Weight is a force that results from the action of gravity on mass. At Earth’s surface, gravity attracts all masses downward with a force of 9.8 N/kg. This gravitational force is called weight, which is calculated by multiplying its mass by the strength of gravity in newtons per kilogram. For example, a 10 kg object has a weight of  9.8 N/kg × 10 kg = 98 N. Read the text aloud
(5.1) F w =mg
Fw  = weight force (N)
m  = mass (kg)
g  = acceleration of gravity = 9.8 N/kg at Earth’s surface
The value of 9.8 N/kg is used so often that it has its own symbol, g. When you see “g” in an equation such as F = mg, substitute the strength of gravity at Earth’s surface g = 9.8 N/kg. The value of g may also be given as g = 9.8 m/s2. This is equivalent because 1 N of force is defined as the force that causes a 1 kg object to accelerate at 1 m/s2. Read the text aloud
Weight is not mass. Mass is measured in kilograms and grams. Weight is measured in newtons or pounds. The source of confusion is that we use weight to measure mass! When you place an object on an electronic balance, the sensor in the balance measures the force of gravity acting on the object. Since this force is proportional to mass, a calculation done inside the balance divides the force by 9.8 N/kg to read mass in kilograms, or by 0.0098 N/g to read mass in grams. A balance calibrated to work on Earth will not be accurate on the Moon or anyplace where gravity is not exactly the same as it is on Earth. In the extreme case, far from any planet or star, an object will still have mass, but it may be weightless because of the absence of gravity. Read the text aloud
Force conversion factorsEquation (5.1) relates weight in newtons to mass in kilograms. If force is in newtons and g is in newtons per kilogram, then mass must be in kilograms. Many physics problems require you to convert units, such as pounds to newtons. Do these conversions before substituting any values into the equation to calculate your results. Read the text aloud Show Where does the conversion factor come from?
If a person has a weight of 125 lb, then what is that person’s mass in kilograms?
Asked: mass
Given: weight Fw = 125 lb
Relationships: equation for weight: Fw = mg
conversion factor: (444.8 N)/(1 lb) = 1
acceleration due to gravity: g = 9.8 N/kg
Solution: Convert weight from pounds to newtons: 125 lb=( 125 lb )( 4.448 N 1 lb )=556 N Calculate mass using weight equation: F w =mg m= F w g = 556 N 9.8 N/kg =56.7 kg
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How many newtons of gravitational force is exerted on a man with a mass of 80 kg who is standing on the Moon, where g = 1.6 N/kg?
  1. 128 N
  2. 64 N
  3. 784 N
  4. 50 N

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