A combat engineer squad is using a motorized winch to pull a 2,500 \text{ kg} concrete bar… — Armed Services Vocational Aptitude Battery (ASVAB)

A combat engineer squad is using a motorized winch to pull a $2,500 \text{ kg}$ concrete barrier horizontally across rough ground to construct a defensive position. The winch applies a constant tension of $12,000 \text{ N}$ to the towing cable. If the friction between the barrier and the ground opposes the motion with a force of $7,000 \text{ N}$ , what is the acceleration of the barrier?

A
$0.5 \text{ m/s}^2$
$2.0 \text{ m/s}^2$ Answer
C
$4.8 \text{ m/s}^2$
D
$0.2 \text{ m/s}^2$

Answer

2.0 \text{ m/s}^2

The correct answer is found by first calculating the net force, which is the applied tension minus the opposing friction (

12,000 \text{ N} - 7,000 \text{ N} = 5,000 \text{ N}

). Then, using Newton's Second Law (

a = \frac{F}{m}

), the net force is divided by the mass of the barrier (

\frac{5,000 \text{ N}}{2,500 \text{ kg}}

) to yield an acceleration of

2.0 \text{ m/s}^2

Step-by-Step Solution

Identify the applied force and the opposing force acting on the barrier.

Applied Force =

12,000 \text{ N}

, Opposing Friction =

7,000 \text{ N}

To find the net force, all horizontal forces acting on the object must be accounted for.

Calculate the net force (

F_{net}

) acting on the concrete barrier.

F_{net} = 12,000 \text{ N} - 7,000 \text{ N} = 5,000 \text{ N}

Net force is the vector sum of all forces; opposite forces are subtracted.

Apply Newton's Second Law (

F = ma

) to find the acceleration.

a = \frac{F_{net}}{m} = \frac{5,000 \text{ N}}{2,500 \text{ kg}} = 2.0 \text{ m/s}^2

Acceleration is directly proportional to net force and inversely proportional to mass.

Key Concept

Newton's Second Law (F=ma) and Net Force

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Key Concept

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