An industrial robotic actuator pushes a 2,000 \text{ kg} steel casting along a horizontal … — Armed Services Vocational Aptitude Battery (ASVAB)

An industrial robotic actuator pushes a $2,000 \text{ kg}$ steel casting along a horizontal assembly rail. The actuator applies a continuous forward force of $5,000 \text{ N}$ , while friction from the rail creates an opposing force of $1,000 \text{ N}$ . What is the forward acceleration of the steel casting?

A
$0.5 \text{ m/s}^2$
$2.0 \text{ m/s}^2$ Answer
C
$2.5 \text{ m/s}^2$
D
$20.0 \text{ m/s}^2$

Answer

The correct forward acceleration is

2.0 \text{ m/s}^2

The correct answer is found by first determining the net force acting on the casting. Subtract the

1,000 \text{ N}

opposing friction from the

5,000 \text{ N}

applied force to get a net force of

4,000 \text{ N}

. Then, apply Newton's Second Law (

a = F/m

) by dividing the

4,000 \text{ N}

net force by the

2,000 \text{ kg}

mass, resulting in

2.0 \text{ m/s}^2

Step-by-Step Solution

Determine the net force acting on the steel casting.

F_{\text{net}} = 5,000 \text{ N} \text{ (applied)} - 1,000 \text{ N} \text{ (friction)} = 4,000 \text{ N}

When multiple forces act on an object, you must find the overall net force before calculating acceleration. Opposing forces are subtracted.

Use Newton's Second Law (

F = ma

) to solve for acceleration (

a = F/m

a = \frac{4,000 \text{ N}}{2,000 \text{ kg}} = 2.0 \text{ m/s}^2

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

Key Concept

Newton's Second Law and Net Force Calculation

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