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By the end of the section, you will be able to:
  • Explain the difference between mass and weight
  • Explain why falling objects on Earth are never truly in free fall
  • Describe the concept of weightlessness

Mass and weight are often used interchangeably in everyday conversation. For example, our medical records often show our weight in kilograms but never in the correct units of newtons. In physics, however, there is an important distinction. Weight is the pull of Earth on an object. It depends on the distance from the center of Earth. Unlike weight, mass does not vary with location. The mass of an object is the same on Earth, in orbit, or on the surface of the Moon.

Units of force

The equation F net = m a is used to define net force in terms of mass, length, and time. As explained earlier, the SI unit of force is the newton. Since F net = m a ,

1 N = 1 kg · m/s 2 .

Although almost the entire world uses the newton for the unit of force, in the United States, the most familiar unit of force is the pound (lb), where 1 N = 0.225 lb. Thus, a 225-lb person weighs 1000 N.

Weight and gravitational force

When an object is dropped, it accelerates toward the center of Earth. Newton’s second law says that a net force on an object is responsible for its acceleration. If air resistance is negligible, the net force on a falling object is the gravitational force, commonly called its weight     w , or its force due to gravity acting on an object of mass m . Weight can be denoted as a vector because it has a direction; down is, by definition, the direction of gravity, and hence, weight is a downward force. The magnitude of weight is denoted as w . Galileo was instrumental in showing that, in the absence of air resistance, all objects fall with the same acceleration g . Using Galileo’s result and Newton’s second law, we can derive an equation for weight.

Consider an object with mass m falling toward Earth. It experiences only the downward force of gravity, which is the weight w . Newton’s second law says that the magnitude of the net external force on an object is F net = m a . We know that the acceleration of an object due to gravity is g , or a = g . Substituting these into Newton’s second law gives us the following equations.

Weight

The gravitational force on a mass is its weight. We can write this in vector form, where w is weight and m is mass, as

w = m g .

In scalar form, we can write

w = m g .

Since g = 9.80 m/s 2 on Earth, the weight of a 1.00-kg object on Earth is 9.80 N:

w = m g = ( 1.00 kg ) ( 9.80 m/s 2 ) = 9.80 N .

When the net external force on an object is its weight, we say that it is in free fall    , that is, the only force acting on the object is gravity. However, when objects on Earth fall downward, they are never truly in free fall because there is always some upward resistance force from the air acting on the object.

Acceleration due to gravity g varies slightly over the surface of Earth, so the weight of an object depends on its location and is not an intrinsic property of the object. Weight varies dramatically if we leave Earth’s surface. On the Moon, for example, acceleration due to gravity is only 1.67 m/s 2 . A 1.0-kg mass thus has a weight of 9.8 N on Earth and only about 1.7 N on the Moon.

Questions & Answers

how to find time moved by a mass on a spring
CHIDERA Reply
Questions based on conversion
Geetu Reply
why hot soup is more tastier than cold soup?
Hamisi Reply
energy is involved
michael
what is the importance of banking road in the circular path
Hamisi Reply
the coefficient of static friction of the tires and the pavement becomes less important because the angle of the banked curve helps friction to prevent slipping
Jose
an insect is at the end of the ring and the ring is rotating at an angular speed 'w' and it reaches to centre find its angular speed.
Bharani Reply
Angular speed is the rate at which an object changes its angle (measured) in radians, in a given time period. Angular speed has a magnitude (a value) only.  v represents the linear speed of a rotating object, r its radius, and ω its angular velocity in units of radians per unit of time, then v = rω
Lady
Angular speed = (final angle) - (initial angle) / time = change in position/time. ω = θ /t. ω = angular speed in radians/sec.
Lady
a boy through a ball with minimum velocity of 60 m/s and the ball reach ground 300 metre from him calculate angle of inclination
Emmanuel Reply
what is the fomula for work done
Martha Reply
work= force x distance
Guest
force × distance
Akash
Foece and displacement along the same direction as that of the force
nalin
force×displacement×cos∆ where ∆ is the angle between displacement and force.....i.e dot product of force and displacement
Mohammad
Is the angle between direcrion and force...
Arzoodan
what is d relationship between mass and energy
Odunze Reply
Energy its work condensed, and mass is so
Antonio
E=m×c^2 and c^2=k
Antonio
what is difference between torque and couples? ?
Subhrodip Reply
Well only the name
Antonio
Torque its the effect of a couple of forces
Antonio
two vectorhe angs A and B have equal magnitude of 8.00N of the angels betle teter and the resultant (magnitude and direction) of the resultant vectors between, A an B
UDUAK Reply
acceleration due to gravity on surface of earth is
aqib Reply
it's 9.8m/s, isn't it?
김동현
It's 9.86m/s^2 , since we're talking about acceleration and not speed!
TONY
Equal for all the bodyes 9,8 more or less since is not the same in all places m\s^2
Antonio
when the frame of reference in which we apply the laws is an inertial frame of reference.please check internet for details about inertial frame of references.
ashok Reply
specify that which law of newton you have to apply
paresh Reply
when do newton laws apply in science?
مسعود Reply
Only on classical macroscopy relative low speed
Antonio
Verify that nothing has zero energy
Dartz Reply
Practice Key Terms 2

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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