Transcript Gravity PP
Gravity ISCI 2002 More Free Fall Projectiles – Trajectories – Path of free fall – “Trajectory” – Vertical (y) and Horizontal velocities(x) – Vi = 0 Vertical velocity – effects of gravity – (y) has no effect on (x) – Horizontal is constant – Vertical is changing! Free Fall Vertical and Horizontal Components of Free Fall Problem • A ball is thrown horizontally at 25 meters per second from a roof that is 15 meters high. How far does it travel before hitting the ground? – What do you want to know? Distance – What do you know? Vx ; Roof Height – What information do you not have? Time • Equations: – D = ½ at2 – V = d/t Gravity What is Gravity? – All objects pull on each other – “Gravitational Force” Gravitation force is proportional to the mass of an object Moon and Earth – Pull on each other – Earth ‘Wobbles’ – Force is the same in both directions • Fgravity α (mEarth) (mMoon) Mass and Gravity Gravity • Force inversely related to the square of the distance from Earth to the object – Fgravity = 1/d2 • What happens to the force of gravity when: – Mass is constant • Distance doubles? Distance reduced by ½ between the objects? – Distance is constant • Mass is doubled for both objects? Mass is reduced by ½ for both objects? • Inverse-Square Law – The intensity/gravity decreases as the inverse square of the distance. • Gravitation Force ~ 1/d2 Inverse Square Law Gravity and Distance Universal Law of Gravitation • F = G(m1 x m2) _________ d2 G is the “Universal Gravitational Constant” – 6.67 x 10-11 (N x m2)/kg2 – Gravitational force measured between two 1-kg objects • Gravitational effects- small objects – Very small – Significant Gravitational force • Large objects! What does it mean to be Weightless? • Weight = (m)(g) • If zero acceleration, no weight! – No support force • Falling elevator with scales! • Astronauts in space – All things are falling at the same rate – Including the shuttle Centripetal Force • Objects that travel in circular path – Accelerated (directional change) – Velocity is constant • Acceleration – Centripetal – Maintained - constant force exerted on object – Force (perpendicular to the velocity as the direction of the velocity changes) – Force - directed towards the center of the circle • Applications – Car (CF supplied by friction of road against front tires) – Satellite (CF is Earth’s gravity pulling it toward center, perpendicular to satellite’s velocity) Centripetal Force Objects in Free Fall around the Earth • Satellites, Space Labs, Moon – All are in free fall! • Horizontal velocity = curvature of the Earth • 8000m Earth drops 5 m (tangent to the surface) – 8 km/s or 29,000 km/hr or 18,000 mi/hr • Rockets last stage – satellite placed in horizontal path-projection – If velocity correct, follow curvature of Earth – Launched high into the atmosphere? Why? Satellite Orbits In B a circular orbit is maintained. Speed must equal 8 km/s. Planets Stay in Elliptical Orbits • If speed of a satellite > 8 km/s – Follows an elliptical orbit around Earth – Overshoots object - loses speed; regains speed as it approaches center of object • Earth – Sun – Kepler’s First Law: The orbits of the planets are ellipses, with the sun at one focus of the ellipse.