A __________ is an idea used to explain how objects can ________________ on each another without touching ("at a _____________" forces) even if separated by a ____________: field exert forces distance vacuum the 2 fields ____________ with each other interact object 1 object 2 field of 1 field of 2 Examples of fields: __________________ _________________ electric All fields are _________ because they represent ____________ . vectors magnetic gravitational forces

The force of ______________ is explained by saying gravity, Fg The force of ______________ is explained by saying that a gravitational ___________ exists around every______________ . Here is how it works: field, g mass, m To study the field, put a ______ mass m in it, and measure the gravitational ________ Fg pulling on it: test force Suppose there is a _______ somewhere near here (not shown). Because of that, there must be a ________________ field all around it. mass m Fg gravitational

Then the ____________ (magnitude) of the field g is given by the force _______ mass: strength per g = Fg / m same as Fg direction of g: ____________________ units of g: [g] = [ ] / [ ] Fg m [g] = N / kg And since 1 N = __________ , these units can be written: kgm/s2 [g] = kgm/s2 / kg = m/s2 N/kg derived _________ = __________  fundamental m/s2

Ex: A 5.0 kg mass experiences a gravitational force of 30.0 N when placed at the position shown here. 5.0 kg 30 N Determine the strength (magnitude) and direction of the gravitational field at the point shown. strength: g = = Fg / m 30.0 N / 5.0 kg 6.0 N/kg 6.0 m/s2 Fg direction: Same direction as_____

When Fg is due to a planet, we call it _________. So you can write: weight g =  same as  g = Fg/m w/m Ex: What will a 0.10 kg stick of butter weigh when placed in the gravitational field shown? g = = w/m g = 8.2 N/kg w/ 0.10 kg 8.2 N/kg w 0.82 N planet Butterway What is the force of gravity acting on the butter? 0.82 N

Ex: To find the shape of the g field around a "point" mass m, use a “test” mass mt. > Fg strong m mt one _____ field line in the circle out here _____ field lines in the circle in here two weak force lines The force arrows are connected into ____________ .

The lines are ___________ to the forces. They are Notes: The lines are ___________ to the forces. They are “__________________ " that act on a test mass m. 2. Closer lines  _____________ field ________ the mass. Also, the lines ________________ because then one point would have _______________ 3. The arrows show______________ by pointing in towards the mass. We say g is directed _______________________ . tangent lines of force stronger near never cross F? two forces F? attraction radially inward

Closer ____________ to Earth, As seen from far the lines don’t spread away, Earth's field is very similar to a __________ mass. The g field lines are ______________ to the surface. ____________ to Earth, the lines don’t spread out as much: point perpendicular surface > E Coming even closer, ________ spreading less surface

Close to the surface, the lines appear __________ spaced and ___________ . equally > parallel surface g at Earth's surface is ___________ because on the surface you remain the same ___________ from Earth's center (one Earth _____________ ). In fact, g is simply the _________________ due to gravity. Its value is ____________ near Earth's surface. This means that an easy way to find g would be to __________ an object and measure its ____________________ in free fall. constant distance radius acceleration 9.81 m/s2 drop acceleration

(Note: For any planet, use: gp = ) The field g around Earth (or a point mass) is proportional to ________ because _______ is . 1/r2 Fg g = /m Fg > E GMem r2 g = ( )/m GMe r2 r2 1 g = ~ GMe Re2 Re At the surface, r = ___ , so g = = But at greater r's, g will be _________ . (Note: For any planet, use: gp = ) 9.81 m/s2 less GMp Rp2

Ex. g as a function of distance from Earth's center: 9.81 g = ____ /42 = _____ 0.61 4Re 9.81 g = ____ /32 = _____ 1.09 3Re > E g = ____ /22 = _____ 9.81 2.45 2Re 1Re g = ____ 9.81 9.8 inverse square g r 1Re 2Re 3Re 4Re Compare: Big G = ________________________ never changes! 6.67 x 10-11 Nm2/kg2

In sum: g = the gravitational ____________ = the ________________ due to gravity direction: _____________________________ units of g: derived: ______________ fundamental: ______________ How to find g: Take a mass and weigh it (find Fg):  Calculate: g = = Drop an object and find its _________________ . For a planet of mass Mp and radius Rp:  Calculate: g = field acceleration same as gravity N/kg m/s2 w/m Fg/m acceleration GMp Rp2

Ex: Astronauts experiencing “g forces” 0 g  weightless 1 g =  what you feel on Earth 2 g =  when your acceleration upwards is 9.8 m/s2, you feel twice as heavy 3 g = when your acceleration upwards is 2 x (9.8 m/s2), you feel three times as heavy etc Highest survived g forces…..

Ex. To experience “artificial gravity” on earth, use a centrifuge to accelerate: ac = v2 r Higher v  more a  more “gravity” Centrifuges are used in biology and chemistry to separate out substances according to their densities.