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Theme A — Space, Time and Motion

A.3.3 Work Done — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 34 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

A.3.3 Work Done — IB PHYSICS SL notes: Calculate the work done by a constant force, including at an angle, and from the area under a force–displacement graph.Mechanical work = the transfer of energy when an external force causes an object to move over a distance.Constant force al…

  • Constant force along the displacement
  • What the symbols mean
  • Energy transfer
  • Perpendicular component
  • Choosing the component
  • Data booklet

Part 1 of 7Definition of work

Definition of work
Mechanical work
Mechanical work the transfer of energy when an external force causes an object to move over a distance.
Constant force along the displacement
  • W = Fs.
    What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)
  • W is the work done in J, F the constant force in N and s the displacement in m.
Unit
  • 1 N m = 1 J, and in base units kg m2 s−2.
Energy transfer
  • Energy transfer the work done by the resultant force on a system equals the change in energy of the system.
Scalar
  • Scalar work has size only, but its sign matters.

Part 2 of 7Force at an angle

Force at an angle
Equation
  • W = Fs cos θ.
  • θ is the angle between the force and the displacement.
Component
  • Component only F cos θ, the component parallel to the displacement, does work.
Perpendicular component
  • Perpendicular component it does no work.
Choosing the component
  • Choosing the component always resolve the force and use the part parallel to the displacement.
Data booklet
  • Data booklet the cos form is given, but is needed only when the force is at an angle.
Angle θWork doneExample
0°W = Fs (maximum positive)Push along the motion
90°W = 0Centripetal force; normal force on a sliding block
180°W = −Fs (negative)Friction opposing motion

Part 3 of 7Positive, negative and zero work

Positive, negative and zero work
Positive work
  • Positive work it increases the energy of the object.
Negative work
  • Negative work it decreases the energy of the object.
Zero displacement
  • Zero displacement a weight-lifter holding a barbell still does no work in the physics sense.
Carrying a bag horizontally
  • Carrying a bag horizontally the vertical supporting force does no work.
Pushing at constant speed
  • Pushing at constant speed the push does positive work and friction an equal negative amount, so the net work is zero.

Part 4 of 7Variable forces and graphs

Variable forces and graphs
Force–displacement graph
  • Force–displacement graph the area between the line and the displacement axis is the work done.
Constant force
  • Constant force the area is a rectangle, Fs.
Force rising from zero (spring)
  • Force rising from zero (spring) the area is a triangle, ½Fs.
Curved graph
  • Curved graph count squares.
Below the axis
  • Below the axis areas where the force opposes the displacement count as negative.

Part 5 of 7Work and energy transfer

Work–energy theorem
  • Work–energy theorem the work done by the net force equals the change in kinetic energy.
Against gravity
  • Against gravity it raises gravitational potential energy.
Against friction
  • Against friction it increases thermal energy.
Over time
  • Over time work done per second defines power, P = W/t.
    What the symbols mean: P = power (W = J s−1) · W or E = work done / energy transferred (J) · t = time (s) · F = force (N) · v = velocity (m s−1)
Other forms of work
  • Other forms of work electric fields moving charge, and a gas expanding against pressure, W = pΔV.

Part 6 of 7Method

1
Identify the force and find the displacement in the line of the force, or the angle between them.
2
Write W = Fs cos θ.
3
Substitute SI units and attach a sign.
4
For several forces, add the work of each or find the net force first.
5
Check units: N m is J, and any other base units signal an error.
Extra data
  • Extra data questions may give values that are not needed, such as masses, so use only what the method requires.
Check
  • Check the work can also be found from the change in kinetic energy.

Part 7 of 7More from the specification

1
Mechanical work done by an electric motor
  • Mechanical work done by an electric motor electrical energy supplied to a drive motor performs mechanical work, providing a means of lifting loads.
2
Work Done and Elastic Potential Energy
  • When an external force deforms an elastic material, the work done is stored as elastic potential energy: Ep = 1/2 * k * x2,
    • (such as drawing an arrow on a bowstring)
  • where k is spring constant and x is extension.
3
Principle of Conservation of Energy
  • Energy cannot be created or destroyed, only transformed between stores;
    • in mechanical systems, gravitational potential energy lost when falling through height h converts into kinetic energy and wasted thermal dissipation.
4
Efficiency and Energy Flow in Sankey Diagrams
  • A Sankey diagram visually represents energy conservation,
  • where the input arrow width equals the sum of useful energy output and wasted thermal or sound dissipation, defining efficiency as useful energy / total input.
5
Gravitational Energy of Water Columns
  • Hydroelectric systems convert the gravitational potential energy of an elevated water reservoir of mass m and density rho into kinetic energy to drive power generation turbines.
    • (Ep = m * g * h)
      What the symbols mean: Ep = gravitational potential energy gained (J) · m = mass (kg) · g = 9.81 N kg−1 · h = change in height (m)
6
Elastic
  • Returns to original shape when force is removed.
7
Efficiency
  • Useful output divided by total input.
8
Density
  • Mass per unit volume.
9
Wasted energy
  • Energy transferred to stores that are not useful, usually thermal in the surroundings.
10
Energy density
  • The energy available per unit mass or area of a resource.
11
Sankey diagram
  • Diagram where arrow width shows energy amount.
12
Energy conservation
  • Mgh = ½Mv2 + ½Iω2.
13
Final speed
  • Speed at the end, v

Key terms

TermMeaning
Work doneEnergy transferred when a force moves an object, W = Fs cos θ
Joule (J)Unit of work and energy; 1 J = 1 N m
DisplacementDistance moved in a given direction
Component of a forcePart of a force along a chosen direction
Negative workWork that removes energy from an object
Force–displacement graphGraph whose area gives the work done

Avoid these mistakes

1
Using the whole force when it is at an angle — use F cos θ.
2
Saying a force that does not move its point of application does work — zero displacement means zero work.
3
Treating work as a vector — it is a scalar with a sign.
4
Forgetting that friction does negative work — it removes energy from the object.
5
Using the angle with the wrong function — cos θ is for the angle between force and displacement.

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