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Quick subject briefing
Before this lesson: Consolidation after kinetic/GPE equations, SI units and simple rearrangement have been taught. Both courses and tiers follow the same tasks. No spring, work-done or power calculations are required.
Moving objects have kinetic energy: at fixed mass it grows with speed squared. Lifting changes the gravitational potential energy of the load-Earth system: it depends on vertical rise, not cable length or path. A time change alone does not change mgh. Convert mass to kg first. When energy and mass are given, rearrange for speed squared and then take its positive square root. Use the g supplied in each question.
Words and symbols you will need
- Ek, kinetic energy
- Energy associated with motion, in joules (J).
- GPE change, mgh
- Gravitational potential energy gained/lost with vertical height change h, in J.
- m and v
- Total moving mass in kg; speed in m/s. v² means speed multiplied by itself.
- g and h
- Gravitational field strength in N/kg, and vertical height change in m.
- Square root
- The positive number which multiplies by itself to give v²; required for speed.
Help pupils choose a method
- Identify motion or a vertical change; write the matching equation.
- Convert grams to kilograms. Use the question’s g and its vertical rise where needed.
- Substitute or rearrange with brackets; distinguish a squared speed from the final speed.
- State the unit and check the physical meaning or comparison.
Use the supplied model — pupil page 2
Pupil page 2 gives all three models. Football speed is squared to give 10 J. The box uses its stated 9.8 N/kg and gains 78.4 J. In the separate trolley example v²=9, so speed is 3 m/s, not 9. Worksheet lifts use their explicitly stated 10 N/kg.
Follow three complete models. A 0.80 kg football moves at 5.0 m/s: find Ek. A 2.0 kg box rises 4.0 m with g=9.8 N/kg: find its GPE increase. A different 4.0 kg trolley has Ek=18 J: find its speed.
Worked answer: Football: Ek=0.5×0.80×5.0²=10 J. Box: GPE increase=2.0×9.8×4.0=78.4 J (78 J to two significant figures). Different trolley: v²=2Ek/m=2×18/4.0=9.0 m²/s², so v=3.0 m/s. Square a given speed before multiplying; take a positive square root when the unknown is speed. The box model uses its supplied 9.8, while later worksheet lifts explicitly supply 10.
If pupils are still stuck
Use the matching Say/Ask/Expect route and fresh named retry within its replacement time. If still insecure, help label the given quantities, units and equation, record the precise remaining error, and return it to the usual teacher. Do not extend today’s lesson for the next-lesson retry.
KEEP THIS OPEN DURING THE LESSON
Timed teacher run sheet
- Print the complete 8-page pupil booklet, one per pupil, stapled in order. Double-sided printing is fine.
- Read teacher page 1, then use the timed run sheet on page 2. Keep the 10-page teacher guide separate from pupil copies.
- Pupils need pens, a ruler and a calculator. Reading, data and figures are supplied. No login, pupil devices or practical apparatus are required.
0-5 minPupil page / Q
1 / 1-3
Read aloud / check: Start from memory; check all three responses at 5 minutes.
Next: If insecure A uses first 2 reading minutes.
Answers: 1, 2, 3.
Open check 1 and its coaching →
5-15 minPupil page / Q
2 / reading
Read aloud / check: Read equations, units and complete models.
Next: Check A if used; emphasise square versus square root and supplied g.
15-20 minPupil page / Q
3 / 4
Read aloud / check: Choose a letter and justify both factors; stop.
Next: If insecure B replaces 9-10, not the comparisons that use 5-7.
Answers: 4.
Open check 2 and its coaching →
20-30 minPupil page / Q
4 / 5-10
Read aloud / check: Calculate trolley energies and compare the tests.
Next: If B was used complete 5-8 only; leave 9-10 blank.
Answers: 5, 6, 7, 8, 9, 10.
30-33 minPupil page / Q
5 / 11
33-45 minPupil page / Q
6-7 / 12-17
Read aloud / check: Use the lift and ramp figures with g=10 N/kg.
Next: If C was used complete 12 and 15-17; leave 13-14 blank.
Answers: 12, 13, 14, 15, 16, 17.
45-55 minPupil page / Q
8 / 18
Read aloud / check: Share practice answers; correct and explain one method.
Next: Keep the exit answers hidden.
Answers: 18.
55-60 minPupil page / Q
8 / 19
Read aloud / check: Cover earlier pages; complete the fresh exit independently.
Next: Collect all pages. D is next lesson only.
Answers: 19.
Open check 4 and its coaching →
Estimated 60 minutes. Practice is 10 minutes, a 3-minute mid-check and 12 minutes. A uses reading time; B replaces 9-10; C replaces 13-14; D is next lesson only. Timings not classroom-trialled.
Check entry, hinge and mid-practice at the marked pauses. At 45 minutes share only practice answers. Keep the independent exit and next-lesson answers hidden until submission.
Download teacher guide & answers ↓If several pupils are stuck
Use the matching Say/Ask/Expect route and fresh named retry within its replacement time. If still insecure, help label the given quantities, units and equation, record the precise remaining error, and return it to the usual teacher. Do not extend today’s lesson for the next-lesson retry.
