[중3 과학] 3단원(운동과 에너지) 핵심정리(18분) + 교재

Main ideas / lessons

1) Speed (운동의 속력)

• Speed is a physical quantity describing how far an object travels over time.

• Formula: [ \text{speed}=\frac{\text{distance}}{\text{time}} ]

• Common units: m/s, km/h

Interpreting motion with “multiple-star photographs” (strobe-like snapshots)

• If the distance between successive stars is constant → object moves at constant speed.
• If the distance between stars increases → the object moves at an increasingly faster speed.
• If one object’s successive positions spread out more than another’s → it has greater speed.

Converting position vs time to speed (example logic)

• “Position over time” example:
  • Takes 0.2 s to travel 20 cm
  • Speed: [ \frac{20\text{ cm}}{0.2\text{ s}} = 100\text{ cm/s} = 1\text{ m/s} ]

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2) Comparing speeds with different units

• Method: Convert everything to a common unit (meters per second) before comparing.

Example:

• 120 m in 1 minute (60 s) [ 120/60 = 2\text{ m/s} ]

• 36 km/h

  • (36\text{ km} = 36{,}000\text{ m}), (1\text{ h}=3600\text{ s})
  • [ 36{,}000/3600 = 10\text{ m/s} ]

Conclusion in that example:

• Object a has the smallest speed, and b and c are the same.

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3) Average speed (평균 속력)

• Average speed is used when speed is not constant.
• Definition / formula: [ \text{average speed}=\frac{\text{total distance}}{\text{total time}} ]

Example:

• 100 m race: first 50 m in 5 s, next 50 m takes 10 s total (as described) → Average speed becomes 5 m/s.

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Uniform motion and motion graphs (등속운동, 그래프)

4) Uniform motion (등속 운동)

• Uniform motion: speed is constant.
• Distance increases proportionally to time.
• Example situations: escalators, moving walkways, conveyor belts.

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5) Graph interpretation

Time–distance graph (시간-거리 그래프)

• Appears as a straight slanted line.

• Slope = speed

  • Example: In 5 s, distance is 40 m [ 40/5=8 \Rightarrow \text{speed } = 8\text{ m/s} ]

• Distance traveled corresponds to the change in y over the time interval.

Time–speed graph (시간-속력 그래프)

• Appears as a straight line parallel to the time axis.
• Area under the graph = distance traveled
  • Example: Speed = 8 m/s for 5 s [ 8 \times 5=40\text{ m} \Rightarrow \text{distance } = 40\text{ m} ]

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6) Comparing speeds using graphs

• Time–distance graphs: greater speed → steeper slope
• Using area: greater speed → larger area under the time–speed graph

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7) More complex graph analysis (step-by-step)

(A) Piecewise time–distance graph

• Speeds for sections are found by calculating slopes for each segment:
  • Section a slope → speed 20 m/s
  • Section b slope → speed 10 m/s
  • Section c slope → speed 5 m/s
• Average speed from 0 to 4 s:
  • total distance = 40 m
  • time = 4 s [ 40/4=10\text{ m/s} ]

(B) Piecewise time–speed graph

• For each time interval, distance = area under the graph:
  • 0 to 2 s: area = 10 m
  • 2 to 5 s: area = 30 m
  • 5 to 6 s: area = 5 m

• Total distance in 6 s: [ 10+30+5=45\text{ m} ]

• Distance during uniform-motion part (2 to 5 s):

  • 30 m

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Free fall and falling with air resistance (자유낙하)

8) Free fall definition (자유낙하)

• Free fall: an object starts from rest and falls downward due to its own weight:
  • No air resistance
  • Only gravity acts

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9) Key rule for speed during free fall

• Speed increases at a constant rate:
  • approximately 9.8 m/s every second
• This acceleration rate is independent of mass.

Example:

• Release 1 kg and 2 kg from the same height:
  • after 1 s: both about 9.8 m/s
  • after 2 s: both about 19.6 m/s

Therefore:

• all objects not in free fall from the same height (in the same conditions) reach Earth simultaneously, regardless of mass.

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10) Time–speed graph for free fall

• Appears as a slanted straight line
• Since speed increases by 9.8 m/s each second:
  • slope = 9.8

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11) Gravitational force vs mass (reconciliation)

• Gravitational force magnitude:
  • proportional to mass (given as (9.8 \times \text{mass}))
• Example:
  • 1 kg → gravity ≈ 9.8 N
  • 2 kg → gravity ≈ 19.6 N
• Yet:
  • acceleration rate (change in speed per second) stays the same.

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12) Air resistance effect

• If dropped in air:
  • a heavier object (steel ball) experiences relatively less effect from air resistance and reaches the ground first
• In vacuum:
  • only gravity acts → both reach at the same time

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13) Calculating speed and height after 3 s in free fall

• After 3 s:

  • speed: [ 9.8 \times 3 = 29.4\text{ m/s} ]

• Distance fallen in 3 s:

  • given as 44.1 m (as the area under the time–speed graph)
• Initial height (same as distance fallen before impact):
  • 44.1 m

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Work (일)

14) Definition of work

Work is done when:

1) a force acts on an object, and 2) the object moves in the direction of the force.

