The distribution of material within an object can be as important in determining how it will respond to efforts to move it…

F

F

…as is the direction of the applied force

with respect to its center of mass.

mR

rm

d h

Work is performed by applying a force (down on this end) over the distance d.

Which changes thepotential energy ofthe load on this end. By how much?

FdW mghPE Conservation of energy requires:

mghFd

d

mghF

mgR

rF

mgd

h

hd

=?A. d

hB. R

rC. d

r

D. rR

E. hr

Raising the handlebars d raises the load h

r

R

d

h

Again: Fd = mgh

hd

should be in the same proportion as

1. R/r 2. r/R 3. R/d 4. r/h

So mgR

rmg

d

hF

Weight

When an object is on a ramp its weight pulls it into the supporting surface

and down along its surface.

Gravity’s pull straight DOWN is both pulling both into and along the ramp

at the same time!

This component of the weight iscompensated by the normal force.

This component represents the unbalancedforce that will accelerate the car downhill.

At which position does the pedalist get the greatest acceleration by bearing

down with his full weight?

In both position A and D

the force is exerted straight

along a line toward the

center of the axlewhich can do

nothing in cranking the

sprocket.

r

F

F

rF

r

When F and r are perpendicular we define the torque as

rFT Notice the units on torque are Newton-meters.

CENTEROF MASS

This “off-center” pushconsists of a component of force directed along

the line to the center(which will launch the book into an trajectory)

and a component perpendicular to the line

to center (the torque which will set it spinning as well).

Together these two torques work torotate this refrigerator out from its corner.

F1

F2

F2 is perpendicular to the line back to center.so it contributes a torque = F2R2

R2

F1 is not perpendicular to R1, the line to center.Instead we use the “lever arm” R, the distanceF1 misses the center by. This torque = F2R2

R1

R

The light turns green and you’re in a hurry!Will the car accelerate faster if you floorthe pedal and “burn rubber” or if instead

you accelerate so as to just avoid skidding your wheels?

A. Skid your tires and burn rubber.B. Just barely avoid skidding the tires.

Beginner skiers learn to ski-plowto slow down orstop.

The skis dig into the snow, and do work in plowing the snow aside.

This work comes at a cost: it depletes the skier’s kinetic energy…slowing her to a stop.

But the snow also pushes back on the skier!

Perhaps more tangible if the encounter waswith a boulder rather than a pile of soft snow.

How do you turn right when skiing downhill?

When snow-plowing you actually push out with your LEFT skit o turn right! In more advanced parallel skiing you lean right to dig the inside (right) edge of your skis into the snow…pushing LEFT against the hill!

You push LEFT against the snow!

The tennis ballpushes into theracquet’s netting, stretching its strings.

The net pushes against the tennis ball (see howit has been deformed?) slowing it to a stop, then sending it back.

The place-kicker’s toepushes into the football.

Note how it has been deformed! This forcewill send it flying.

Contact always produces pairs of forces.

The kicker’s toe will feelthe football.This force will ever-so-slightlyslow his foot down.

The cue ball traveling with speed vstrikes a stationary billiard ball head-on.

A. The cue ball rebounds backward, while its target is sent moving forward.B. The cue ball stops while its target continues forward with the speed v.C. The cue ball and target ball roll forward together with a speed <v.D. The cue ball comes to rest in place next to the target ball.

Consider this rear end collision with a parked car.

The force of impact stops this car.

If left in neutral without the parking brake set, the force of impact will send this car rolling forward.

If this involves speeds over 5-10 mph, both vehicles will sustain damage. Which one “feels” or experiences the force of impact?

The cue ball loses its energyin this head-on collision.The force of the impact pushes back in stopping it.

The force of impact pushes the target forward.The cue ball decelerates from v to 0 in the same

fraction of a second (the time both balls in contact) that its target accelerates from 0 to v.

A boxer’s right hook delivers a knock-out punch!

The force this punch delivers to hisopponent’s face/head/neck is

A. greater thanB. exactly equal toC. less than

the force the boxer’s hand experiences from the blow.

A fly is struck against by windshield ofa car traveling 65mph down the highway.

The force experienced by the fly on impact

A. is greater thanB. is equal toC. is less than

the force of impact experienced by the windshield due to the impact.

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

1

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.

2

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

4

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