An engineer on an unknown planet evaluates a solid metallic crate using two different inst… — Armed Services Vocational Aptitude Battery (ASVAB)

An engineer on an unknown planet evaluates a solid metallic crate using two different instruments. First, the crate perfectly balances on a double-pan beam balance against standard reference masses totaling $150\text{ kg}$ . Second, the crate is suspended from a calibrated spring scale, which gives a reading of $600\text{ N}$ . If the crate is transported back to Earth (where gravitational acceleration is $10\text{ m/s}^2$ ), what will the spring scale and the beam balance read, respectively?

Spring scale: $1500\text{ N}$ ; Beam balance: $150\text{ kg}$ Answer
B
Spring scale: $600\text{ N}$ ; Beam balance: $150\text{ kg}$
C
Spring scale: $1500\text{ N}$ ; Beam balance: $375\text{ kg}$
D
Spring scale: $150\text{ N}$ ; Beam balance: $1500\text{ kg}$

Answer

The spring scale will read

1500\text{ N}

and the beam balance will read

150\text{ kg}

The correct answer accurately distinguishes between mass and weight. Mass is the amount of matter and does not change regardless of location, meaning the beam balance will still read

150\text{ kg}

on Earth. Weight is the force of gravity acting on that mass. A spring scale measures this downward force. On Earth, the force is

W = mg = 150\text{ kg} \times 10\text{ m/s}^2 = 1500\text{ N}

Step-by-Step Solution

Determine the true mass of the crate using the beam balance reading.

Mass (

m

) =

150\text{ kg}

A double-pan beam balance compares unknown mass against known reference masses. Because local gravity acts equally on both pans, gravity cancels out, meaning the balance directly measures true mass, which is invariant.

Calculate the weight of the crate on Earth.

Weight on Earth (

W

) =

1500\text{ N}

Weight is the gravitational force exerted on an object, calculated using

W = mg

. Using Earth's gravity (

g = 10\text{ m/s}^2

), the weight is

150\text{ kg} \times 10\text{ m/s}^2 = 1500\text{ N}

Determine what each instrument will read on Earth.

Spring scale reads

1500\text{ N}

; Beam balance reads

150\text{ kg}

The spring scale measures the downward force of weight (

1500\text{ N}

), while the beam balance continues to measure the invariant mass (

150\text{ kg}

Key Concept

Mass is an invariant property of an object measured by a balance, while weight is a force dependent on local gravity measured by a spring scale.

Alternative Method

You can verify the unknown planet's gravity (

g = W/m = 600\text{ N} / 150\text{ kg} = 4\text{ m/s}^2

) to confirm the initial readings are consistent, then reapply the logic to Earth (

g = 10\text{ m/s}^2

) to find the new weight.

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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