Physics Lesson 12/2

Physics Lesson 12/2

Free-fall acceleration, The Gravitational Field, and Two-Kinds of Mass

Open Ended

What is Geosynchronous orbit?

Free Fall Acceleration

• The acceleration of objects due to Earth's gravity can be found by using Newton's law of universal gravitation and his second law of motion

• By the time you make all the substitutions you end up with the following.

•  $a=g\left(\frac{r_E^3}{r}\right)^2$  

Free Fall Acceleration

• On the surface of Earth, r=r_E and so a=g.

• As you move farther away from Earth's center, r becomes larger than r_E, and the free fall acceleration is reduced according to this inverse square relationship.

So, what happens to your mass as you move farther away from Earth's center?

Weight and weightlessness

• You have seen photos like this one where the astronauts are experiencing zero-g or weightlessness

• Spacecrafts orbit at about 400 km above the Earth's surface.

Weight and Weightlessness

• At that distance, g=8.7 N/kg

• This is only slightly less than the value of g on Earth's surface.

• Gravity is definitely not absent, in fact gravity causes the spacecraft to orbit.

• Why then do the astronauts appear to have no weight?

Weight and Weightlessness

Very simply, it is because the spacecraft is in free fall as it orbits. Therefore there are no contact forces on the astronauts. This makes the apparent weight of the astronauts zero.

The Gravitational Field

• Remember from our discussion of Forces that Gravity is a Field Force, in other words, gravity acts over a distance.

• It acts upon items that are not touching or that are not even close together.

Field Concept

Michael Faraday developed the idea of a field while working with magnets. This concept was later used to explain gravitational fields.

Field Concept

• Any object with a mass is surrounded by a gravitational field, which exerts a force that is directly proportional to the mass of the object and inversely proportional to the square of the distance from the object's center

• The greater the mass, the greater the object's gravitational field.

• The further you go away from the center of the object, the weaker the field gets.

Gravitational Field Equation

 $g\ =\ \frac{Gm}{r^2}$  

Two kinds of Mass

• Inertial Mass

• Gravitational Mass

Inertial Mass

•  $m_{inertial}\ =\ \frac{F_{net}}{a}$  

• Inertial mass is measured by exerting a force on an object and measuring the object's acceleration.

• The more inertial mass an object has the less acceleration it undergoes as a result of  a net force exerted on it.

Gravitational Mass

•  $m_g\ =\ \frac{r^2F_g}{Gm}$  

• Law of universal gravitation also involves mass, but a different kind of mass.

• Mass used in the law of universal gravitation can be measured by using a simple balance.

• If you measure the magnitude of the attraction force of another object of mass m, at a distrance r, then you can defined the gravitational mass.

How different are these two kinds of mass?

• Suppose you have a watermelon in the trunk of your car.

• If you accelerate the car forward, the watermelon will roll backwar relative to the trunk.

• This is a result of its inertial mass, it resistance to acceleration.

How different are these two kinds of masses?

• Now suppose your car climbs a steep hill at a constant speed.

• The watermelon will again roll backward.

• But this time, it moves as a result of its gravitational mass.

• The watermelon is pulled downward toward Earth.

Two kinds of mass

• Newton claimed that inertial and gravitational mass are equal in magnitude.

• This hypothesis is called the principle of equivalence.

• All evidence so far seems to support this

• Einstein was intrigued by the principle of equivalence and that's were we will pick up tomorrow.

Open Ended

Exit Ticket: Why do astronauts experience weightlessness as they orbit the Earth?