## Mass and Weight

Learn the difference between mass (m) and weight (F_{w}). Find out how to convert to mass from weight and from weight to mass.

**Mass** is a measurement of matter an object contains. Matter is the molecular composition with all the atoms that make up an object. So mass never changes when an object changes location.

**Weight** is a measure of the pull of gravity on an object. This is directly related to mass but will change as the acceleration due to gravity changes. This will change when you change your location like going to the moon.

Natalia's weight changes on the moon which has less mass and a lower acceleration due to gravity. Natalia's mass is the same both locations.

**Weight Equation (F**_{W} = mg)

_{W}= mg)

**F**= weight (N)_{W}**m**= mass (kg)**g**= acceleration due to gravity (m/s^{2})

On earth the accepted value for acceleration due to gravity (g) is 9.8 m/s^{2} but in many classes the rounded number of 10 m/s^{2} is used.

Another way to find weight seen in a later unit is using the universal gravitation equation. The mass of any objects is attracted to another and the force increases the closer they are together. The universal gravitation constant relates the masses and distance to each other within the equation.

**F**= force of gravity_{g}**m**= mass of object 1_{1}**m**= mass of object 2_{2}**d**= distance between objects**G**= Universal Gravitation Constant (6.67430×10^{−11}N⋅m^{2}/kg^{2})

If you were to calculate your weight this way, you would use the earth's mass and yours. The radius of the earth would be the distance used. The acceleration due to gravity (g) is a result of the gravitation force present.

### Example Questions (Mass and Weight)

**1. What is 76 kg Natalia's weight on earth where the acceleration due to gravity is 9.8 m/s ^{2}?**

**2. What is her weight on the moon where the acceleration due to gravity is 1.6 m/s ^{2}?**

**3. If Natalia went to Neptune where the surface acceleration due to gravity is 11.15 m/s ^{2}, would her mass or weight change and what would each be?**

**4. Which changes based on how close you are to another mass? (Mass or Weight)**

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