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Zorluk: ZorNewton's Second Law (F=ma)

Match each physical scenario with the magnitude of its resulting acceleration. Apply Newton's Second Law of Motion (F=maF=ma) and ensure you calculate the net force for each situation.

  • A 4,000 kg transport vehicle on a level surface experiences a forward thrust of 12,000 N, a headwind drag of 2,000 N, and rolling friction of 2,000 N.2.0 m/s22.0 \text{ m/s}^2
  • A 1,500 kg hovercraft on water is pushed by two rear propellers providing 3,000 N of thrust each, while facing a 1,500 N opposing water current.3.0 m/s23.0 \text{ m/s}^2
  • A 500 kg payload is hoisted vertically upward by a crane whose cable exerts an upward tension of 8,000 N. (Assume g=10 m/s2g = 10 \text{ m/s}^2)6.0 m/s26.0 \text{ m/s}^2
  • An 800 kg elevator descends as its support cable applies an upward tension of 4,800 N. (Assume g=10 m/s2g = 10 \text{ m/s}^2)4.0 m/s24.0 \text{ m/s}^2

Cevap

The correct matches are: Transport vehicle maps to 2.0 m/s², Hovercraft maps to 3.0 m/s², Hoisted payload maps to 6.0 m/s², and Descending elevator maps to 4.0 m/s².
Each correct match is derived by first identifying all acting forces on the object, determining the net force (FnetF_{net}), and then dividing by the mass (a=Fnet/ma = F_{net}/m). For horizontal motion, opposing forces (friction, drag) are subtracted from applied thrust. For vertical motion, the object's weight (mgmg) must be calculated and subtracted from the cable tension.

Adım Adım Çözüm

1
Calculate the acceleration for the transport vehicle.
Net force = 12,000 N - 2,000 N - 2,000 N = 8,000 N. Acceleration = 8,000 N / 4,000 kg = 2.0 m/s².
Forces acting in the opposite direction of motion (drag and friction) must be subtracted from the forward thrust.
2
Calculate the acceleration for the hovercraft.
Net force = (2 * 3,000 N) - 1,500 N = 4,500 N. Acceleration = 4,500 N / 1,500 kg = 3.0 m/s².
The total thrust from both propellers must be combined before subtracting the opposing water current.
3
Calculate the acceleration for the hoisted payload.
Weight = 500 kg * 10 m/s² = 5,000 N. Net upward force = 8,000 N - 5,000 N = 3,000 N. Acceleration = 3,000 N / 500 kg = 6.0 m/s².
In vertical motion, the downward force of gravity (weight) must be calculated and subtracted from the upward tension to find the net force.
4
Calculate the acceleration for the descending elevator.
Weight = 800 kg * 10 m/s² = 8,000 N. Net downward force = 8,000 N - 4,800 N = 3,200 N. Acceleration = 3,200 N / 800 kg = 4.0 m/s².
Because the elevator descends, the downward gravitational force exceeds the upward tension. Net force is weight minus tension.

Anahtar Kavram

Newton's Second Law of Motion (Fnet=maF_{net} = ma)
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Konular

Newton's Second Law (F=ma)

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