4.8 The Normal Force. Apparent Weight

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1 4.8 The Normal Force Apparent Weight Definition: The apparent weight of an object is the reading of the scale. It is equal to the normal force the man exerts on the scale. For a man standing on a scale in an elevator consider the four cases shown below Elevator moving at Constant speed

2 Apparent Weightlessness and Artificial Gravity An object in free fall is not subjected to a normal force and hence appears weightless. However when an object falls in our atmosphere is feels the rush of air as it travels towards the ground. Hence the object does not feel completely weightless. Lecture 13

To accomplish this a plane it used to fly passengers first upwards at a high acceleration.

3 Apparent Weightlessness and Artificial Gravity In order to simulate weightlessness it is necessary to eliminate the effect of air resistance. To accomplish this a plane it used to fly passengers first upwards at a high acceleration. When the plane begins to maintain a steady arc at the top, the normal force becomes zero giving the impression of weightlessness. NASA Low g plane Lecture 13

4 Neat Videos Drinking coffee in Low g Drinking water Water Balloons in Low g

In order to make space-goers more comfortable it is possible to use the effects of uniform circular motion to

5 Apparent Weightlessness and Artificial Gravity In space far from the earth astronauts are in a perpetual state of weightlessness. In order to make space-goers more comfortable it is possible to use the effects of uniform circular motion to simulate the effects of gravity. By constructing a space station is the form of the cylinder the floor would provide the necessary centripetal force necessary to get objects going around in a circle. Lecture 13

6 4.7 The Gravitational Force Newton s Law of Universal Gravitation Every particle in the universe exerts an attractive force on every other particle. A particle is a piece of matter, small enough in size to be regarded as a mathematical point. The force that each exerts on the other is directed along the line joining the particles.

7 4.7 The Gravitational Force For two particles that have masses m 1 and m 2 and are separated by a distance r, the force has a magnitude given by m m F G 1 2 r 2 G N m 2 kg 2

8 Three interesting examples: a. Calculate the gravitational force between the earth and a 60 kg person b. Calculate the gravitational force between two 60 kg people one meter apart c. Calculate the gravitational force between the earth and moon Example a: THESE NUMERICAL EXAMPLES ARE ONLY PRESENTED TO SHOW THE SIZE OF THE GRAITATINAL FORCE.YOU DON T NEED TO BE ABLE TO DO THEM! F g GM pm E r x10 11 * 60 * 6x10 24 (6.38x10 6 ) 2 N 588N and W = mg = 60kg * 9.8m/s 2 588N (same answer!) Formula for weight and universal law of gravity give the same answer. This is because in formula W=mg g GM E r 2

Example B: FORCE BETWEEN TWO 60 KG PEOPLE F g GM p M E r 2 6.67x10 11 * 60 * 60 (1) 2 N.00000024N THE FORCE IS VERY SMALL! Example C: FORCE BETWEEN EARTH AND MOON F g GM p M E r 2 6.

9 Example B: FORCE BETWEEN TWO 60 KG PEOPLE F g GM p M E r x10 11 * 60 * 60 (1) 2 N N THE FORCE IS VERY SMALL! Example C: FORCE BETWEEN EARTH AND MOON F g GM p M E r x10 11 * 6x10 24 * 7.35x10 22 (3.85x10 8 ) 2 THIS FORCE IS VERY LARGE! N 1.98X10 20 N GRAVITY IS THE WEAKEST OF THE FOUR FUNDAMENTAL FORCES BUT CAN BE LARGE WHEN THE MASSES INVOLVED ARE LARGE

10 Satellite Motion A projectile launched from the center of the earth will fall back to earth until...

11 The speed of a satellite at a distance r from the earth s center is: V S GM Earth r Note that the mass of the satellite does not appear in the equation. This means that the speed of a satellite in orbit DOES NOT depend on the satellite mass so all objects in this orbit will move at the same speed irregardless of size. How fast is this speed?

12 Example: International Space Station r=6380km+340 km=6780km M Earth =6x10 24 kg V S GM r 6.67x x10 24 Earth 6780x10 3 = 7683m/s = 27,658 km/h!! The ISS which is only 340km above the earth must travel at 27,658 km/h in order to stay in that orbit. THIS IS VERY FAST!!

13 Some Interesting stuff...

GLOBAL POSITIONING SYSTEM(GPS) The first GPS satellite was launched in 1978.

Each satellite is built to last about 10 years.

14 GLOBAL POSITIONING SYSTEM(GPS) The first GPS satellite was launched in A full constellation of 24 satellites was achieved in Each satellite is built to last about 10 years. Replacements are constantly being built and launched into orbit. A GPS satellite weighs approximately 2,000 pounds and is about 17 feet across with the solar panels extended. Transmitter power is only 50 watts or less.

15 Global Positioning System

16 Global Positioning System The GPS system works by having the satellite send radio waves which carry precise time measurements. When receivers on the earth detect the waves they can calculate the radial distance they are from the satellite.

17 Global Positioning System Therefore the signal from one satellite allows people to determine where they are located within a circle. When two other satellites are used, the receiver can determine a more precise location.

The Force of Gravity exists between any two masses! Always attractive do you feel the attraction? Slide 6-35

The Force of Gravity exists between any two masses! Always attractive do you feel the attraction? Slide 6-35 Summary Newton s law of gravity describes the gravitational force between A. the earth and the