[PDF] - Ramps Ramps Yes Yes Y Y A. A. No No B. B. Ramps 3 Ramps PDF Document

SLIDE 1

1

Ramps 1

Ramps Ramps

Ramps 2

Introductory Question Introductory Question

Can a ball ever push downward on a table with

Can a ball ever push downward on a table with a force greater than the ball’s weight? a force greater than the ball’s weight? Y Y

A. A.

Yes Yes

B. B.

No No

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Observations About Ramps Observations About Ramps

It’s difficult to lift a heavy cart straight up

It’s easer to push a heavy cart up a ramp

The ease depends on the ramp’s steepness

Gradual ramps involve gentler pushes

Gradual ramps involve longer distances

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4 Questions about Ramps 4 Questions about Ramps

Why doesn’t the cart fall through the ramp?

Are the cart and ramp pushing on each other?

Why is it easier to push the cart up a ramp?

Is there a physical quantity that’s the same for

Is there a physical quantity that’s the same for any trip up the ramp, regardless of its steepness? any trip up the ramp, regardless of its steepness?

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Question 1 Question 1

Why doesn’t the

Why doesn’t the cart cart fall through the fall through the ramp ramp? ?

Why doesn’t a

Why doesn’t a ball ball fall through a fall through a table table? ?

Is the table pushing up on the ball?

H

n n p rd p h pr nt f llin ? H n n p rd p h pr nt f llin ?

How can an upward push prevent falling?

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Support Forces Support Forces

A support force

prevents the ball from penetrating the table’s surface

points directly away from the table’s surface

F l f f i i ( f f i i (

Forces

Forces along along surface are friction ( surface are friction (ignore for now)

ignore for now)

SLIDE 2

2

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Adding up the Forces Adding up the Forces

As it sits on the table, the ball experiences

As it sits on the table, the ball experiences

its weight downward

a support from the table upward

Si h b ll i ’ l i Si h b ll i ’ l i

Since the ball isn’t accelerating,

the

the sum sum of forces (the

f forces (the net force)

net force) on the ball is zero

n the ball is zero

so the support force must balance ball’s weight!

Since cart isn’t accelerating into ramp,

the ramp’s support force must keep cart on surface

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Question 2 Question 2

Are the

Are the cart cart and and ramp ramp pushing on each other? pushing on each other?

Are the

Are the ball ball and and table table pushing on each other? pushing on each other?

Is the

Is the table table pushing on the pushing on the ball ball? ? I h I h b ll b ll hi h hi h bl bl ? ?

Is the

Is the ball ball pushing on the pushing on the table table? ?

Which is pushing harder?

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Clicker Question Clicker Question

If you push on a friend, will that friend

If you push on a friend, will that friend always always push back on you? push back on you? Y

A. A.

Yes Yes

B. B.

No No

Ramps 10

Newton’s Third Law Newton’s Third Law

For every force that one object exerts on a

For every force that one object exerts on a second object, there is an equal but oppositely second object, there is an equal but oppositely directed force that the second object exerts on directed force that the second object exerts on the first object the first object the first object. the first object.

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Clicker Question Clicker Question

If you push on a friend who is moving away

If you push on a friend who is moving away from you, how will the force you exert on your from you, how will the force you exert on your friend compare to the force your friend exerts friend compare to the force your friend exerts

n you?
n you?
n you?
n you?

A. A.

You push harder You push harder

B. B.

Your friend pushes harder Your friend pushes harder

C. C.

The forces are equal in magnitude The forces are equal in magnitude

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Forces Present Forces Present (Part 1)

(Part 1)

For the ball resting on the table, the forces are

For the ball resting on the table, the forces are

1. 1.

On On ball ball due to due to gravity gravity (its weight) (its weight) zero

2. 2.

On On ball ball due to support from due to support from table table

3. 3.

On On table table due to support from due to support from ball ball

These forces all have the same magnitude

These forces all have the same magnitude

Where is the other 3

Where is the other 3rd

rd law pair?

law pair? acceleration 3rd law pair

SLIDE 3

3

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Forces Present Forces Present (Part 2)

(Part 2)

1. 1.

On On earth earth due to gravity from the due to gravity from the ball ball

2. 2.

On On ball ball due to gravity from the due to gravity from the earth earth 3rd law pair

3. 3.

On On ball ball due to support from due to support from table table

4. 4.

