilibrium if there were no frictional forces?

Explain.

No friction

Question 8-19 p 257. A tall ladder is leaning

against a wall, as shown. There is no friction

between the top of the ladder and the wall. The

coefficient of static friction between the bottom

of the ladder and the ground is small but not

zero. A painter climbs up the ladder to reach a

high spot on the wall. At

- Which location should the painter be most worried

about the ladder slipping? - Near the bottom.
- At the middle of the ladder
- Near the top.
- The risk is the same at all locations.

Problem 8-4 p 257. How much torque must the

pin exert to keep the rod in the above figure

from rotating? Calculate this torque about a

point where the pin enters the rod and is

perpendicular to the plane of the figure.

npin

4.9 N

40 cm

Wrod 19.6 N

Problem 36 p 259. An 80 kg construction worker

sits down 2.0 m from the end of a 1450 kg steel

beam to eat his lunch, as shown above. The cable

supporting the beam is rated a 15,000 N. Should

the worker be worried?

T

784 N

14,210 N

3 m

1 m

Are there any other forces acting on the beam?

Fwall

T

784 N

14,210 N

3 m

1 m

Are there any other forces acting on the beam? Of

course, the wall holds on to the beam.

Fwall

T

784 N

14,210 N

3 m

1 m

Are there any other forces acting on the beam? Of

course, the wall holds on to the beam.

T

784 N

14,210 N

3 m

1 m

Are there any other forces acting on the beam? Of

course, the wall holds on to the beam.

Problem 37 p 259 A forearm can be modeled as a

1.2 kg, 35 cm long beam that pivots at the

elbow and is supported by the biceps, as shown.

How much force must the biceps exert to hold a

500 g ball with the forearm parallel to the floor?

Problem 37 p 259 A forearm can be modeled as a

1.2 kg, 35 cm long beam that pivots at the

elbow and is supported by the biceps, as shown.

How much force must the biceps exert to hold a

500 g ball with the forearm parallel to the

floor? Any other forces on the forearm?

Fbiceps

Warm

Wball

Problem 37 p 259 A forearm can be modeled as a

1.2 kg, 35 cm long beam that pivots at the

elbow and is supported by the biceps, as shown.

How much force must the biceps exert to hold a

500 g ball with the forearm parallel to the

floor? Any other forces on the forearm? Yes!

Fbiceps

Warm

Wball