GRAVITY AND MOTION

Honelako gehiago

UNIT 8: Applications of Vectors

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by Jennifer Hanke

GRAVITY AND MOTION

Inclined planes

the sliding force is the force parallel to the plane

the vertical component of the force is equal to the normal force

Circular motion

Tangential velocity (direction is at a tangent to the circular path at that moment)

Centripetal force is directed towards the centre

Centripetal acceleration is directed towards the centre

Gravitational field strength at any height

*r is measured from the centre of the planet

G is the universal gravitational constant

Newton's Law of Universal Gravitation

aka the inverse square law

Projectile motion

Projection at an angle

Case 3: Landing at a higher height than launch e.g. basketball

Sy is some positive quantity i.e. Sy =3.1 - 1.6 = +1.5m

Case 2: Landing at a lower height than launch

Sy is some -ve quantity

Case 1: Landing at the same height as at launch

Total hang time is twice the time taken to reach max ht Sy = 0

impact velocity is the same as the initial (launch) velocity

Horizontal projection

free fall vs horizontal projection: time taken to reach the ground is exactly the same

Vx = Ux i.e. Horizontal component of the velocity is constant

$Vx = Ux$

Equations

horizontal range Sx = Uxt

final vertical velocity Vy = gt + Uy Vy2 = 2gSy + Uy2

initial vertical velocity Uy = U sin theta

initial horizontal velocity Ux = U cos theta

Kepler's Law of Planetary motion

3rd Law: the law of period

2nd Law: the law of areas: a radius vector joining any planet to the sun sweeps out equal areas in equal lengths of time

1st Law: Law of orbits: all planets move about the sun in elliptical orbits, having the sun as one of their foci