Work in a mechanical system
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Unit 6. Work in a Mechanical System. Unit Vocabulary Pg 1 - 14. Force applied Mechanical work Work done Joule. Efficiency Ratio Radian. Unit Review Pg 15-16. # 1-18. Work involves forces that cause movement.

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Work in a mechanical system

Unit 6

Work in a Mechanical System


Unit vocabulary pg 1 14

Unit VocabularyPg 1 - 14

Force applied

Mechanical work

Work done

Joule

Efficiency

Ratio

Radian


Unit review pg 15 16

Unit ReviewPg 15-16

# 1-18


Work involves forces that cause movement

Work involves forces that cause movement


Work in a mechanical system

“Work is getting something done. You can spend a lot of time and effort on something, but if nothing is accomplished, then no work has been done.”


When is work done

When is work done?

  • When a force or force like quantity causes something to move or change

  • It can be as big as a crane lifting tons of steel or as small as a tiny charge moving in computer memory


Mechanical work

Mechanical Work

  • An applied force must act on an object

  • The object must move when the force is applied


Mechanical work1

Mechanical Work

  • Work is also done when a torque causes something to rotate


Mechanical work fluid

Mechanical Work Fluid

  • A constant pressure causes a fluid to flow from one place to another


Mechanical work electrical

Mechanical Work Electrical

  • Voltage causes charge to move from one place to another


Mechanical work unified

Mechanical Work Unified

  • We can write ONE equation for work that serves as a pattern for the previous four equations


Mechanical work2

Mechanical Work

  • When a force or torque moves an object

  • Mechanical systems use force and torque to cause movement and, thus, to do useful work


Mechanical work3

Mechanical Work

  • Using symbols the equation can be shortened to:

Units = Force x distance

= foot-pound or Newton-meters


Work lifting a barbell

Work Lifting a Barbell

  • Given: A weight lifter applies a vertical force to raise a 200-lb barbell 5 ft.

  • Find: The amount of mechanical work done in lifting the barbell


Work lifting a barbell solution

Work Lifting a Barbell Solution

  • Work = Force x Distance

  • = (200lb)(5ft)

  • = 1000 ft-lb


Football work

Football Work

  • Given: A football player pushes a pile of 4 lineman 6 yards. Each lineman weighs 200 pounds.

  • Find: The amount of mechanical work done pushing the pile.


Football solution

Football Solution

Work = Force x Distance

Force = (4 lineman x 200lbs)

Distance = 6 yards = 18 feet

Work = Force x Distance

Work = (800lb)(18ft)

= 14400 ft-lb


Work done pulling a cart

Work Done Pulling a Cart

  • Given: An electric truck is used to pull a loaded cart a distance of 100 meters. A force of 900 newtons is required to keep the cart moving at a constant speed.

  • Find: The amount of mechanical work done on the cart.


Work done pulling a cart1

Work Done Pulling a Cart

  • Work = Force x Distance

  • = (900N)(100m)

  • = 90,000 N-m


Joule j

Joule (J)

  • A common SI unit for work or energy

  • 1 N-m = 1 Joule

  • 90,000 N-m = 90,000 J

  • 55 N-m = 55 J


Work in a mechanical system

Work

  • Given: 75 Joules are acted on a tennis ball that is thrown

  • If the tennis ball is thrown with a force of 15 Newtons

  • Find: How far did the ball travel while the work was applied?


Work in a mechanical system

Work

  • 75 J = 75 N-m

  • Work = (F) x (D)

  • 75 N-m = (15 N) x (D)

  • 5 m = D


Work in a mechanical system

  • It is important to know that work is only done while the force is applied

  • Examples: Throwing a ball or a vehicle coasting to a stop

  • No work is done when the force is no longer applied (even if something is still moving)


Work and efficiency

Work and Efficiency

  • When work is done it can be rated by efficiency

  • Comparison of the output work by the input work

  • A pulley system = block and tackle


Work and efficiency1

Work and Efficiency

  • Pull with force

    • (F)

  • Moves a distance

    • (D)

  • Load of weight

    • (w)

  • Raised a distance

    • (y)


  • Work and efficiency2

    Work and Efficiency

    • Input work = (F) x (D)

    • Output work = (w) x (y)

    • Efficiency is equal to a ratio of the output work to the input work


    Work and efficiency3

    Work and Efficiency

    % Efficiency =

    Output Work

    Input Work

    x 100%


    Work and efficiency4

    Work and Efficiency

    • Given: The block and tackle shown is used to lift a 600 lb engine. It is raised 0.9 ft as the operator pulls with a force of 100lb over a distance of 6 ft.

    • Find:

      • Input work

      • Output work

      • Efficiency


    Input work

    Input work

    • Input work = F x D

      • F = 100 lb

      • D = 6 ft

  • Input work = 100 lb x 6 ft

  • Input work = 600 ft-lb


  • Output work

    Output work

    • Output work = w x y

      • w = 600 lb

      • y = 0.9 ft

  • Output work = 600 lb x 0.9 ft

  • Output work = 540 ft-lb


  • Efficiency

    Efficiency

    • Efficiency = (Output/Input) x 100%

      • Output = 540 ft-lb

      • Input = 600 ft-lb

  • Efficiency = (540 ft-lb)/(600ft-lb) x 100%

  • Efficiency = 0.9 x 100%

  • Efficiency = 90%


  • Work and efficiency5

    Work and Efficiency

    • Given: The block and tackle shown is used to lift a 1 kg mass. It is raised 15 cm as it is pulled with a force of 5.5 N over a distance of 34 cm.

