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Difficulty: MediumNewton's Second Law (F=ma)

A naval response boat is towing a disabled speedboat through choppy waters. The disabled speedboat has a mass of 4,000 kg4,000 \text{ kg}. The response boat's winch maintains a constant forward tension of 14,000 N14,000 \text{ N} on the tow cable. Meanwhile, the water and wind create a combined resistive drag force of 4,400 N4,400 \text{ N} acting against the speedboat.

What is the forward acceleration of the disabled speedboat in m/s2\text{m/s}^2?

Answer: 2.4 m/s^2

Answer

2.4
The acceleration is determined by first finding the net force (14,000 N−4,400 N=9,600 N14,000 \text{ N} - 4,400 \text{ N} = 9,600 \text{ N}) and then dividing it by the mass (4,000 kg4,000 \text{ kg}) according to Newton's Second Law (a=Fnet/ma = F_{net}/m), resulting in 2.4 m/s22.4 \text{ m/s}^2.

Step-by-Step Solution

1
Identify all horizontal forces acting on the speedboat.
Forward tension force = 14,000 N14,000 \text{ N}, Backward resistive drag force = 4,400 N4,400 \text{ N}.
Newton's Second Law requires the total net force, not just the applied force, to find the resulting acceleration.
2
Calculate the net horizontal force (FnetF_{net}).
Fnet=14,000 N−4,400 N=9,600 NF_{net} = 14,000 \text{ N} - 4,400 \text{ N} = 9,600 \text{ N}.
The drag force acts in the opposite direction of the tow cable, so it must be subtracted.
3
Use Newton's Second Law to solve for acceleration.
a=Fnetm=9,600 N4,000 kg=2.4 m/s2a = \frac{F_{net}}{m} = \frac{9,600 \text{ N}}{4,000 \text{ kg}} = 2.4 \text{ m/s}^2.
Acceleration is directly proportional to net force and inversely proportional to mass.

Key Concept

Newton's Second Law (F=maF=ma) requires first calculating the net force by combining all opposing forces (like applied tension and drag friction) before dividing by the mass to find the resulting acceleration.
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Newton's Second Law (F=ma)

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