Physics 5.2
Galilei Galileo 1600 s Studied how things fell Didn t have a good clock Rolled balls down an inclined plane Found that the speed increased as it rolled down the ramp 1st person to explain acceleration of moving objects and falling bodies.
Galileo t = 0 t = 1 second t = 2 seconds t = 3 seconds
Galileo Free Fall Acceleration Due to the Earth s Gravity When dropped, these two different masses will fall with the same acceleration!
Free Fall All objects fall at the same rate If you drop a coin and a feather at the same time you will notice that the coin reaches the ground way before the feather. Why??? However, if you were to take the air out of the container (vacuum) you would find that the coin and feather fall together and hit the bottom at the same time!
Acceleration due to gravity, g We don t feel the attraction of most objects because their mass is small relative to the Earth which has a huge mass. The Earth pulls so that objects experience an acceleration of about 9.81 m/s 2. This acceleration is given a special letter, g. g = 9.81 m/s 2 m or 32 ft/s 2. (These numbers are important, remember it!) So during each second an object is in free fall, its velocity increases by 9.81 m/s. If the object experiences air resistance its velocity won t increase as fast because air resistance will slow it down.
Free Fall The constant acceleration of an object moving only under the force of gravity is "g". The acceleration caused by gravity is 9.81 m/s 2 If there was no air (vacuum), all objects would fall at the same speed Doesn t depend on mass After 1 second falling at 9.81 m/s After 2 seconds 19.62 m/s 3 seconds 29.43 m/s
Videos http://www.youtube.com/watch?v=zxdzwkmrxi0&feature=related http://www.youtube.com/watch?v=kdp1tiuszw8 http://www.youtube.com/watch?v=_xjcz-kol9o
Terminal Velocity You can assume that a = g = 9.81 m/sec 2 for speeds up to several meters per second. The resistance from air friction increases as a falling object s speed increases. Eventually, the rate of acceleration is reduced to zero and the object falls with constant speed. The maximum speed at which an object falls when limited by air friction is called the terminal velocity.
Since acceleration is a vector and vectors must have magnitude and direction we will always use the following system in our acceleration problems: Y-Axis Initial Motion is always positive (+) from reference point Opposite Direction of Initial Motion is always negative (-) from reference point X-Axis Direction of movement is positive (+) GRAVITY g = + / - 9.81 m/s 2 or + / - 32 ft/s 2 (Depending on direction of reference point)
Acceleration as a Vector
A pebble dropped from a bridge The vector is oriented down.
A baseball tossed up in the air, halfway up the path The vector is oriented down.
A baseball tossed up in the air, at the top The vector is oriented down.
A baseball tossed up in the air, right before it strikes the ground The vector is oriented down.
A football is thrown at a 45 0 angle, at the top of its path The vector is oriented down.
A cannonball rolling off a table The vector is oriented down.
Example #1 A body falls freely from rest. Find: (a) Its acceleration (b) The distance it falls in 3 s (c) Its speed after falling 70 m (d) The time required to reach a speed of 25 m/s (e) The time taken to fall 300 m.
Example #2 A stone falls from rest from a fourth-floor window that is 14 meters above ground level. How long does it take to reach the ground? What is the velocity just before it strikes the ground?
Example #3 A stone is thrown vertically upward with a velocity of 10 m/s from a fourth-floor window 14 meters above ground level. What is the velocity just before striking the ground? How long does it take to reach the ground?
Example #4 A ball dropped from a bridge strikes the water in 5 seconds. Neglecting air resistance, find: (a) The speed with which it strikes the water (b) The height of the bridge
Example #5 A stone is thrown vertically upward with a velocity 40 m/s at the edge of a cliff having a height of 110 m. Neglecting air resistance, find: (a) With what velocity does it strike? (b) The time required to strike the ground at the base of the cliff.
Example #6 A ball is thrown vertically downward from the edge of a high cliff with an initial velocity of 25 ft/s. (a) How fast is it moving after 1.5 s? (b) How far has it moved after 1.5 s?
Values of g in different places There are various different values of g. Since g is due to the attraction of the earth, it will decrease as we get farther from the earth s center. Acceleration due to gravity is smaller at higher elevations Acceleration due to gravity is larger at a higher latitude City Elevation Latitude G (m/s 2 ) Washington DC 8 m 38⁰ 54 N 9.8008 Denver 1,640 m 39⁰ 43 N 9.7961 London 30 m 51⁰ 30 N 9.8228 Therefore; 9.81 m/s 2 is an average figure. This value includes effects due to the earth s rotation and the value excludes effects due to air resistance. So, we will treat all free falling bodies as undergoing constant acceleration.