During a facility upgrade, an industrial overhead crane is lifting a large generator compo… — Armed Services Vocational Aptitude Battery (ASVAB)

During a facility upgrade, an industrial overhead crane is lifting a large generator component vertically. The component has a mass of $2,500 \text{ kg}$ . The crane's hoist mechanism applies an upward tension force of $35,000 \text{ N}$ . Assuming the acceleration due to gravity is $10 \text{ m/s}^2$ , what is the upward acceleration of the generator component?

A
$0.25 \text{ m/s}^2$
$4.0 \text{ m/s}^2$ Cevap
C
$12.8 \text{ m/s}^2$
D
$14.0 \text{ m/s}^2$

Cevap

The upward acceleration of the generator component is

4.0 \text{ m/s}^2

To find the acceleration, we first determine the net force acting on the component. The crane pulls up with

35,000 \text{ N}

, but gravity pulls down with a force equal to the object's weight. The weight is the mass times gravity (

2,500 \text{ kg} \times 10 \text{ m/s}^2 = 25,000 \text{ N}

). The net upward force is the difference between these two opposing forces (

35,000 \text{ N} - 25,000 \text{ N} = 10,000 \text{ N}

). Finally, applying Newton's Second Law (

a = F_{net} / m

), we divide the net force by the mass (

10,000 \text{ N} / 2,500 \text{ kg}

) to find an acceleration of

4.0 \text{ m/s}^2

Adım Adım Çözüm

Calculate the downward weight force of the generator component.

Weight (

W

) =

m \times g

2,500 \text{ kg} \times 10 \text{ m/s}^2

25,000 \text{ N}

Gravity pulls down on the mass, creating an opposing force that must be overcome to lift the component.

Determine the net force acting on the component.

Net Force (

F_{net}

) = Upward Force - Downward Weight =

35,000 \text{ N} - 25,000 \text{ N}

10,000 \text{ N}

Newton's Second Law requires the total net force, taking all acting forces (tension and gravity) into account.

Calculate the acceleration using Newton's Second Law (

F = ma

Acceleration (

a

) =

F_{net} / m

10,000 \text{ N} / 2,500 \text{ kg}

4.0 \text{ m/s}^2

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

Anahtar Kavram

Newton's Second Law requires determining the net force by summing all forces acting on an object (including gravity) before dividing by mass to find acceleration.

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