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Mass vs Weight

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Practice Mass vs Weight
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Mass vs Weight

“Space exploration is an international endeavor.”

Three Japan Aerospace Exploration Agency astronauts -- Akihiko Hoshide, Satoshi Furukawa and Naoko Yamazaki -- are training with the 11-member astronaut candidate class of 2004.   JAXA astronauts Satoshi Furukawa, Akihiko Hoshide and Naoko Yamazaki experience near-weightlessness on the KC-135 training airplane.

Mass and Weight

The mass of an object is defined as the amount of matter in the object.  It is measured by comparing the mass to known masses on an instrument known as a balance.  The mass of an object is measured in kilograms and will be the same whether it is measured on the earth or on the moon.  The weight of an object on the earth is defined as the force acting on the object by the earth’s gravity.  If the object were sitting on the moon, then its weight on the moon would be the force acting on the object by the moon’s gravity.  Weight is measured by a spring scale that has been calibrated for wherever the scale is placed and it reads in Newtons.

The force of gravity is given by Newton’s Second Law, $F = ma$ , when  $F$ is the force of gravity in Newtons,  $m$ is the mass of the object in kilograms, and  $a$ is the acceleration due to gravity, 9.80 m/s 2 .  When the formula is used specifically for finding weight from mass or vice versa, it may appear as $W = mg$ .

Example Problem:  What is the weight of an object sitting on the earth’s surface if the mass of the object is 43.7 kg?

Solution:   $W = mg = (43.7 \ \text{kg})(9.80 \ \text{m/s}^2) = 428 \ \text{N}$

Example Problem:  What is the mass of an object whose weight sitting on the earth is 2570 N?

$m=\frac{W}{a}=\frac{2570 \ \text{N}}{9.80 \ \text{m/s}^2}=262 \ \text{kg}$

Summary

• The mass of an object is measured in kilograms and is defined as the amount of matter in an object.
• The mass of an object is determined by comparing the mass to known masses on a balance.
• The weight of an object on the earth is defined as the force acting on the object by the earth’s gravity.
• Weight is measured by a calibrated spring scale.
• The formula relating mass and weight is $W = mg$ .

Practice

A song about the difference between mass and weight sung by Mr. Edmunds to the tune of Sweet Caroline.  Remember to make allowances for the fact that he is a teacher, not a profession singer. Use this resource to answer the questions that follow.

1. What is used to measure mass?
2. What is used to measure weight?
3. What units are used to measure mass?
4. What units are used to measure weight?

This video shows what appears to be a magic trick but is actually a center of gravity demonstration.

Review

1. The mass of an object on the earth is 100. kg.
1. What is the weight of the object on the earth?
2. What is the mass of the object on the moon?
3. Assuming the acceleration due to gravity on the moon is EXACTLY one-sixth of the acceleration due to gravity on earth, what is the weight of the object on the moon?
2. A man standing on the Earth can exert the same force with his legs as when he is standing on the moon. We know that the mass of the man is the same on the Earth and the Moon. We also know that $F = ma$  is true on both the Earth and the Moon. Will the man be able to jump higher on the Moon than the Earth? Why or why not?