    • Find:

      • Input work

      • Output work

      • Efficiency

    1 kg = 9.8 N

    100 cm = 1 m


    Input work1

    1 kg = 9.8 N

    100 cm = 1 m

    Input work

    • Input work = F x D

      • F = 5.5 N

      • D = 34 cm = 0.34 m

    • Input work = F x D

      • F = 5.5 N

      • D = 34 cm

    Input work = 5.5 N x 0.34 m

    Input work = 1.87 N-m

    Input work = 1.87 Joules


    Output work1

    1 kg = 9.8 N

    100 cm = 1 m

    Output work

    • Output work = (w) x (y)

      • w = 1 kg = 9.8 N

      • y = 15 cm = 0.15 m

    • Output work = (w) x (y)

      • w = 1 kg

      • y = 15 cm

    Output work = 9.8 N x 0.15 m

    Output work = 1.47 N-m

    Output work = 1.47 Joules


    Efficiency1

    Efficiency

    • Efficiency = (Output/Input) x 100%

      • Output = 1.47 N-m = 1.47 J

      • Input = 1.87 N-m = 1.87 J

  • Efficiency = (1.47 J)/(1.87 J) x 100%

  • Efficiency = 0.786 x 100%

  • Efficiency = 78.6%


  • How do you measure angles in radians

    How do you measure angles in radians?

    • Rotational work occurs when torque causes a mass to rotate through an angle

    • The size of angles is commonly measured in degrees

    • It can also be measured in radians “rad”

    • For this we must know π= 3.1416

    • And Circumference = 2π r


    How do you measure angles in radians1

    How do you measure angles in radians?

    Circumference = 360o = 2π r = 6.28 rad


    How do you measure angles in radians2

    How do you measure angles in radians?

    Circumference = 360o = 2π r = 6.28 rad½ Circumference = 180o = π r = 3.14 rad


    How do you measure angles in radians3

    How do you measure angles in radians?

    Circumference = 360o = 2π r = 6.28 rad¼ Circumference = 90o = ½ π r = 1.57 rad


    How do you measure angles in radians4

    How do you measure angles in radians?

    Circumference = 360o = 2π r = 6.28 rad1/8 Circumference = 45o = ¼ π r = 0.785 rad


    How do you measure angles in radians5

    How do you measure angles in radians?

    • This figure shows 1 radian is equal to 57.3 degrees

    Circumference = 2 π r

    Therefore a full circle must equal 2π r = (2)(3.14)(r) = 6.28 rad


    How do you measure angles in radians6

    How do you measure angles in radians?

    1 Revolution = 6.28 radians1 Radian = 57.3 degrees


    How do you measure angles in radians7

    How do you measure angles in radians?

    1 Revolution = 6.28 radians1 Radian = 57.3 degrees

    • 7 revolutions

    • 435 degrees

    • ¾ revolutions

    • 14 revolutions

    • 26 degrees


    Work done by torque

    Work Done by Torque

    • Note: The angle θmust be measured in radians


    Work done to operate a pump

    Work Done to operate a pump

    Given: An electric motor is used to drive a water pump. The motor provides a torque of 150 N-m.

    Find: How much work is done while the motor turns 40 revolutions?

    Torque = Force x Lever arm

    Work = Torque x Angle

    1 revolution = 6.28 rad


    Work done to turn a crank

    Work Done to turn a crank

    Torque (is given)= 150 N-m

    Torque = Force x Lever arm

    1 revolution = 6.28rad

    40 revolutions = 251.2 rad

    Θ = 251.2 rad

    Work = Torque x Angle

    Work = (150 N-m)(40 revolutions?)

    Work = (150 N-m) (251.2 rad)

    Work = 37,680 N-m or …

    37,680 Joules


    Work done to turn a crank1

    Work Done to turn a crank

    • Given: A simple mechanical winch has a crank handle 1 foot long. A force of 20 pounds is required to turn the crank.

    • Find: How much work is done in turning the crank 5 revolutions.

    • Hint: First we must find torque and the angle in radians in order to find work

    Torque = Force x Lever arm

    Work = Torque x Angle


    Work done to turn a crank2

    Work Done to turn a crank

    Torque = Force x Lever arm

    • Torque = (20 lb) (1 ft)

    • Torque = 20 lb-ft

    1 revolution = 2π rad

    Work = Torque x Angle

    Work = (20 lb-ft)(5 revolutions?)

    Work = (20 lb-ft) (31.4 rad)

    Work = 628 ft-lb

    Θ = (10)(3.14)

    Θ = 31.4 rad


    4 types of mechanical work

    4 Types of Mechanical Work

    ?

    Linear

    Angular

    Electrical

    Thermal


    Work done by a winch activity

    Work Done by a Winch Activity


    Work done by a winch activity1

    Work Done by a Winch Activity


    Work done by a winch activity2

    Work Done by a Winch Activity


    Work done by a winch activity3

    Work Done by a Winch Activity


    Work done by a winch activity4

    Work Done by a Winch Activity

    Done together during lab period


    Work done by a winch activity5

    Work Done by a Winch Activity

    Done individually during lab write up


    Work done by a winch laboratory

    Work Done by a Winch Laboratory


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