Contributed by:

Elevators, Apparent weight, Friction, Pulleys, Free fall, Air drag

1.
Today: (Ch. 3)

Apparent weight

Friction

Free Fall

Air Drag and Terminal Velocity

Tomorrow: (Ch. 4)

Forces and Motion in Two and

Three Dimensions

Apparent weight

Friction

Free Fall

Air Drag and Terminal Velocity

Tomorrow: (Ch. 4)

Forces and Motion in Two and

Three Dimensions

2.
Elevators

Why do you feel heavier or lighter sometimes

when you are riding in an elevator?

Why do you feel heavier or lighter sometimes

when you are riding in an elevator?

3.
Elevators

There are 5 basic cases in the elevator:

moving up and speeding up

moving up and slowing down

moving down and speeding up

moving down and slowing down

moving up or down at a constant

speed

There are 5 basic cases in the elevator:

moving up and speeding up

moving up and slowing down

moving down and speeding up

moving down and slowing down

moving up or down at a constant

speed

4.
Apparent Weight

• The normal force is not

always equal to the weight

e.g. in elevator

• Letting upward be positive:

• ΣF = m a = N – mg

N=ma+mg

• If the elevator moved

downward, N = m g – m a

• The normal force is called

the object’s apparent weight

• The normal force is not

always equal to the weight

e.g. in elevator

• Letting upward be positive:

• ΣF = m a = N – mg

N=ma+mg

• If the elevator moved

downward, N = m g – m a

• The normal force is called

the object’s apparent weight

5.
Apparent weight

6.
Example

A passenger weighing 598 N rides in an elevator.

The gravitational field strength is 9.8 N/kg. What is

the apparent weight of the passenger in each of the

following situations? In each case the magnitude of

elevator’s acceleration is 0.5 m/s2.

(a)The passenger is on the 1st floor and has pushed

the button for the 15th floor i. e. the elevator is

beginning to move upward.

(b)The elevator is slowing down as it nears the 15 th

floor.

A passenger weighing 598 N rides in an elevator.

The gravitational field strength is 9.8 N/kg. What is

the apparent weight of the passenger in each of the

following situations? In each case the magnitude of

elevator’s acceleration is 0.5 m/s2.

(a)The passenger is on the 1st floor and has pushed

the button for the 15th floor i. e. the elevator is

beginning to move upward.

(b)The elevator is slowing down as it nears the 15 th

floor.

7.
Friction

• Friction can be

– Kinetic

• Related to moving

– Static

• When objects are at rest

• The force of friction opposes the motion

& the magnitude of the frictional force is

related to the magnitude of the normal

force

• Force of kinetic friction

– Ffriction = μk N

– μk is called the coefficient of kinetic

friction

• Friction can be

– Kinetic

• Related to moving

– Static

• When objects are at rest

• The force of friction opposes the motion

& the magnitude of the frictional force is

related to the magnitude of the normal

force

• Force of kinetic friction

– Ffriction = μk N

– μk is called the coefficient of kinetic

friction

8.
Static Friction

• |Ffriction | ≤ μs N

μs Coefficient of static

– Static indicates that the two

friction

surfaces are not moving

relative to each other

• If the push is increased, the

force of static friction also

increases and again cancels

the force of the push

• The magnitude of the static

friction has an upper limit of

μs N

– The magnitude of the force

of static friction cannot be

greater than this upper limit

• |Ffriction | ≤ μs N

μs Coefficient of static

– Static indicates that the two

friction

surfaces are not moving

relative to each other

• If the push is increased, the

force of static friction also

increases and again cancels

the force of the push

• The magnitude of the static

friction has an upper limit of

μs N

– The magnitude of the force

of static friction cannot be

greater than this upper limit

9.
Kinetic Friction Vs Static Friction

• Only difference is coefficients of friction

• The force of kinetic friction is just Ffriction = μk N

• Force of static friction given by |Ffriction | ≤ μs N

• For a given combination of surfaces, generally μs

> μk

– It is more difficult to start something moving than

it is to keep it moving once started

• Only difference is coefficients of friction

• The force of kinetic friction is just Ffriction = μk N

• Force of static friction given by |Ffriction | ≤ μs N

• For a given combination of surfaces, generally μs

> μk

– It is more difficult to start something moving than

it is to keep it moving once started

10.
Example: Friction and Walking

• The person “pushes” off during each step

• Force exerted by the shoe on the ground : Fon ground

• If the shoes do not slip, the force is due to static friction

– The shoes do not move relative to the ground

• By Newton’s third law Reaction force : Fon shoe

• If the surface was so slippery

that there was no frictional

force, the person would slip

• The person “pushes” off during each step

• Force exerted by the shoe on the ground : Fon ground

• If the shoes do not slip, the force is due to static friction

– The shoes do not move relative to the ground

• By Newton’s third law Reaction force : Fon shoe

• If the surface was so slippery

that there was no frictional

force, the person would slip

11.
Friction and Rolling

• The car’s tire does not slip

• There

is a frictional force between the tire and road

– Fon ground

• There

is a reaction force on the tire

– Fon tire

• The car’s tire does not slip

• There

is a frictional force between the tire and road

– Fon ground

• There

is a reaction force on the tire

– Fon tire

12.
Free Fall

• A specific type of motion

• Only gravity acts on the

object

– Some air drag, but it is

generally considered

negligible

• Analyze the motion in

terms of acceleration,

velocity, and position

• A specific type of motion

• Only gravity acts on the

object

– Some air drag, but it is

generally considered

negligible

• Analyze the motion in

terms of acceleration,

velocity, and position

13.
Free Fall – Acceleration

• t = 0 be the instant after the object is released

• Choose a coordinate system that measures

position as the height y above the ground

• Using Newton’s Second Law:

