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## Physics library

### Course: Physics library>Unit 3

Lesson 2: Normal force and contact force

# What is weight?

Weight is another word for the force of gravity.

## What is weight?

Weight W is just another word for the force of gravity F, start subscript, g, end subscript. Weight is a force that acts at all times on all objects near Earth. The Earth pulls on all objects with a force of gravity downward toward the center of the Earth. The magnitude of the force of gravity can be found by multiplying the mass m of the object by the magnitude of the acceleration due to gravity g, equals, plus, 9, point, 8, start fraction, start text, m, end text, divided by, start text, space, s, end text, squared, end fraction.
This force of gravity F, start subscript, g, end subscript, equals, m, g (or "weight") is exerted on all objects by the Earth regardless of which way those objects are moving, and what other forces are exerted on the objects. In other words, there will be a gravitational force of magnitude m, g exerted downward on all objects near the Earth whether they are falling down, flying up at an angle, sitting at rest on a table, or accelerating upward in an elevator. There may be other forces that contribute to the acceleration of the object, but the force of gravity is always present.

## Is weight different from mass?

Yes, weight is different from mass. Weight W is the force of gravity F, start subscript, g, end subscript exerted on an object. Mass m is a measure of the inertia of the object (i.e. how much it resists changes in velocity). They are related since larger masses will have larger weights due to W, equals, m, g. For example, a mass of 2, start text, k, g, end text will have a weight of magnitude W, equals, left parenthesis, 2, start text, space, k, g, end text, right parenthesis, left parenthesis, 9, point, 8, start fraction, start text, m, end text, divided by, start text, space, s, end text, squared, end fraction, right parenthesis, equals, 19, point, 6, start text, space, N, end text.
The weight of an object will change if the object is brought farther away from Earth, or placed on a different planet, since the force of gravity on the object will change. However the mass of the object will remain the same regardless of whether the object is on Earth, in outer space, or on the Moon.
Many people confuse mass with weight. Keep in mind that mass has units of start text, k, g, end text, but since weight is a force it has units of start text, N, end text.

## What do examples involving weight (force of gravity) look like?

### Example 1: Airplane weight

An airplane of mass 4, comma, 500, start text, space, k, g, end text is taking off, flying through the air accelerating forward and upward. There is a thruster force of 6, comma, 700, start text, space, N, end text on the plane in the direction of motion and an air resistance force of 4, comma, 300, start text, space, N, end text.
What is the force of gravity on the airplane during takeoff?
The force of gravity is always nothing more nor less than m, g regardless of any other forces or accelerations involved. So we can find the force of gravity on the plane (i.e. weight) by simply using,
F, start subscript, g, end subscript, equals, m, g, start text, left parenthesis, u, s, e, space, t, h, e, space, f, o, r, m, u, l, a, space, f, o, r, space, w, e, i, g, h, t, right parenthesis, end text
F, start subscript, g, end subscript, equals, left parenthesis, 4, comma, 500, start text, space, k, g, end text, right parenthesis, left parenthesis, 9, point, 8, start fraction, start text, space, m, end text, divided by, start text, space, s, end text, squared, end fraction, right parenthesis, equals, 44, comma, 100, start text, space, N, end text, start text, left parenthesis, c, a, l, c, u, l, a, t, e, space, a, n, d, space, c, e, l, e, b, r, a, t, e, right parenthesis, end text

### Example 2: Finding mass

An African forest elephant has a weight of 25, comma, 000, start text, space, N, end text.
What is the mass of the African forest elephant?
Weight is another word for the force of gravity m, g. We can solve for the mass using the formula W, equals, F, start subscript, g, end subscript, equals, m, g, point
W, equals, m, g, start text, left parenthesis, u, s, e, space, t, h, e, space, f, o, r, m, u, l, a, space, f, o, r, space, w, e, i, g, h, t, right parenthesis, end text
25, comma, 000, start text, space, N, end text, equals, m, left parenthesis, 9, point, 8, start fraction, start text, space, m, end text, divided by, start text, space, s, end text, squared, end fraction, right parenthesis, start text, left parenthesis, p, l, u, g, space, i, n, space, v, a, l, u, e, s, space, f, o, r, space, w, e, i, g, h, t, space, a, n, d, space, g, right parenthesis, end text
m, equals, start fraction, 25, comma, 000, start text, space, N, end text, divided by, left parenthesis, 9, point, 8, start fraction, start text, space, m, end text, divided by, start text, space, s, end text, squared, end fraction, right parenthesis, end fraction, start text, left parenthesis, s, o, l, v, e, space, f, o, r, space, m, a, s, s, space, end text, m, right parenthesis
m, equals, start fraction, 25, comma, 000, start text, space, N, end text, divided by, left parenthesis, 9, point, 8, start fraction, start text, space, m, end text, divided by, start text, space, s, end text, squared, end fraction, right parenthesis, end fraction, equals, 2, comma, 551, start text, space, k, g, end text, start text, left parenthesis, c, a, l, c, u, l, a, t, e, space, a, n, d, space, c, e, l, e, b, r, a, t, e, end text, right parenthesis