Estimated 60 minutes. Practice is 10 minutes, a 3-minute mid-check and 12 minutes. A uses reading time; B replaces 9-10; C replaces 13-14; D is next lesson only. Timings not classroom-trialled.
ENTRY CHECK
Check 1: Question 1, Question 2, Question 3
Look for: Q1 0.750 kg; Q2 gravitational potential; Q3 9.0 J with squared speed.
If secure: Continue to page 2 reading and models.
If: Mass remains 750 or uses an incorrect conversion.Open coaching
Likely issue: Grams have not been converted to kilograms.
- Say
- The equation expects kilograms. One kilogram contains 1000 grams, so divide the number of grams by 1000 before calculating.
- Ask
- For question 1, how many kilograms is 750 grams?
- Expect
- 0.750 kg; it is less than one kilogram.
Next: Use page 2’s equations/units, then complete Try again A on page 1 in the first 2 reading minutes.
Pupil page 2, conversions row.
If: Gives 3 J or 18 J for question 3, or names the wrong store for lifting.Open coaching
Likely issue: The squared speed, factor one-half or choice of store needs checking.
- Say
- Motion uses kinetic energy with half the mass times speed squared. Lifting between stationary positions increases gravitational potential energy; it does not leave extra kinetic energy.
- Ask
- In question 3, what is 3² and then 0.5×2×9? Which store increases in question 2?
- Expect
- 9, then 9 J; gravitational potential energy increases in the lift.
Next: Use page 2’s equations/units, then complete Try again A on page 1 in the first 2 reading minutes.
Pupil page 2, equation choices and worked models.
HINGE CHECK
Check 2: Question 4
Look for: D with kinetic ×4 from speed squared and GPE ×2 from unsquared height.
If secure: Continue to questions 5-10.
If: A: doubles both energies.Open coaching
Likely issue: The kinetic-energy dependence on speed has been treated as linear.
- Say
- Only speed is squared in the kinetic equation. Doubling it multiplies that squared factor by four; doubling a height multiplies mgh by two.
- Ask
- In question 4, what is (2v)² compared with v²?
- Expect
- 4v², so kinetic energy is four times as large at fixed mass.
Next: Use page 2’s equation comparison, then complete Try again B on page 3 instead of questions 9-10; complete 5-8 on page 4.
Pupil page 2, squared-speed row.
If: B: quadruples both energies.Open coaching
Likely issue: The square rule has been applied to height.
- Say
- The height appears once in mgh. With m and g fixed, twice the vertical rise gives twice the GPE increase.
- Ask
- In question 4, compare mg(2h) with mgh.
- Expect
- mg(2h)=2mgh, so GPE increase doubles.
Next: Use page 2’s equation comparison, then complete Try again B on page 3 instead of questions 9-10; complete 5-8 on page 4.
Pupil page 2, GPE row.
If: C, or D without a reason.Open coaching
Likely issue: The two relationships may be swapped or the letter guessed.
- Say
- Match each change to its own equation before choosing factors. A correct letter needs a reason for both quantities.
- Ask
- Point to the squared variable in Ek and the height variable in mgh; which factor follows for each?
- Expect
- v is squared: ×4. h is not: ×2.
Next: Use page 2’s equation comparison, then complete Try again B on page 3 instead of questions 9-10; complete 5-8 on page 4.
Pupil page 2, two-equation comparison.
MID PRACTICE CHECK
Check 3: Question 11
Look for: h=3.0 m from 180/(6×10), and cable length is not vertical rise.
If secure: Continue to questions 12-17 using the supplied figures.
If: Multiplies by mg or gives 30 m/1800 m.Open coaching
Likely issue: The rearrangement or division by both m and g is insecure.
- Say
- The GPE change is mg multiplied by height. To recover height, divide the energy by the full product mg, with brackets around that denominator.
- Ask
- For question 11, what is mg, then 180/(6×10)?
- Expect
- mg=60 N; height=3.0 m.
Next: Use page 2’s height rearrangement, then complete Try again C on page 5 instead of 13-14; complete 12 and 15-17.
Pupil page 2, height-unknown row.
If: Uses 5.0 m cable length or labels the result J.Open coaching
Likely issue: The physical height or resulting unit has been confused.
- Say
- The height is how far the load changes vertically. Dividing joules by newtons gives metres; a cable’s full length does not tell you the rise.
- Ask
- In question 11, which quantity is unknown, and which unit should h have?
- Expect
- Vertical rise is unknown, in metres. The given energy implies 3.0 m, not cable length.
Next: Use page 2’s height rearrangement, then complete Try again C on page 5 instead of 13-14; complete 12 and 15-17.
Pupil page 2, vertical-change and units rows.
EXIT CHECK
Check 4: Question 19
Look for: Q19: 0.600 kg, v²=36, v=6.0 m/s; h=4.0 m; new Ek=43.2 J with ×4 reason.
If secure: Record which equation, unit and comparison skills are independently secure.
