Gravity

Force at Impact  A falling ball on a paper surface can break through. The ball is exerting a force  A falling ball on a hard surface rebounds. The surface is exerting a force  There are forces both ways at contact. force of the ball on the surface force of the surface on the ball

Force is Not Motion  The ball breaking paper doesn’t stop. The force needed to break through is small. But that small force is also exerted on the ball.  On a rebound the ground doesn’t move. The force needed to break through is large A force acted in both ways force of the ball on the surface force of the surface on the ball

Third Law: Law of Reaction 3 For every action there is an equal and opposite reaction.  Forces between two objects act in pairs.  F 12 =  F 21 (Newton’s third law) rocket reaction force acts on the rocket rocket and gas are both affected hot gas is forced out

Equal and Opposite  Newton’s law of reaction also applies to the force of gravity. The Earth pulls the MoonThe Earth pulls the Moon The Moon pulls the EarthThe Moon pulls the Earth  Newton used this to describe a Law of Gravity. Moon Earth F ME F EM

Universal Gravity  Newton realized that all objects obey that Law. Other planetsOther planets ApplesApples PeoplePeople  The gravitational force is universal. The gravitational constant is G = 6.67 x Nm 2 /kg 2.The gravitational constant is G = 6.67 x Nm 2 /kg 2.  What is the gravitational force between two students sitting in adjacent seats? Assume the students have a mass of 70 kg each. Assume that they are separated by 1m.  F = (6.67 x Nm 2 /kg 2 ) x (70 kg) 2 / (1 m) 2  F = 3.3 x N.

Surface Gravity  The force of gravity on a mass is its weight.  The force of gravity compared to the mass is the field strength. Consider the force on an unknown mass m.Consider the force on an unknown mass m. Use Earth’s mass M and Earth’s radius RUse Earth’s mass M and Earth’s radius R  Calculate the field strength. g = F/m = GM/R 2 M = 5.97 x kg R = 6.37 x 10 6 m g = 9.81 N/kg = 9.81 m/s 2  This field strength g only applies at Earth’s surface.  Approximately, g is equal to 9.8 N/kg or 9.8 m/s 2.

Variations  Gravity varies over the surface of the Earth. The height of the surface varies – so the radius does, tooThe height of the surface varies – so the radius does, too The material under the surface is not uniformThe material under the surface is not uniform The earth isn’t exactly roundThe earth isn’t exactly round The tides affect the earth as well as the oceansThe tides affect the earth as well as the oceans  One unit of gravitational acceleration used on the Earth is the Galileo. 1 Gal = 1 cm/s 2 = 0.01 m/s 2 = 0.01 N/kg.1 Gal = 1 cm/s 2 = 0.01 m/s 2 = 0.01 N/kg. g = 981 Galg = 981 Gal

Effect of Height  High areas have a greater distance from the center of the Earth. An increase of 1 km should decrease g by 300 mGal. Type of rock affects g. USGS

Latitude Changes  As the Earth spins the equator slightly bulges.  The radius is about 22 km bigger compared to the pole.  Expect a few Gal difference from equator to pole. Equator: m/s 2 North Pole: m/s 2 Colorado School of Mines

Earth’s Rotation  The earth is made of layers of different types of rock.  These rocks can move due to daily tides. Much less than ocean tidesMuch less than ocean tides Period is 12 hours like the oceanPeriod is 12 hours like the ocean  The force of gravity from the Moon is countering some of the force of the Earth. Colorado School of Mines next