Nothing’s moving, but not from lack of trying!

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6

3

1. Stranded motorist pushes on car.

2. Car pushes back on her. How do we know?

5. With feet dug in, she pushes back into the sand.6. The sand pushes back on her.

This is what balances 2.

3. Because it is mired in sand, the car’s tires have a mound of sand to push up against.

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4. Sand pushes back on car.How do we know?

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5

What needs to be changed to get out?

How do you walk? What are the forces involved that allow you to walk?

As bracing yourself to push a car showed, you push back against the ground below you

to propel yourself forward.

Imaginetrying towalk across a surfacewithoutfriction!

Smooth plastic surface

Micro-polished glass

500 m

50 m

A smoothly varnished surface.

Polished carbon steel surfaces

Since even the smoothest of surfaces are microscopically rough, friction results from the sliding up and over

of craggy surfaces, and even the chipping and breaking of jagged peaks.

There are TWO TYPES of friction.

Static Friction Acts to prevent objects from starting to slide Forces can range from zero to an upper limit Sliding Friction Acts to stop objects that are already sliding Forces of sliding friction have a fixed value that depends on the particular surfaces involved.

force the sliding surfaces together more tightly (increase an object’s weight).

Frictional forces increase when you:

The peak static force is always greater than sliding force

Surface features interpenetrate more deeply when stationary objects settle.Friction force drops when sliding begins Cold welds are broken and moving objects ride across the craggy surfaces higher.

W

f

The force of friction, f, is directly proportional to the total force (usually W for objects sliding horizontally) thatpresses the sliding surfaces together:

Wf

We write: f = W

where is known as the “coefficient of friction”

Typical coefficients of friction maximum

Material static slidingRubber on dry concrete 0.90 0.80Steel against steel 0.74 0.57Glass across glass 0.94 0.40Wood on wood 0.58 0.40Wood on leather 0.50 0.40Copper on steel 0.53 0.36Rubber on wet concrete 0.30 0.25Steel on ice 0.10 0.06Waxed skis on snow 0.10 0.05Steel across teflon 0.04 0.04Synovial joints (hip, elbow) 0.01 0.01

What happens when objects slide to rest?

Where does the lost kinetic energy go?

It generates heat, an additional form of energy.

Rotation

Velocity

Wheels can circumvent friction by using the fact that objects can roll without sliding

If friction prevents slipping at this point,the foot planted at bottom stays stationary as the entire assembly tips forward, rotating about its axis.

Notice while the planted foot stays put, the axle moves forward at half the speedthat the top edgeof our wheel does!

v = 0

v

2v

Remember:pathlength out a distance r from the center of a rotation:

s = r and the tangential speed at that point:

v = r

Each time this tethered ball comes around, a wack of the paddlegives it a boost of speed speed v .

2

21 )( vmdF

But this v is directly related to an angular velocity, (in radians/sec)

v = r2

21 )( rmdF

r

22

21 )( mrdF

For an individual mass m rotating in an orbit of radius r

2mrI

2

21 )( IdF rotational

kinetic energy

m

d

F

We’ve noted that an unbalanced forceacting continuously over a distance ddelivers kinetic energy to the object being pushed:

2

21 mvFd

work done kinetic energy

d

Often the distance over which the forces act in a collision becomes difficult to measure directly.

Particularly for sudden, jarring “impulses”where the contact forces act

for only brief instances.

Impulse is a physics term describing how sudden the application of force

during such collisions is.

Analogous to our definition of work, consider:

tmaFt )(Force time over which it acts

)(0

vvm

v = v0 + atRecall:

)(atm

0mvmv

producing a change in “momentum”

Momentum is inertia of motion

Easy to start

Hard to start

While inertia depends on mass

Momentum depends on both mass and velocity

Easy to stop

Easy to stop

Hard to stop

Hard to stop

v

v v

vm

m

m

m

momentum = mass velocity

“Quantity of motion”

To change velocity ForceTo change momentum Impulse

Ft (mv) Ft (mv)

Ft (mv)

short “twang” small momentum

long “twang” larger momentum

Ft (mv)Small forcemay not break! Short time large force