Free-Falling What goes up must come down! Presentation 2003 R. McDermott

Free Fall  An object is “free-falling” whenever it is moving, unsupported, through the air  It may be moving straight up or down  It may be moving sideways as well as up or down  It may have been dropped  It may have been thrown downward  It may have been thrown upward

Free Fall Free-falling objects obey acceleration equations, and the acceleration is a constant 9.81 m/s 2 downward no matter how the object was initially moving.

Free Fall All free-falling objects fall at the same rate:

If it’s Rising, How can it be Falling?  An object “falls” 4.9 meters in the first second  If it is dropped from rest, it will be 4.9 meters down after one second  If it is thrown upward at 10 m/s, it will be 5.1 meters above its starting point after one second (10 – 4.9)  However it may be moving, it will be lower than it would have been without gravity acting, by an amount equal to what it lost by falling.

Gravity-Free Path

Free Fall (cont)  If an object is “free-falling”, its vertical motion may be treated as linear motion  All linear motion equations apply  The object starts at rest if you drop it (V i = 0)  The object is at rest (V f = 0) at its highest point if it is initially thrown upward  When an object falls, it speeds up. As it rises, it slows down

Falling (cont)  The acceleration for a free-falling object is 9.8 m/s 2 downward regardless of the object’s motion  A falling object gains 9.8 m/s of speed each second it falls  A rising object loses 9.8 m/s of speed each second it rises  The acceleration of gravity (9.8 m/s 2 ) is given the symbol “g” in equations. For example: V f = V i + gt

Example #1: An object is dropped and falls for 3.0 seconds. How far does it fall? Identify symbols: Identify Equation: V i = 0 m/s, a = g, t = 3.0 s,  x = ?  x = V i t + ½ at 2

Example #1 (cont): An object is dropped and falls for 3.0 seconds. How far does it fall? Determine the sign of “g”: Substitute: Since the object is falling and speeding up, acceleration has the same sign as the velocity (negative).  x = (0 m/s)(3.0s) + ½(-9.8 m/s 2 )(3.0s) 2

#1 (cont): An object is dropped and falls for 3.0 seconds. How far does it fall? Solve the equation: Write the solution:  x =  x = m (9.0)

Example #2: An object is thrown upward at a speed of 49 m/s. How long does it rise? Identify symbols: Identify Equation: V i = 49 m/s, a = g, V f = 0 m/s, t = ? V f = V i + at

Example #2 (cont): An object is thrown upward at a speed of 49 m/s. How long does it rise? Determine the sign of “g”: Substitute: Since the object is rising and slowing down, acceleration is opposite velocity (negative). t = 0 m/s – 49 m/s -9.8 m/s 2 Rearrange the equation: t = V f - V i g

#2 (cont): An object is thrown upward at a speed of 49 m/s. For how long does it rise? Solve the equation: Write the solution: t = t = 5.0 seconds

How Does Gravity Work?  Force between two masses  The force is proportional to the product of the masses, and inversely proportional to the square of their separation  F = GM 1 M 2 R 2 R

G – Gravitational Constant  Same value everywhere in the universe  6.67x N-m 2 /kg 2  Don’t confuse G and g!  Big G is constant  Small g is the gravitational field strength, which changes value depending on the planet and your altitude.

Proportions:

g - Gravitational Field Strength  The field strength of object 1 is generally expressed as the force acting on object 2 divided by object 2’s field characteristic  For gravity, the field characteristic is mass so: g = F/m 2 g = GM 1 R 2

Distance and g

Orbiting Conditions  Gravitational force supplies the centripetal force needed  GM 1 M 2 = M 2 v 2 R 2 R Io orbiting Jupiter – Courtesy NASA Jet Propulsion Lab