Main content

### Course: AP®︎/College Physics 1 > Unit 3

Lesson 2: Newton's first law: Mass and inertia# 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 ${F}_{g}$ . 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 $g=+9.8{\displaystyle \frac{\text{m}}{{\text{s}}^{2}}}$ .

This force of gravity ${F}_{g}=mg$ (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 $mg$ 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 ${F}_{g}$ 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 $W=mg$ . For example, a mass of $2\text{kg}$ will have a weight of magnitude $W=(2\text{kg})(9.8{\displaystyle \frac{\text{m}}{{\text{s}}^{2}}})=19.6\text{N}$ .

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 $\text{kg}$ , but since weight is a force it has units of $\text{N}$ .

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

### Example 1: Airplane weight

An airplane of mass $4,500\text{kg}$ is taking off, flying through the air accelerating forward and upward. There is a thruster force of $6,700\text{N}$ on the plane in the direction of motion and an air resistance force of $4,300\text{N}$ .

**What is the force of gravity on the airplane during takeoff?**

The force of gravity is always nothing more nor less than $mg$ 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,

### Example 2: Finding mass

An African forest elephant has a weight of $25,000\text{N}$ .

**What is the mass of the African forest elephant?**

Weight is another word for the force of gravity $mg$ . We can solve for the mass using the formula $W={F}_{g}=mg.$

## 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?(86 votes)
- 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.(175 votes)

- How do we define how much is a kilogram, or a pound, etc?(14 votes)
- An excellent question.

This video provides an excellent answer.

https://www.youtube.com/watch?v=ZMByI4s-D-Y(33 votes)

- 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! :)(16 votes)
- 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.(24 votes)

- 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??(7 votes)
- You can calculate the vertical and horizontal components of forces separately.

The extra numbers are "red herrings" meant to trip up students who have some idea of what to do but not a solid foundation. This sort of tactic is used on tests a lot.(11 votes)

- 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!(8 votes)
- They're given as additional information to test whether the student understands the concept of weight which remains a constant or gets befuddled by the presence of extra forces.(9 votes)

- 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.(5 votes)
- 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.(8 votes)

- 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?(4 votes)
- yes they wuld fall eventually, but they are travelling in a circular path, very quickly. In fact they need some way to slow them down so they can fall towards the Earth...(10 votes)

- If an airplane is flying at a constant velocity, how is there no net forces acting on it ?(3 votes)
- The key word here is "net". There are many individual forces acting on the plane in this situation, like the forces of gravity, drag, lift, and thrust. When the plane is flying at a constant velocity, though, it isn't experiencing any acceleration. Newton's second law tells us that an object with 0 acceleration must have 0 net force acting on it, which is the same as saying that all of the forces acting on the plane cancel each other out. In the vertical direction, for instance, the downward force of gravity must be equal and opposite to the lift for the plane to have no vertical acceleration.

Does that help?(4 votes)

- 'The astronauts in the International Space Station experience weightlessness not because there is no force of gravity, but since they are in a free fall orbit around the Earth.' What do you mean by ' a free fall orbit' ?(3 votes)
- Yes, they are falling all the time toward the earth. Hard to understand till you see an example. Put a dot on a piece of paper and draw a Circle around the dot with a 10 cm radius. Now, put another dote 15 cm directly above from the center dot (it should be 5cm above the surface of the circle). Have your dot go 15 cm to the right and 15 cm down the paper. You should still be 5cm from the circle (same as before) even though your dot fell for 15 cm; that's because it's moving forward in a way that keeps it getting any closer to the surface. If you repeat (15 cm down, plus 15 cm back to to the left now) you should still be 5cm from the middle circle; even though your dot 'fell' toward the circle another 15cm. Once you see it, it makes sense.(4 votes)

- what is the difference bw gravity and gravitational force(3 votes)
- 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.(3 votes)