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Difficulty: MediumMeasurement of Mass and Weight

A beam balance measures the mass of a metal block as 15 kg15\text{ kg} on Earth. The block is then transported to a planet where the acceleration due to gravity is 3.8 m s−23.8\text{ m s}^{-2} and suspended from a spring balance calibrated in newtons. If the spring balance has a positive zero error of +2.0 N+2.0\text{ N} (reading +2.0 N+2.0\text{ N} when unloaded), what is the displayed reading on the spring balance in newtons?

Answer: 59 N

Answer

The displayed reading on the spring balance is 59 N59\text{ N}.
The beam balance establishes that the block has a constant mass of 15 kg15\text{ kg}. On the planet, the gravitational pull on this mass is W=15 kg×3.8 m s−2=57 NW = 15\text{ kg} \times 3.8\text{ m s}^{-2} = 57\text{ N}. Because the spring balance reads +2.0 N+2.0\text{ N} when unloaded, suspending the block causes the pointer to register 57 N+2.0 N=59 N57\text{ N} + 2.0\text{ N} = 59\text{ N}.

Step-by-Step Solution

1
Determine the true mass using beam balance principles
Mass m=15 kgm = 15\text{ kg}
An equal-arm beam balance measures invariant scalar mass independently of local gravitational field strength.
2
Calculate the true weight on the planet
Weight W=57 NW = 57\text{ N}
Weight is the force of gravity acting on mass, calculated as W=mg=15 kg×3.8 m s−2=57 NW = mg = 15\text{ kg} \times 3.8\text{ m s}^{-2} = 57\text{ N}.
3
Incorporate the positive zero error to find the scale pointer reading
Displayed reading = 59 N59\text{ N}
A positive zero error means the scale indicates +2.0 N+2.0\text{ N} when no load is attached. Therefore, Scale Reading = Actual Weight + Zero Offset = 57 N+2.0 N=59 N57\text{ N} + 2.0\text{ N} = 59\text{ N}.

Key Concept

Mass is an intrinsic property measured by a beam balance, whereas weight is a force measured by a spring balance and affected by zero errors.
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Topics

Measurement of Mass and Weight

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