Examkin

Question

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

A military transport truck with a mass of 8,000 kg8,000 \text{ kg} is towing a loaded artillery trailer with a mass of 4,000 kg4,000 \text{ kg} along a level, straight road. The truck's engine generates a total forward driving force of 36,000 N36,000 \text{ N}. During motion, the truck experiences a resistive drag force of 8,000 N8,000 \text{ N}, and the trailer experiences its own resistive drag force of 4,000 N4,000 \text{ N}. Assuming the tow bar connecting them is perfectly rigid and horizontal, what is the tension force in the tow bar?

  1. A
    6,000 N6,000 \text{ N}
  2. 12,000 N12,000 \text{ N}Answer
  3. C
    40,000 N40,000 \text{ N}
  4. D
    8,000 N8,000 \text{ N}

Answer

The tension force in the tow bar is 12,000 N12,000 \text{ N}.
To find the tension, you must analyze the forces. First, calculate the acceleration of the entire system. The total mass is 12,000 kg12,000 \text{ kg}. The net force on the system is the driving force minus both drag forces: 36,000 N−(8,000 N+4,000 N)=24,000 N36,000 \text{ N} - (8,000 \text{ N} + 4,000 \text{ N}) = 24,000 \text{ N}. Using a=Fnet/ma = F_{net}/m, the system's acceleration is 24,000 N/12,000 kg=2.0 m/s224,000 \text{ N} / 12,000 \text{ kg} = 2.0 \text{ m/s}^2. Next, isolate the trailer to find the tension. The net force required to accelerate just the trailer is 4,000 kg×2.0 m/s2=8,000 N4,000 \text{ kg} \times 2.0 \text{ m/s}^2 = 8,000 \text{ N}. The tension must provide this net force PLUS overcome the trailer's 4,000 N4,000 \text{ N} drag. Therefore, Tension = Net Force + Drag = 8,000 N+4,000 N=12,000 N8,000 \text{ N} + 4,000 \text{ N} = 12,000 \text{ N}.

Step-by-Step Solution

1
Calculate the total mass and the net forward force for the entire two-vehicle system.
Total mass = 12,000 kg12,000 \text{ kg}. Net force = 36,000 N−(8,000 N+4,000 N)=24,000 N36,000 \text{ N} - (8,000 \text{ N} + 4,000 \text{ N}) = 24,000 \text{ N}.
Newton's Second Law must first be applied to the system as a whole to determine their shared acceleration.
2
Calculate the acceleration of the system using Newton's Second Law (a=Fnet/ma = F_{net}/m).
a=24,000 N/12,000 kg=2.0 m/s2a = 24,000 \text{ N} / 12,000 \text{ kg} = 2.0 \text{ m/s}^2.
Because the tow bar is rigid, the truck and trailer accelerate at the exact same rate.
3
Isolate the trailer as a free body and apply Newton's Second Law to find the tension (TT) in the tow bar.
The net force on the trailer is m×a=4,000 kg×2.0 m/s2=8,000 Nm \times a = 4,000 \text{ kg} \times 2.0 \text{ m/s}^2 = 8,000 \text{ N}. Since Fnet=T−FdragF_{net} = T - F_{drag}, we get 8,000 N=T−4,000 N8,000 \text{ N} = T - 4,000 \text{ N}, which means T=12,000 NT = 12,000 \text{ N}.
The tension in the tow bar must provide enough force to both overcome the trailer's drag and accelerate its mass.

Key Concept

Newton's Second Law applied to Multi-Body Systems
Rate this question

Topics

Newton's Second Law (F=ma)

More questions from this topic