## Want to join the conversation?

• Why do we say "I am 70 kilograms" then if weight has units of Newton and mass has units of kg? If i am 70 kg, is my mass 7,14? •   The kilogram is not actually a unit of weight, although people use it as such. It is actually a measure of mass, measurable only because we rarely need to have a force of gravity other than Earth's. The Newton is the real measure of weight, although it is used almost never. So 70 kg is your mass, not your weight.
I hope this helps.
• How do we define how much is a kilogram, or a pound, etc? • this article says that astronauts in the int'l space station experience weightlessness because they are in a free fall orbit around earth. if it's free fall, then why are they remaining in orbit and not falling to the ground where gravity is pulling it? thanks! :) • It's not contadictory. The object is still falling. Just because it never reaches ground doesn't mean it isn't falling toward that ground.
Essentially, an object in orbit means that object is constantly falling toward another object (an object in orbit around Earth constantly falls toward Earth), but because it is also moving sideways (and not just straight down, imagine throwing a ball how it moves 2 directions: down and in the direction you threw it) then it never actually hits the ground. If you could throw a baseball fast enough, it would circle the earth because the farther the ball goes forward the further down "ground" is since the earth is curved, if you would move in a straight line the ground would eventually recede beneath you. (If you are having trouble seeing this just imagine the horizon and how ships can go 'over' it. It's because the earth curves that the ships will drop below a point where they can be seen.)
That's what makes science and math so great is that it explains why things like this, that initially sound counterintuitive, are actually correct.
• Normally, even when filling up medical records, how much you weigh is called weight, not mass. But when you step down on a weighing scale, the downward pull of gravity gives you the weight you're seeing in the scale as lbs or kgs which are units of mass, not weight. Are you saying that we've been perceiving weight and mass incorrectly all this time? I mean you explain all these stuff about weight vs. mass to other people and they'd just give you a big "huh?" and might even laugh at you and think you're being ridiculous. • Since the conversion between mass and weight is fairly constant for every day activities they have been used fairly interchangeably. When you are dealing with science you usually have to be more precise about the terms you use because you can be dealing with conditions that are not as simple as you standing on a stationary scale in a doctors office where.

For pounds it is considered a unit of mass and can be used as force, also referred to as the pound-force, but that causes confusion with formula like F = m * a for example if you have a 1 pound (mass) object accelerated by gravity at 32 ft/s^2 you have a force of 32 pounds (force) but a 1 pound mass produces a 1 pound-force force under standard gravity. Because of this there is a unit called a slug that is used for mass where a 1 slug mass will accelerate at 1 ft/s^2 when a 1 pound force is applied and using this a 1 slug mass will produce 32 pound-force under standard gravity. If you don't use slug & pounds you need to modify F = m * a to be something like F = k * m * a where k is a unitless scaling constant equal to 1/32 to adjust the result so that 1 pound mass under standard gravity produces 1 pound-force.
• Whats the point of the 6700 N force of the thrusters and 4300 N of the air resistance have to do with problem 1? Are they just there to confuse us? Thanks for your help! • In example 1, the thruster force of the airplane as well as the air resistance is given. But why we are not taking them into consideration while solving the problem?? • The text says that the Earth still exercises a gravitational force at the height at which the ISS orbits. Would an astronaut who jumps out of the ISS fall down to earth? And do the pods that bring astronauts back from ISS missions need an engine for acceleration? • what is the difference bw gravity and gravitational force • The terms Gravity and Gravitational Force are mostly used interchangeably, and it is more or less permissible to do so. However, the difference between these two terms is considered prominent in some studies.

Gravitational Force describes the attraction force between any two masses. Gravity specifically describes the resultant force with which a mass is attracted towards the Earth.

Gravitational Force means the force of attraction between any two masses. Weight is the Gravitational force with which the Earth attracts the masses towards its center.

Gravity is related to the resultant force with which a mass is attracted to Earth. So, this happens only between Earth and a mass, unlike gravitational force which occurs between any two masses.

Hope this helps.  