Physics Final Study Guide 10 14 Ch 10 Projectiles Near Earth s Surface When g remains unchanged Without gravity a tossed object follows a straight line path With gravity it follows a curved path In free fall the projectile is only influenced by gravity Projectile motion is a combination of gravity vertical and horizontal motion EX red ball rolled off table while a green ball is dropped at rest which hits floor first Both hit at the same time Why are vertical and horizontal motions separate Adding vertical vector doesn t change the horizontal component So a vertical force causing a vertical change in velocity cannot change its horizontal component Describing horizontal motion No horizontal acceleration So horizontal velocity is constant the equation is Change is horizontal direction horizontal velocity x time Describing vertical motion Constant downward acceleration of 9 8m s2 Taking upward direction as positive the equation is Change in vertical velocity 9 8 x change in time Putting it all together paths of projectile following a parabolic trajectory Horizontal component along the path remains unchanged Only vertical component changes EX roll ball of a table what determines how long take to hit ground The table height NOT mass or ball s horizontal speed before rolling off Time of the flight is usually determine entirely by the vertical motion It is the time the object takes to fall down EX ball launched into the air at 45 degrees to the horizontal initially has Equal horizontal and vertical components EX three stones shot off a cliff at height h at the speed v Stone A is fired at an angle above horizontal stone B is fired at an angle below the horizontal and stone C is fired horizontally Which hits the ground after the longest time interval Stone A but they all hit with the same speed Projectiles Satellites and Planets Follow a parabolic trajectory without air resistance Horizontal component along trajectory remains unchanged Only vertical component changes Velocity at any point can computed with the Pythagorean theorem No matter how far you throw an object its vertical height from which you throw it will remain the same Newton s Mountain paths followed by projectiles fired from a very tall mountain if fired fast enough will never fall to the ground Circular Satellite Orbits Satellite in circular orbit Speed must be great enough to ensure that its falling distance matches Earth s curvature Speed is also constant only the direction changes It is unchanged by gravity EX the moon falls toward Earth in the sense that it falls Beneath the straight line path it would follow without gravity EX two satellites are in circular orbits around two different planets the same distance R away from their centers If planet 1 is more massive than planet 2 the satellite orbiting planet 1 would be moving Faster than the satellite orbiting planet 2 Kepler s Laws of Planetary Motion 1st law the path of each planet around the Sun is an ellipse with the Sun at one focus 2nd law the line from the Sun to any planet sweeps out equal areas of space in equal time intervals 3rd law the square of the orbital period of a planet is directly proportional to the cube of the average distance of the planet from the Sun for al planets What is an ellipse It has two foci the sum of distances to any point on an ellipse from the two foci is a constant EX a satellite in circular orbit travels at a speed and a satellite in an elliptical orbit travels at a speed EX dashed lines show three circular orbit of three satellites around Earth Rank the satellites from greater to least in terms of the length of their orbital period The one with the wider diameter has the longer period and the slowest tangential speed The Atomic Laws of Nature Characteristics of atoms incredibly tiny numerous perpetually in motion ageless Atoms are smaller than the wavelength of visible light Atoms consist of protons neutrons and electrons The electron has the smallest mass When you add or subtract a proton you have a completely different atom The size of an atom is mostly determined by the space occupied by its electrons The reason you don t fall between the atoms in the floor you stand on is because of the electrical forces Molecules two or more atoms bonded together EX NH3 Atoms combine to form molecules by way of shared or exchanged electrons Structure of Solids In crystalline solid atoms are arranged in a regular pattern In amorphous solid atoms are still tightly bound but arranged randomly Shining light through solid the beam is scattered because it bounces off atoms EX patterns produced by X rays scattered through a crystal give direct information about The spacing between the atoms in the crystal Metals electrically conductive shiny cold to touch Non metallic crystals electrically insulating transparent feel regular to touch Atoms in a crystal are held together by electrical bonding forces Density Mass Volume and the units are kg m 3 or gm cm3 Depends upon the mass of atoms and the spacing between atoms Is a property of the material it does not matter how much material you have EX which has the greatest density 10kg concrete 2kg concrete 3 kg iron or 1g of lead 1 g of lead does Elasticity an object subjected to external forces may undergo changes in shape and or size Elasticity is a measure of how much it changes and how well it returns to its original shape materials that do not return to their original shape are inelastic EX 10 cm long spring extends to 12 cm when a 1 kg load is suspended from it What would its length be if 3kg load were suspended from it 16 cm Steel ball EX which will bounce higher off a hard surface rubber ball steel ball or the same Tension when something is pulled Compression when something is squashed On a tree branch pulled at the end the top is on tension and the bottom has compression Scaling Liquids and Pressure EX suppose you drill a hole horizontally through a tree branch as shown Where will the hold weaken the branch the least Near the middle EX two concrete dams one dam with curved wall and one with concave wall which is stronger The one with the concaved wall Scaling for increase in linear dimension cross sectional area and strength grow as the square of the increase volume and weight grow as the cube of the increase EX if a 1cm3 cube is scaled up to a cube that is 10 cm long on each side how does the surface area to volume ratio change 1 10 of original Liquids don t hold shape fluids nearly constant density