Work Work is only done by a force on an is only done by a force on an object if the object if the forceforce causes the object causes the object to move in the direction of the to move in the direction of the forceforce..

Objects that are Objects that are at restat rest may have many may have many forces acting on them, but forces acting on them, but NO workNO work is is done if the done if the object does not moveobject does not move ( (zero zero displacementdisplacement).).

WORK = FORCE X WORK = FORCE X DISTANCEDISTANCE

W = F d cos W = F d cos ΘΘJoule (J) = Newton-meterJoule (J) = Newton-meterIn this definition, only the force in In this definition, only the force in

the direction of motion counts.the direction of motion counts. motion

We only consider this!Θ

FORCE

The SI unit of workis the Joule,

named in honor ofJames Prescott Joule.

One One JouleJoule, , JJ, , is the work done whenis the work done when1.0 N of force1.0 N of force is applied is applied

through a through a distance of 1.0 mdistance of 1.0 m..

Graphically, work isGraphically, work isthe area under athe area under a

““Force vs. Displacement” graph.Force vs. Displacement” graph.

displacement, mdisplacement, m

WORK

Work Work

can be done can be done

by or againstby or against

the the

Earth’s gravitational fieldEarth’s gravitational field..

Work is Work is done by gravitydone by gravity when an when an object:object:

- - slides downslides down an incline an incline

- is in - is in free-fallsfree-falls

- undergoes any - undergoes any downwarddownward verticalvertical displacementdisplacement,, including moving including moving down at an angledown at an angle

Work is done against gravity when an Work is done against gravity when an objectobject::

- moves moves upup an an inclineincline

- is is liftedlifted

- - undergoes any undergoes any upwardupward verticalvertical displacementdisplacement,, including moving including moving up at an angleup at an angle

Which car does the greater amount of Which car does the greater amount of work?work?

Each vehicle does the Each vehicle does the same amountsame amount of of work to get to the top of the hill, work to get to the top of the hill, regardless of the path taken. Only regardless of the path taken. Only forceforce and and vertical displacementvertical displacement are are important in determining the amount of important in determining the amount of work done.work done.

A A 5-kg5-kg block of wood is pushed block of wood is pushed across a frictionless surface by a across a frictionless surface by a horizontally applied force of horizontally applied force of 12 12 NN. As a result, the block is . As a result, the block is displaced displaced 6.0 m6.0 m. How much work . How much work is done on the block?is done on the block?

F = 12 N

m = 5 kg

∆x = 6.0 m

W = F∆xW = F∆xW = 12 N x 6.0 mW = 12 N x 6.0 mW = 72 JW = 72 J

The The 5-kg5-kg block of wood is now pulled block of wood is now pulled across a across a wood surfacewood surface by an applied by an applied force of force of 24 N24 N. How much work is done . How much work is done on the wood to displace it on the wood to displace it 6.0 m6.0 m??

F = 24 N

m = 5 kg

Ff

∆x = 6.0 m

First find FFirst find Ffkfk F Ffk fk = μ= μkkFFN N μ μk k = 0.30= 0.30

To find FTo find Ffkfk, you need to first find , you need to first find FFNN

FFNN = F = FWW = mg = mg m = 5 kg m = 5 kg

FFN N = (5 kg)(9.8 m/s= (5 kg)(9.8 m/s22))

FFN N = 49 N= 49 N

FFfkfk = μ = μkkFFNN

FFfkfk = (0.30)(49 N) = (0.30)(49 N)

FFfkfk = 14.7 N = 14.7 N

Next, find Next, find FFnet net FFnet net = F= Faa - F - Ffk fk

FFnetnet = 24 N - 14.7 N = 24 N - 14.7 N

FFnetnet = 9.3 N = 9.3 NFinally, find Finally, find WW::

W = FW = Fnetnet∆x∆x W = (9.3 N)(6.0 m) W = (9.3 N)(6.0 m)

W = 56 JW = 56 J

The same block of wood is now pulled The same block of wood is now pulled across a across a frictionlessfrictionless surface by a surface by a 30 30 NN force applied at an angle of force applied at an angle of 30º30º to to the horizontal. How much work is the horizontal. How much work is done if the wood is displaced done if the wood is displaced 6.0 m6.0 m??

m

∆x

F

Fx

ө = 30 º

W = F cosө ∆xW = (30 N)(cos 30º)(6.0 m)W = 156 J

A A 10-kg10-kg wood block is placed at the top wood block is placed at the top of a frictionless of a frictionless 30º30º inclined plane. inclined plane. How much work is done on the block How much work is done on the block as it slides down the as it slides down the 10-m10-m incline? incline?

ө = 30º

ℓ = 10 m

m = 10 kg

The force that does work on the block is The force that does work on the block is the parallel component of the object’s the parallel component of the object’s weight.weight.Construct a Construct a free-body diagramfree-body diagram::

Find Fp:Find Fp:

Fp = FFp = FWW•sin •sin өө

Fp = (98 N)(sin 30º)Fp = (98 N)(sin 30º)

Fp = 49 NFp = 49 N

Find W: Find W:

W = F∆xW = F∆x

W = (49 N)(10 m)W = (49 N)(10 m)

W = 490 JW = 490 J

Fp

F┴FW

ө

Hooke’s LawHooke’s Law F = kxF = kx k = spring constantk = spring constant

x = displacement from x = displacement from equilibrium position equilibrium position

A given force “F” will stretch A given force “F” will stretch a a spring an amount “x”. spring an amount “x”.

The ratio F/x is a constant The ratio F/x is a constant value for a spring of a value for a spring of a particular length, material, particular length, material,

diameter, etc.diameter, etc.

The The workwork done in stretching a spring done in stretching a spring is is variablevariable over the distance x over the distance x because the because the forceforce required to required to stretch the spring stretch the spring anan increasingly increasingly greater distance from equilibriumgreater distance from equilibrium increasesincreases as as x increasesx increases..

Therefore, the simple equation Therefore, the simple equation W = W = F∆x DOES NOT WORK for springsF∆x DOES NOT WORK for springs and other elastic materials.and other elastic materials.

Graph of Hooke’s LawGraph of Hooke’s LawFor Hooke’s Law, the force is linear.For Hooke’s Law, the force is linear.

In a force vs. time graph, the In a force vs. time graph, the workwork is is equal to the equal to the area under the curvearea under the curve. .

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