• Formula: [ W = F \times s ]

• Units: joules (J)

  • (W): work, (F): force, (s): distance

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15) Example calculations

• If (F=16\text{ N}) and (s=5\text{ m}): [ W=16 \times 5=50\text{ J} ]

• If (F=5\text{ N}) and (s=2\text{ m}): [ W=5 \times 2=10\text{ J} ]

• If a 5 kg object is lifted 2 m:

  • weight (=9.8 \times 5 = 49\text{ N}) (stated result used)
  • [ W=49 \times 2 = 98\text{ J} ]

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16) Work from a force–distance graph

• Area under the force vs distance graph = work

Example using the graph:

• From 0 to 3 m: area = 15
• From 3 to 5 m: area = 20
• Total work for 5 m: [ 15+20=35\text{ J} ]

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17) Cases where work = 0

Work is zero when:

• No force acts, even if the object moves
• Force acts but no displacement (distance traveled = 0)
• Force is perpendicular to displacement direction
  • e.g., force upward while moving horizontally → (W=0)

Examples mentioned:

• Moving on frictionless ice with constant velocity:
  • applied force effectively 0 → work 0
• Pushing a wall:
  • force acts, but object doesn’t move → work 0
• Standing while holding an object:
  • no movement → work 0
• Walking forward while holding an object:
  • upward force is perpendicular to horizontal motion → work 0

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18) Work on stairs

• When climbing stairs: use vertical height change (ignore horizontal distance for work in the described simplification).
• Example:
  • object weight = 10 N, height climbed = 4 m [ W=10 \times 4 = 40\text{ J} ]

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Gravitational potential energy (중력 위치에너지)

19) Definition and formula

• Gravitational potential energy is energy due to height above a reference plane.
• If mass (m) is at height (h): [ U = 9.8mh ]

Example:

• (m=10\text{ kg}, h=5\text{ m}) [ U=9.8 \times 10 \times 5 = 490\text{ J} ]

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20) Importance of the reference plane

• The chosen reference plane changes the numerical value of potential energy.
• Example:
  • reference at a: height 10 m → 980 J
  • reference at b: height 5 m → 490 J
  • reference at c (on the plane): height 0 → 0 J

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21) Potential energy conversion (to work)

When a mass is dropped from height (h) onto a pile:

• potential energy converts into work driving the pile.

Relationship described:

• (U = \text{work done})
• (U = 9.8mh = F \times s)

Scaling conclusions:

• If mass doubles → potential energy doubles → pile penetration depth (s) doubles
• If height triples (mass same) → potential energy triples → (s) triples
• Therefore: pile depth is proportional to potential energy

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22) Numerical prediction example

• Given: 2 kg from 5 m drives pile 20 cm
• Ask: 4 kg from 10 m on the same pile

Scaling:

• mass doubles and height doubles → potential energy becomes 4×
• depth becomes 4×

Result: [ 20\text{ cm} \times 4 = 80\text{ cm} ]

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Kinetic energy (운동에너지)

23) Definition and formula

• Kinetic energy = energy of a moving object.
• If mass (m) moves at speed (v): [ K=\frac{1}{2}mv^2 ]

Example:

• (m=5\text{ kg}, v=2\text{ m/s}) [ K = \frac{1}{2}\cdot 5 \cdot 2^2 = 10\text{ J} ]

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24) Conversion of kinetic energy

• When a moving object collides with a stationary wooden block:
  • kinetic energy converts into work pushing the block

Equality concept:

• kinetic energy = work done by the pushing force on the block

Scaling rules:

• If mass doubles (speed same):
  • kinetic energy doubles → distance pushed doubles
• If speed doubles (mass same):
  • kinetic energy becomes 4× → distance pushed becomes 4×

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25) Example: finding force from kinetic energy/work

Given:

• mass 5 kg
• speed 2 m/s

• distance pushed = 4 m

• Kinetic energy: [ \frac{1}{2}mv^2 ]

• Work: [ F \times s ]

• Solve for (F):

  • stated result: 2.5 N

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26) Braking distance (conceptual link)

• Braking distance increases proportionally to kinetic energy.
• If speed doubles:
  • kinetic energy becomes 4×
  • braking distance becomes 4× (as stated)
• Example:
  • 30 m braking at 50 km/h
  • at 100 km/h → 120 m braking (stated)

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Work-energy principle (work ↔ kinetic energy)

27) “Work changes kinetic energy”

If work is done on a moving object:

• its speed increases
• kinetic energy increases

Rule: [ K_f = K_i + W ]

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28) Numerical examples

Example 1

• Initial kinetic energy: 100 J

• Force = 16 (N), distance = 5 m → work: [ W=16\times 5=50\text{ J} ]

• Final kinetic energy: [ K_f=100+50=150\text{ J} ]

Example 2

• Mass = 2 kg, initial speed = 3 m/s
• Work done = 27 J
• Final speed:
  • stated result: 6 m/s

Example 3

• “Work was done on a 4 kg object moving at 10 m/s”
• Final velocity stated: 20 m/s
• Work:
  • initial kinetic energy = 200 J
  • final kinetic energy = 800 J
  • [ W = 800 - 200 = 600\text{ J} ]

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Speakers / sources

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• Source referenced by context: YouTube video titled “[중3 과학] 3단원(운동과 에너지) 핵심정리(18분) + 교재” (title shown in the prompt).