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Difficulty: HardNewton'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

Answer

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.

Step-by-Step Solution

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.

Key Concept

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

Newton's Second Law (F=ma)

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