Fgrav

mg

a g

m m

– The negative sign comes from gravity acting

downward

• t = 0 be the instant after the object is released

• Choose a coordinate system that measures

position as the height y above the ground

• Using Newton’s Second Law:

Fgrav

mg

a g

m m

– The negative sign comes from gravity acting

downward

14.
Free Fall – Velocity and Position

• Velocity and position as functions

of time:

v v o a t v o g t

1 2

y y o v o t a t

2

1

y o v ot g t 2

2

• The motion can be expressed

graphically as well. Note the

constant acceleration

• The velocity and acceleration are

not always in the same direction

• Velocity and position as functions

of time:

v v o a t v o g t

1 2

y y o v o t a t

2

1

y o v ot g t 2

2

• The motion can be expressed

graphically as well. Note the

constant acceleration

• The velocity and acceleration are

not always in the same direction

15.
Free Fall – Final Notes

• The ball’s speed just before it hits the ground = initial

speed

– The velocities are in opposite directions

• The time spent on the way up is equal to the time

spent falling back down

vo 2v o

tup and t ground

g g

• The ball’s speed just before it hits the ground = initial

speed

– The velocities are in opposite directions

• The time spent on the way up is equal to the time

spent falling back down

vo 2v o

tup and t ground

g g

16.
Tension Example – Elevator Cable

• Two forces: Upward

Acceleration

– Gravity acting downward

– Tension in cable acting

upward, T

• Newton’s Second Law gives

T = mg + ma

• Assume massless cable

• Applying Newton’s Second

Law gives: TC = T

• Tension has force units

• Two forces: Upward

Acceleration

– Gravity acting downward

– Tension in cable acting

upward, T

• Newton’s Second Law gives

T = mg + ma

• Assume massless cable

• Applying Newton’s Second

Law gives: TC = T

• Tension has force units

17.
Cables with Mass

• Newton’s Second Law

• The upper tension, T1 must

be larger than the tension

from the box, T2

• T1 = T2 + mcable g

• If no acceleration

• Can assume a massless

cable if the mass of the

cable is small compared to

the other tensions present

• Newton’s Second Law

• The upper tension, T1 must

be larger than the tension

from the box, T2

• T1 = T2 + mcable g

• If no acceleration

• Can assume a massless

cable if the mass of the

cable is small compared to

the other tensions present

18.
Single & Multiple Pulleys

19.
Air Drag

• Air drag depends on speed & Area, so at higher

speeds and area it becomes more of an effect

• An estimate of air drag can be found by using

– Fdrag = ½ ρ A v2

• A more complete equation is

– Fdrag = ½ CD ρ A v2

– CD is the drag coefficient and depends on the

aerodynamic shape

– CD is 1 for boxy shapes and less than 1 for many

streamlined shapes

• Air drag depends on speed & Area, so at higher

speeds and area it becomes more of an effect

• An estimate of air drag can be found by using

– Fdrag = ½ ρ A v2

• A more complete equation is

– Fdrag = ½ CD ρ A v2

– CD is the drag coefficient and depends on the

aerodynamic shape

– CD is 1 for boxy shapes and less than 1 for many

streamlined shapes

20.
Skydiving & Terminal Velocity

• The skydiver will reach

a constant velocity

when Fdrag = Fgrav

– Called the terminal

velocity

2m g

v term

A

• The skydiver will reach

a constant velocity

when Fdrag = Fgrav

– Called the terminal

velocity

2m g

v term

A

21.
Tomorrow: (Ch. 4)

Forces and Motion in Two and Three

Dimensions

Forces and Motion in Two and Three

Dimensions

22.
Some Problem solving tips

23.
Reasoning and Relationships-Problem

Notes

• We may need to identify important information that is

“missing” from the initial description of the problem

– We need to recognize that additional information

is needed

– Then make reasonable estimates of the “missing”

quantities

• An approximate mathematical solution and an

approximate numerical answer are generally

sufficient

– The estimates of the “missing” values will vary

from case to case

Notes

• We may need to identify important information that is

“missing” from the initial description of the problem

– We need to recognize that additional information

is needed

– Then make reasonable estimates of the “missing”

quantities

• An approximate mathematical solution and an

approximate numerical answer are generally

sufficient

– The estimates of the “missing” values will vary

from case to case

24.
Reasoning and Relationships –

Problem Solving Strategy

• Recognize the principle

– Determine the key physics ideas central to the problem

– What principles connect the quantity you want to calculate

with the quantities you know

• Sketch the problem

– Show all the given information

– Draw a free body diagram, if needed

• Include all the forces, velocities, etc.

• Identify the relationships

– Motion equations are an example of a set of relationships

– If some values are unknown, make estimates for these

values

Problem Solving Strategy

• Recognize the principle

– Determine the key physics ideas central to the problem

– What principles connect the quantity you want to calculate

with the quantities you know

• Sketch the problem

– Show all the given information

– Draw a free body diagram, if needed

• Include all the forces, velocities, etc.

• Identify the relationships

– Motion equations are an example of a set of relationships

– If some values are unknown, make estimates for these

values

25.
Reasoning and Relationships –

Problem Solving Strategy, cont.

• Solve

– An exact mathematical solution typically is not

needed

– Cast the problem into one that is easy to

solve mathematically

• Check

– Consider what your answer means

– Check to be sure the answer makes sense

Problem Solving Strategy, cont.

• Solve

– An exact mathematical solution typically is not

needed

– Cast the problem into one that is easy to

solve mathematically

• Check

– Consider what your answer means

– Check to be sure the answer makes sense