**Weight**

### A Brief DefinitionEdit

A lot of the time, society confuses mass and weight. Mass is a measurement of how much of matter an object has, while weight is a measurement of the force due to gravity exterted downward on that object. Weight is only one type of force Mass will remain the same on any planet, but because weight depends on acceleration, it will change if the acceleration does. You can see in the image below how mass never changes depending on the location.

This image is from http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/circles/u6l3c.html

### A HistoryEdit

#### Galileo and the Experimental Discovery of *g*Edit

About 400 years ago, Galileo Galilei(1546-1642) set up an experiment in which he rolled balls down an inclined plane. This allowed him to "dilute" gravity, and therefore he could use less precise instruments to take his measurements. Galileo discovered that no matter what the mass of the object was, the magnitude of the accerleration seemed to equal the same thing (this was neglecting the factor of air resistance). Today we know this acceleration as the "acceleration due to gravity", and is approximately 9.81m/s^2, and denoted "g".

#### Newton and His LawsEdit

Newton's Second Law is F=ma, meaning force is equal to mass times the acceleration. We can find our force due to gravity on earth "our weight" using this equation. For acceleration, we just plug in the variable "g", our mass in kilograms for m, and solve. Assume the average person has a mass of 60 kg. His/her weight would be found the following way:

F=mg F=(60 kg) (9.81m/s^2) F= 588 N, or 600 N (kgm/s^2=1 Newton)

This person would have a weight of 600 Newtons. Newtons are the measurement used for force or weight, and are named after Sir Isaac. Newton also applied Kepler's First Law, which states that force on a planet resulting from the sun varies inversely with the square of the distance between the center of that planet and the sun. Enter Newton and his infamous apple story. Legend has it that Newton was at his birth home trying to escape the plague. While sitting in his yard, an apple fell on his head. Newton recognized that the apple fell straight down because the earth attracted it. Newton hypothesized this force must have been proportional to an object's mass, and using his third law of motion (everything has an equal but opposite reaction), he proposed the law of **Universal Gravitation**. The law is as follows:

F=(Gm1m2)/(d^2)

This means that the force due to gravity anywhere in the universe (Newton was a bit ambitious), is equal to the universal gravitational constant (a very tiny number at 6.67 x 10^-11 Nm^2/kg^2), multiplied by the mass of both objects, and divided by the square of the distance between them.

#### Cavendish and the Experimental Discovery of GEdit

About a century after Newton's discovery, Henry Cavendish discovered the gravitional constant that Newton had proposed in his law. The experiment he used has come to be called **The Cavendish Experiment**Using a light source and a rod with a metal sphere on either end suspended by a wire (you can see the image of this below).He then used a larger lead ball and placed it near the smaller balls. This forced the rod to turn. Eventually, the rod would stop turning when the force required to twist the wire was equal to the gravitational force between the balls. He measured this angle and then used it to calculate the attractive forces between the two balls. He substituted the variables into Newton's Law of Gravitation and found the value of G to be **6.67 x 10^-11 Nm^2/kg^2).**

This image is from http://www.planetz.com/image/CavendishExperiment.com

### Applying What We've Learned so FarEdit

So far, we've learned that on earth, we can calculate our weight using F=mg. Let's practice with a regents question:

*What is the weight of and object with a mass of 15 kg? a.5.2 N b.150 kg c.150 N d.1.5 N

**Solution**: Using the equation, we plug in 15 kg for m, and multiply by g. This gives us 147 N, but we must round to two significant figures, which means the weight is 150 N(C).

We have also learned Newton's Universal Law of Gravitation and can use thist o find objects that are far from earth (because with a larger object, the distance between the earth's center and it's center will be equal to the earth's radius with significant figures). If we did use this equation to find the weight of something small, like a person, we'd end up wasting a lot of time. Watch:

F = (Gm1m2)/d^2 = mg

If we cancel, we can see what "g" is actually equal to, and that in Newton's law, we are essentially multiplying mass by g. We can use this law to calculate much grander things like the gravitational attraction between the earth and the moon. Let's try a regents question:

What is the gravitational attraction between the earth and the moon?

**Solution**:

F=? G Mass (moon) = 7.35 x 10^22 kg Mass (earth) = 5.98 x 10^24 kg Distance (from earth to moon) = 3.84 x 10^8 m

If we plug all of our variables in, we can calculate that F is equal to **2.02 x 10^20 Newtons**.

### But What if We're Not On Earth?Edit

You know those scales in the Planetarium that can tell you how much you weigh on mars? Your weight is different on other planets because each planet has a different acceleration due to gravity. In this case, we use F=ma, where m is still mass in kg, F is the force due to gravity (weight, and a is the acceleration due to gravity on the planet. Let's try another regents problem: What is the gravitational acceleration on a planet where a 2 kg mass has a weight of 16 N? a. 1/8 m/s^2 b. 8 m/s^2 c. 10 m/s^2 d. 32 m/s^2 Solution:

F=ma 16N=(2kg)a a = 8 m/s^2 (b)

Keep in mind that Newton's Law of Gravitation is **UNIVERSAL**, and can be modified depending on which planets/objects are involved.

### And What if We're On Earth and the Accelerations Changes?Edit

It's very possible for acceleration to change on earth, thus affecting your weight. This is called apparent weight. First, let's talk about a scale. A scale tells us our weight. We are being pulled down at an acceleration of 9.8 m/s^2. The force we create is forced down on the scale.

This image is from http://www.cord.edu/dept/physics/p128/Images/weight_scale.com

The scale then applies an equal, but opposite force to our weight and the scale reads this value. By changing our acceleration, we can change this weight. Have you ever noticed how you feel in an elevator? If you are in one going up, the scale reads a larger force and we feel heavier. If we are going down, we feel lighter because there is less acceleration. The force that is exerted byt the scale is our apparent weight And what about feeling weightless? It's defintely possible. There is a term called *weightlessness* that occurs if the acceleration we experience equal to g, there are no contact forces pushing up on us, and our scale would read 0 - without diet and exercise!

This image is from http://panda.unm.edu/Courses/finley/P160/Exams/exam1no1.com

Even Einstein is worried about a being too heavy!

### SourcesEdit

- http://saeta.physics.hmc.edu/Courses/p23a/Experiments/Cavendish.html This source provides a lot of information in language that is very difficult to understand on The Cavendish Experiment.
- http://www.physicsclassroom.com/Class/newtlaws/u2l2b.html

This source provides a look at forces and different types of forces.

This source provides a simple explanation of Newton's Universal Law of Gravitation.

- http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/newtlaws/u2l3a.html This source is a simply explanation of Newton's Second Law
- Barron's Regents Review Book This is the best book for little passages about every physics topic that is covered by the New York State Regents and even more advanced topics.
- Zitzewitz, Paul W.,Ph.D.
**Physics: Problems and Principles**. Colombus,OH: Glencoe/McGraw-Hill, 1999.