GRAVITATIONAL FORCE NEAR EARTH
Recap: Gravitational Force Field Recall that gravity is an action-at-adistance force that pulls on objects (regardless of their size or mass) without making any contact with them This occurs because the Earth is surrounded by a gravitational force A force field is a region of space surrounding an object that can exert a force on other objects To represent the force field around Earth, we draw lines of force that point toward Earth s centre
All of the vectors point toward Earth s centre, and their magnitude indicate that the field becomes weaker as the distance from Earth s centre increases As discussed earlier, it is the direction toward the centre that defines what we mean by downward on Earth s surface
Gravitational Field Strength To determine the magnitude of Earth s gravitational force field at a particular location near its surface, physicists use a quantity called gravitational field strength The gravitational field strength is the force per kilogram (N/kg) acting on an object with a gravitational field **at Earth s surface, the gravitational field strength, on average, is 9.8 N/kg[down] **recall that 1 N = kg-m/s 2.N/kg and m/s 2 are the same
Gravitational Field Strength Since Earth is not a perfect sphere, the magnitude of the gravitational field strength at Earth s surface varies according to geographic location For example, at the North Pole the gravitational field strength is 9.8322 N/kg, whereas at the equator it is 9.7805 N/kg
Gravitational Field Strength (copy) Since the gravitational field strength and the acceleration due to gravity are numerically equal, the same symbol,, is used for both Gravitational Field Strength ( ) Force per unit mass acting on an object in a gravitational field (N/kg) Decreases as altitude increases Varies according to location since Earth is not a perfect sphere On Earth g = 9.8 N/kg or 9/8 m/s 2
Gravitational Field Strength & Force of Gravity The gravitational field strength can be applied using the equation for Newton s second law of motion, Fg = mg, to determine the force of gravity acting on an object at Earth s surface
(remember?)
Practice 1. The force of gravity on a 250 kg spacecraft on the moon s surface is 408 N[down] A) what is the gravitational field strength on the moon? B) what is the acceleration due to gravity of a free-falling object on the surface of the moon? 2. A 50 kg person is standing on a bathroom scale inside an elevator. The scale is calibrated in newton s. Use a FBD to help find the reading on the scale when the elevator is A) at rest B) moving up at a constant speed C) accelerating up at 2.2 m/s/s D) accelerating down at 3.0 m/s/s
Gravitational Field Strength polar ice caps The huge masses of major polar ice caps, such as the one covering much of Greenland, have a large gravitational attraction on nearby ocean waters As polar ice caps melt due to global warming, their gravitational attraction decreases, so they are unable to keep as much water near them Thus, sea levels farther from the melting ice caps will rise more than the seal levels near the ice caps
The Difference Between Mass & Weight The terms mass and weight are used interchangeably in everyday language, but these two word have different meanings *copy Mass (m) -Quantity of matter in an object (kg) -Constant only changes if the quantity of matter changes -Measured using a balance Weight (Fg) -Measure of the force of gravity acting on an object (N) -Varies depends on the magnitude of g in that location -Measured using a spring scale
Practice 1. An astronaut on the surface of Mars finds that a rock accelerates at a magnitude of 3.6 m/s2 when it is dropped. The astronaut also finds that a force scale reads 180 N when the astronaut steps on it. A) what is the astronauts mass as determined on the surface of Mars? B) What should the force scale read if the astronaut stepped on it on Earth?
Free fall, Weightlessness & Microgravity Astronauts aboard the International Space Station experience a sensation often referred to as weightlessness or microgravity while on the station orbiting Earth However, the term weightless and microgravity are misleading because they do not explain what is really happening
Free fall, Weightlessness & Microgravity At the altitude where the space station orbits Earth, the force of gravity acting on the astronauts and the station is about 90% of what it is on Earth s surface With such a large force, microgravity or weightlessness are not good descriptions
Free fall, Weightlessness & Microgravity It was Newton who first saw the connection between falling objects, projectiles, and satellites in orbit Imagine a large cannon on the top of a high mountain firing cannon balls horizontally at greater and greater speeds At first the cannon ball falls quickly to the ground As their initial speeds increase, the cannon balls travel farther and farther At very high speeds, a new factor affects the distance Since the Earth is round, the surface of landing curves downwards
Free fall, Weightlessness & Microgravity The cannonball must travel down and around before landing When a certain critical speed is reached, the cannon ball s path curves downward at the same rate as Earth s curvature The cannon ball is then said to be in orbit a constant free fall, always falling toward Earth, but never landing The space station and everything inside also undergo the same type of accelerated motion as the imaginary cannon ball does
Free Fall, Weightlessness & Microgravity When you jump from a height to the ground, you momentarily experience free fall Virtually no force is acting upward on you as the force of gravity pulls you down toward Earth However, the time interval is so short that the sensation does not really have time to take effect The interval of free fall or weightlessness is extended for astronauts during training
http://www.youtube.com/watch?v=v1vrkwb0l2m
Copy: Weightlessness or Micro Gravity Terms often used to describe falling objects (and the sensation) Are misleading because gravity is still in effect (needed by objects to keep them in orbit around Earth) A better explanation is the object is experiencing constant free-fall effect (i.e. the object is falling towards the Earth s surface but never reaches it)
Practice 1. A 74 kg astronaut goes up to the ISS on a mission. During his stay, the gravitational field strength on the station is 8.6 N/Kg A) what is the mass of the astronaut on the station? B) what is the difference between the astronaut s weight on Earth s surface and his weight on the station? C) why does the weight of the astronaut change but not his mass when moving from the surface of Earth to the station? Wd D) why does the astronaut appear weitghtless on the staton?
Text Pg. 167, #5,6,7,10