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Zorluk: KolayWork, Energy, and Power

A roller coaster car is released from rest at the top of a hill and coasts without friction along a track. Place the following track locations in order from LEAST kinetic energy to GREATEST kinetic energy.

  1. 1At the starting crest of the hill (highest elevation)
  2. 2Halfway down the slope (intermediate elevation)
  3. 3Near the bottom of the incline (low elevation)
  4. 4At the lowest point of the track (ground level)

Cevap

Starting crest (highest elevation) → Halfway down the slope → Near the bottom of the incline → Lowest point of the track (ground level)
By the conservation of energy, gravitational potential energy is continuously converted into kinetic energy as the car moves downhill. Since the car starts from rest at the highest elevation, its initial kinetic energy is zero. As it descends, its speed increases, reaching maximum kinetic energy at the lowest point of the track.

Adım Adım Çözüm

1
Identify the initial energy state and energy transformation mechanism
At rest at the highest point, kinetic energy is zero (Ek=0E_k = 0) and potential energy is at its maximum.
Kinetic energy depends on speed (Ek=12mv2E_k = \frac{1}{2}mv^2), so an object at rest has zero kinetic energy.
2
Apply the law of conservation of mechanical energy as the car descends
As elevation decreases, gravitational potential energy is converted into kinetic energy, increasing the speed of the car.
In a frictionless system, total mechanical energy is conserved (Etotal=Ep+EkE_{total} = E_p + E_k).
3
Rank the positions from lowest to highest kinetic energy based on elevation
Elevation from highest to lowest directly corresponds to kinetic energy from least to greatest: crest (0 J0\text{ J}) < halfway down < near bottom < lowest point (maximum).
Lower elevation yields lower potential energy and higher kinetic energy.

Anahtar Kavram

Conservation of Mechanical Energy and Potential-to-Kinetic Energy Transformation
Tahmini Süre:45s
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Konular

Work, Energy, and Power

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