Ramps 1 Ramps. Ramps 2 Introductory Question Can a ball ever push downward on a table with a force greater than the ball’s weight? Can a ball ever push.

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Observations About Observations About RampsRamps

It’s difficult to lift a heavy cart straight It’s difficult to lift a heavy cart straight upup

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

The ease depends on the ramp’s The ease depends on the ramp’s steepnesssteepness

Gradual ramps involve gentler pushesGradual ramps involve gentler pushes Gradual ramps involve longer Gradual ramps involve longer

distancesdistances

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4 Questions about Ramps4 Questions about Ramps

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

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

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

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

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Question 1Question 1

Why doesn’t the Why doesn’t the cartcart fall through the fall through the rampramp?? Why doesn’t a Why doesn’t a ballball fall through a fall through a tabletable?? Is the table pushing up on the ball?Is the table pushing up on the ball?

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Support ForcesSupport Forces

A support forceA support force prevents the ball from penetrating the prevents the ball from penetrating the

table’s surfacetable’s surface points directly away from the table’s points directly away from the table’s

surfacesurface Forces Forces alongalong surface are friction surface are friction

((ignore for now)ignore for now)

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Net ForceNet Force

The net force on the ball is The net force on the ball is the sum of all forces on that ballthe sum of all forces on that ball responsible for the ball’s accelerationresponsible for the ball’s acceleration

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Adding up the ForcesAdding up the Forces

As it sits on the table, the ball experiencesAs it sits on the table, the ball experiences its weight downwardits weight downward a support from the table upwarda support from the table upward

Since the ball isn’t accelerating, Since the ball isn’t accelerating, the sum of forces (i.e., net force) on the ball is the sum of forces (i.e., net force) on the ball is

zerozero the support force must balance ball’s weight!the support force must balance ball’s weight!

Since cart isn’t accelerating into ramp,Since cart isn’t accelerating into ramp, the ramp’s support force must keep cart on the ramp’s support force must keep cart on

surfacesurface

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Question 2Question 2

Are both Are both cartcart and and rampramp pushing on pushing on each other?each other? Are both Are both ballball and and tabletable pushing on each pushing on each

other?other? Is the Is the tabletable pushing on the pushing on the ballball?? Is the Is the ballball pushing on the pushing on the tabletable?? Which is pushing harder?Which is pushing harder?

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An ExperimentAn Experiment

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

A.A. YesYes

B.B. NoNo

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Newton’s Third LawNewton’s Third Law

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

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Forces Present Forces Present (Part 1)(Part 1)

For the ball resting on the table, the For the ball resting on the table, the forces areforces are

1.1. On On ballball due to due to gravitygravity (its weight) (its weight)

2.2. On On ballball due to support from due to support from tabletable

3.3. On On tabletable due to support from due to support from ballball These forces all have the same These forces all have the same

magnitudemagnitude Where is the other 3Where is the other 3rdrd law pair? law pair?

zero acceleration3rd lawpair

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Forces Present Forces Present (Part 2)(Part 2)

1.1. On On earthearth due to gravity from the due to gravity from the ballball

2.2. On On ballball due to gravity from the due to gravity from the earthearth

3.3. On On ballball due to support from due to support from tabletable

4.4. On On tabletable due to support from due to support from ballball Forces 2 and 3 aren’t a Newton’s 3Forces 2 and 3 aren’t a Newton’s 3rdrd law law

pair!pair! when equal in magnitude, ball doesn’t when equal in magnitude, ball doesn’t

accelerateaccelerate when not equal in magnitude, ball accelerates!when not equal in magnitude, ball accelerates!

3rd lawpair

3rd lawpair

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Two Crucial Notes:Two Crucial Notes:

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

Each force within an equal-but-Each force within an equal-but-opposite pair is exerted on a opposite pair is exerted on a different object, so they don’t cancel different object, so they don’t cancel directly.directly.

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Question 3Question 3

Why is it easier to push the cart up a Why is it easier to push the cart up a ramp?ramp? How hard must you push on the cart?How hard must you push on the cart?

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Forces on a Cart on a Forces on a Cart on a RampRamp

If you balance ramp force, cart won’t accelerateIf you balance ramp force, cart won’t accelerate

weight

support force

ramp force (sum)

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Balanced Cart on RampBalanced Cart on Ramp

If you balance the ramp force, If you balance the ramp force, the cart won’t acceleratethe cart won’t accelerate the cart will coast – at rest, uphill, or the cart will coast – at rest, uphill, or

downhilldownhill The more gradual the ramp,The more gradual the ramp,

the more nearly weight and support the more nearly weight and support balancebalance

the smaller the ramp force on the cartthe smaller the ramp force on the cart the easier it is to balance the ramp force!the easier it is to balance the ramp force!

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Question 4Question 4

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

a long trip up a gradual rampa long trip up a gradual ramp a medium-long trip up a steep rampa medium-long trip up a steep ramp a short trip straight up a vertical rampa short trip straight up a vertical ramp

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Energy and WorkEnergy and Work

Energy – a conserved quantityEnergy – a conserved quantity can’t be created or destroyedcan’t be created or destroyed can be transformed or transferred between can be transformed or transferred between

objectsobjects is the capacity to do workis the capacity to do work

Work – mechanical means of Work – mechanical means of transferring energytransferring energy

work = force · distancework = force · distance (where force and distance in same (where force and distance in same

direction)direction)

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Work Lifting a Cart Work Lifting a Cart (Part 1)(Part 1)

Going straight up:Going straight up:ForceForce is largeis large DistanceDistance is smallis small

work = work = ForceForce · · DistanceDistance

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Work Lifting a Cart Work Lifting a Cart (Part 2)(Part 2)

Going up ramp:Going up ramp: ForceForce is small is smallDistanceDistance is large is large

work = work = ForceForce · · DistanceDistance

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Work Lifting a Cart Work Lifting a Cart (Part 3)(Part 3)

Going straight up:Going straight up:

work = work = ForceForce · · DistanceDistance Going up ramp:Going up ramp:

work = work = ForceForce · · DistanceDistance The work is the same, either way!The work is the same, either way!

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Mechanical AdvantageMechanical Advantage

Mechanical advantageMechanical advantage Doing the same amount of workDoing the same amount of work Redistributing force and distanceRedistributing force and distance

A ramp provides mechanical advantageA ramp provides mechanical advantage You can raise a heavy cart with a modest You can raise a heavy cart with a modest

forceforce You must push that cart a long distanceYou must push that cart a long distance Your work is independent of the ramp’s Your work is independent of the ramp’s

steepnesssteepness

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The Transfer of EnergyThe Transfer of Energy

Energy has two principal formsEnergy has two principal forms Kinetic energy – energy of motionKinetic energy – energy of motion Potential energy – energy stored in forcesPotential energy – energy stored in forces

Your work transfers energy from you Your work transfers energy from you to the cartto the cart You do work on the cartYou do work on the cart Your chemical potential energy decreasesYour chemical potential energy decreases The cart’s gravitational potential energy The cart’s gravitational potential energy

increasesincreases

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Summary about RampsSummary about Ramps

Ramp supports most of the cart’s weightRamp supports most of the cart’s weight You can easily balance the remaining You can easily balance the remaining

ramp forceramp force You do work pushing the cart up the rampYou do work pushing the cart up the ramp Your work is independent of ramp’s Your work is independent of ramp’s

steepnesssteepness The ramp provides mechanical advantageThe ramp provides mechanical advantage

It allows you to push less hardIt allows you to push less hard but you must push for a longer distancebut you must push for a longer distance