No Strings Attached:Normal Forces, Force Vectors, Strings, Springs and Pulleys

Chapter 6.1-6.3

Important Vocabulary:Normal ForceContact ForceTensionCoefficient of Friction

Friction: the most important everyday force, next to gravity!

Fg

NF

Ff

The force of friction ..…..

•Is the result of contact between two bodies.•Always acts to oppose (slow down) the motion.•Is proportional to the Normal force.•Does not depend on area of contact. Why not?

NFf

Friction depends on whether or not the object is moving.

• Static friction: friction for object at rest.• Kinetic friction: friction for moving object.

Two more notes about friction:-Coefficient of static friction is higher than that of kinetic friction (frictional force decreases when object begins to move).-Coefficient of kinetic friction does not change with speed

And finally(?)….frictional force “laws” are an approximation, but a good one.

V>0V=0

Static Kinetic

A problem of frictionA block of mass M = 1.5 kg sits on a hinged inclined plane. The coefficient of static friction is =0.15. At what angle of the inclined plane does the block begin to slide?

1. Draw the picture showing the forces on the block. What are they?

2. Draw the free-body diagram.3. Write down Newton’s law, Fnet = M a4. Think about the problem. When does the acceleration

become greater than zero?

Science Friction.

=0 =.05

V0

A block of mass M=1 kg slides with speed Vo over a frictionless surface. Then, it hits a rough surface with kinetic coefficient of friction =0.05 . How much further does it slide before it stops?

Have I got a tension headache!

• Tension, T, is the “contact force” for pulling objects

• Tension is a real force—you can measure it by cutting the string and inserting a force scale

TENSION

Tension is real—it can be measured.

Tension Problem• Given, M1, M2, and F

• What is acceleration?

• What is the Tension, T in the line?

• What is the force on each block?

M1M2 FT

Case of NO FRICTION.

F1=T T F

F2=F-T

21 MM

Fa

IMPORTANT:Blocks move together, so each has the same acceleration “a” and speed “v”.

FMM

M

aM

FT

21

1

1

1

FMM

M

TFF

21

2

2

Check work: Look a limits of large and small M1, M2.

Pulleys: the beginnings of technology.

A pulley changes the direction of Tension

Compare the tension in the left and right cases.

1. The left is higher.2. The right is higher since the mass is

double.3. They are the same.

Simplest pulley system.

What happens to the tension?

1. It is the same in both cases, the bucket mass doesn’t change.

2. The tension doubles in the right side.

3. The tension is reduced by ½ in the right side.

The “bosun’s chair” problem.

Accelerating blocks: more of a challenge

Given M2, M1 and g.What is a?What is the tension?What are the forces?(ignore friction)

Accelerated blocks and tension.

CAUTION: The TOTAL force on M2 is NOT JUST THE WEIGHT!

Freebody diagram

NOTE: Why is the diagram for mass 2 correct? Isn’t it moving in the y axis?

a a

Accelerating tethered blocks.

aMTgM

aMT

22

1

Block on the table.

Block dropping down.

a

gMM

Ma

21

2

Does this make sense? Check it

by looking at limits of M2.

Tethered blocks: add one more!T1 T2

T2

M3g

aMTgM

aMTT

aMT

323

212

11

Add all three equations together.

gMaMMM 3321 )(

gMMM

Ma

321

3

Do on “board” then reveal