If: Speed is 36 m/s, uses 600 kg or has the wrong unit.Open coaching
Likely issue: Conversion or the final square root still needs follow-up.
- Say
- Convert the mass first. Rearranging kinetic energy gives speed squared, so the final operation is a positive square root; the result is a speed, not an energy.
- Ask
- For question 19(a), what are 600/1000 and the positive square root of 36?
- Expect
- 0.600 kg and 6.0 m/s.
Next: Next lesson revisit the relevant page 2 model, then complete Try again D independently on page 8.
Pupil page 2, speed-unknown model and conversion row.
If: Height wrong or says doubled speed doubles energy.Open coaching
Likely issue: The GPE rearrangement or square relationship needs follow-up.
- Say
- Use a separate equation for each physical change. Divide the lift energy by mg; for a changed speed at fixed mass compare the squares.
- Ask
- For question 19, what is 200/(5×10), and what factor is (2v)²/v²?
- Expect
- Height 4.0 m; factor 4, so new Ek is 43.2 J.
Next: Next lesson revisit the relevant page 2 model, then complete Try again D independently on page 8.
Pupil page 2, height and squared-speed rows.
Answers keyed to the pupil handout
- Question 1
Pupil page 1 - 750/1000=0.750 kg.
- Question 2
Pupil page 1 - Gravitational potential energy store of the load-Earth system. Not kinetic or just “potential”.
- Question 3
Pupil page 1 - Ek=0.5×2.0×3.0²=9.0 J.
- Question 4
Pupil page 3 - D: Ek becomes 4 times as large because (2v)²=4v². GPE increase becomes 2 times as large because h is not squared. Each comparison holds the other quantities fixed.
- Question 5
Pupil page 4 - Ek=0.5×20×0.50²=2.5 J.
- Question 6
Pupil page 4 - Ek=0.5×20×1.0²=10 J.
- Question 7
Pupil page 4 - Ek=0.5×40×1.0²=20 J.
- Question 8
Pupil page 4 - At fixed mass, doubling speed quadruples Ek: 2.5 to 10 J, because speed is squared. At fixed speed, doubling mass doubles Ek: 10 to 20 J. Identify which quantity stays fixed.
- Question 9
Pupil page 4 - v²=2Ek/m=2×24/48=1.0 m²/s². Take the positive square root: v=1.0 m/s.
- Question 10
Pupil page 4 - 800 g=0.800 kg. Ek=0.5×0.800×2.0²=1.6 J.
- Question 11
Pupil page 5 - h=180/(6.0×10)=3.0 m. The required height is the vertical rise of the load; the cable length is not that change. State the equation and unit.
- Question 12
Pupil page 6 - GPE increase=mgh=24×10×2.5=600 J. Use the vertical rise of 2.5 m.
- Question 13
Pupil page 6 - h=GPE increase/(mg)=360/(24×10)=1.5 m.
- Question 14
Pupil page 6 - h is the change in vertical height of the load, 2.5 m, not the cable length. Cable length alone does not give its rise.
- Question 15
Pupil page 6 - The gains are equal: 600 J each. Mass, g and vertical rise are the same; time is not a factor in mgh. No power calculation is asked for.
- Question 16
Pupil page 7 - Use the 0.80 m vertical drop, not the 2.0 m distance along the ramp. GPE change depends on vertical height change.
- Question 17
Pupil page 7 - GPE decrease=2.0×10×0.80=16 J.
- Question 18
Pupil page 8 - Accept a correction with reasoning, such as square speed, convert grams, take the square root or use vertical rise. All-correct route: m, g and vertical drop are unchanged in mgh; ramp path length is not h.
- Question 19
Pupil page 8 - (a) m=0.600 kg; v²=2×10.8/0.600=36 m²/s², v=6.0 m/s. (b) h=200/(5.0×10)=4.0 m. (c) 4×10.8=43.2 J, because speed is squared. Accept equivalent correct working and sensible rounding.
- Try again A
- (a) 1.200 kg. (b) Gravitational potential energy. (c) 0.5×4.0×2.0²=8.0 J.
- Try again B
- Kinetic energy ×9 because (3v)²=9v²; GPE increase ×3 because h appears once. Other quantities stay fixed.
- Try again C
- h=400/(8.0×10)=5.0 m. The load rises vertically 5.0 m; cable length is not the height change.
- Try again D
- (a) m=0.400 kg; v²=2×3.2/0.400=16; v=4.0 m/s. (b) h=90/(3.0×10)=3.0 m. (c) New Ek=3.2/4=0.80 J: halving speed quarters kinetic energy.
Worksheet selection and marking
The 12 source practice parts total 17 marks. Accept equivalent correct working and sensible rounding; require physical reasons for comparisons. No power or spring calculations.
Selection: Q2(a,b,c,e,g,h), Q3(a,c,e,f), Q5(a,b), pages 1-6; 12 parts, 17 marks.
Open the maintained worked solutions →Collect and follow up: Collect every named booklet with working/corrections. Record who needs help with conversion, squared speed/square root, or vertical rise and who needs Try again D next lesson.