On On table table due to support from due to support from ball ball

Forces 2 and 3 aren’t a Newton’s 3

Forces 2 and 3 aren’t a Newton’s 3rd

rd law pair!

law pair!

when equal in magnitude, ball doesn’t accelerate

when equal in magnitude, ball doesn’t accelerate

when not equal in magnitude, ball accelerates!

when not equal in magnitude, ball accelerates!

3rd law pair

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Introductory Question Introductory Question (revisited)

(revisited)

Can a ball ever push downward on a table with

Can a ball ever push downward on a table with a force greater than the ball’s weight? a force greater than the ball’s weight? Y Y

A. A.

Yes Yes

B. B.

No No

Ramps 15

Misconception Alert Misconception Alert

While the forces two objects exert on one

While the forces two objects exert on one another must be equal and opposite, the net another must be equal and opposite, the net force on each object can be anything. force on each object can be anything.

Each force within an eq al

Each force within an eq al b t b t opposite pair is

pposite pair is

Each force within an equal

Each force within an equal-but but-opposite pair is

pposite pair is

exerted on a different object, so they don’t exerted on a different object, so they don’t cancel directly. cancel directly.

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Question 3 Question 3

Why is it easier to push the cart up a ramp?

Why does the ramp’s steepness matter?

Why does the cart tend to roll downhill?

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Forces on a Cart on a Ramp Forces on a Cart on a Ramp

support force f ( )

Ramp force causes cart to accelerate downhill

Ramp force causes cart to accelerate downhill weight ramp force (sum)

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Clicker Question Clicker Question

If I pull uphill on the cart just hard enough to

If I pull uphill on the cart just hard enough to balance the downhill ramp force, the cart will balance the downhill ramp force, the cart will b i l b i l

be motionless.

move at constant velocity.

SLIDE 4

4

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Balanced Cart on Ramp Balanced Cart on Ramp

If you balance the ramp force,

If you balance the ramp force,

the net force on the cart will be zero,

the cart won’t accelerate,

nd it

ill t phill r d nhill r r m in t r t nd it ill t phill r d nhill r r m in t r t

and it will coast uphill or downhill or remain at rest

The more gradual the ramp,

the more nearly its weight and the support balance,

the smaller the ramp force on the cart,

and the easier it is to balance the ramp force!

Ramps 20

Question 4 Question 4

Is there a physical quantity that’s the same for

Is there a physical quantity that’s the same for any trip up the ramp, regardless of its steepness? any trip up the ramp, regardless of its steepness?

What physical quantity is the same for

l i d l l i d l

a long trip up a gradual ramp

a medium trip up a steep ramp

a short trip straight up a vertical ramp

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Energy and Work Energy and Work

Energy

Energy – – a conserved quantity a conserved quantity

it can’t be created or destroyed

it can be transformed or transferred between objects

i th

p it t d rk i th p it t d rk

is the capacity to do work

Work

Work – – mechanical means of transferring energy mechanical means of transferring energy work = force · distance work = force · distance (where force and distance in same direction) (where force and distance in same direction)

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Work Lifting a Cart Work Lifting a Cart

Going straight up:

Going straight up: Force

Force is large,

is large, Distance

Distance is small

is small work = work = Force

Force ·

· Distance

Distance Going up ramp:

Going up ramp: F is small is small Distance

Distance is large

is large

Going up ramp:

Going up ramp: Force

Force is small,

is small, Distance

Distance is large

is large work = work = Force

Force ·

· Distance

Distance

The work is the same, either way!

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Mechanical Advantage Mechanical Advantage

Mechanical advantage:

Doing the same amount of work, but

Doing the same amount of work, but altering the balance between force and distance altering the balance between force and distance

A ramp provides mechanical advantage

You can raise a heavy cart with a modest force,

but you must push that cart a long distance.

Your work is independent of the ramp’s steepness

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The Transfer of Energy The Transfer of Energy

Energy has two principal forms

Kinetic energy

Kinetic energy – – energy of motion energy of motion

Potential energy

Potential energy – – energy stored in forces energy stored in forces

Y k f f h Y k f f h

Your work transfers energy from you to the cart

You do work on the cart

Your chemical potential energy decreases

The cart’s gravitational potential energy increases

SLIDE 5

5

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Summary about Ramps Summary about Ramps

Ramp supports most of the cart’s weight

Ramp supports most of the cart’s weight

You can easily balance the ramp force

You can easily balance the ramp force

You do work pushing the cart up the ramp

You do work pushing the cart up the ramp

Your work is independent of ramp’s steepness

The ramp provides mechanical advantage

It allows you to push less hard

but you must push for a longer distance