The vertical one-dimensional motion Free Fall The vertical one-dimensional motion

Free fall is a state where an object which moves under the sole influence of gravity

history Drop a stone, and it falls. Does the stone fall at constant speed, or is it accelerated? Does the motion of the stone depend on its shape, its size, or its color? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Aristotle explained that each kind of material has a “natural” place where it belonged and toward which it tried to go. Then Galileo (1564 -1642) revolutionized science by performing experiments. He found out that all freely falling objects have the same acceleration at the same place near the Earth’s surface called, ACCELERATION DUE TO GRAVITY (g) and does not have the same value everywhere. The worldwide value of g at sea level is 9.81 m/s2, 9.83 m/s2 at the poles, and 9.78 m/s2 along the equator.

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. However, if you were to take the air out of the container you would find that the coin and feather fall together and hit the bottom at the same time!

Acceleration due to gravity Newton told us that every object with mass attracts every other object with mass and the size of the attraction depends on the mass of each object and the distance between the objects We don’t feel the attraction of most objects because their mass is small relative to the Earth which has a huge mass. So during each second an object is in free fall, its velocity increases by 10 m/s. If the object experiences air resistance its velocity won’t increase as fast because air resistance will slow it down.

“ So that’s why it’s called falling in love, You are attracted to the other’s down-to-earth qualities, The gravity of the other’s decision Will influence you for the rest of your life.”

What Really affects falling objects Air resistance – This is the “friction” present in air, generally running against the direction of motion of the object. The larger the velocity, the larger is the air resistance. Air pressure – this term is altitude or height dependent, usually significant if the height is around 8 to 10 km high (so we don’t give those values of height as our given). The higher the object is, the greater is the air resistance.

Challenge Question Suppose someone throws a ball straight upward with a speed of 30 m/s and at the same time throws one straight down with a speed of 30 m/s. Which ball will be traveling faster when it hits the ground, the one thrown straight upward or the one thrown straight down? Assume there is no air resistance.

Time and velocity for an object in free fall v = gt g v t

Time and Distance for an object in free fall d = ½ gt2

Free Fall Questions – How Fast? 1) In free fall, do a feather and a ball fall side by side? Explain. 2) An apple falls freely from rest for 8 s on Earth, find its speed at 8 s. 3) Suppose a rock is dropped on a planet where the acceleration due to gravity is 5 m/s2, by how much would the speed change each second? 4) If a rocket on the planet in #5 falls from rest for 3 s, what is its speed at the end of the 3 s interval? 5) Challenge: Find g on a planet where a rock has a velocity of 120 m/s after 6s of free fall.

Free Fall Questions – How Far? For a freely falling rock does the distance fallen each second stay the same, increase with time, or decrease with time? A ball is dropped from rest and freely falls for 6 s. How many meters has it fallen in 6 s? A ball is thrown straight upward and travels 5 m until it reaches the top of its path. How far will it fall before it reaches its initial position? How long will it take to fall that distance? How long will the ball be in the air? 4) A ball is thrown straight up and returns to Earth 6 s later. Find its speed at the top of its path. Find its acceleration at the top its path. How long does it take to reach the top of its path? How fast is it traveling when it returns to Earth? Challenge: What is its maximum height?

Additional Free Fall Review If one had only a stopwatch, could one determine the initial speed of a ball launched vertically upward from the earth’s surface? Explain. With only a stopwatch, could one determine how high the ball travels before it stops? Explain.

Take home quiz (acceleration) How long does the car with an acceleration of 2.5 m/s2 take to go from 10 m/s to 40 m/s? A car with initial velocity of 10 m/s accelerates at 3 m/s2. Find its velocity after the first 10s in m. How far has it gone at this time? The time between a driver noticing a curve ahead and his application of the brakes is typically 0.85 sec. The maximum acceleration produced by the brakes of an average car might be - 5.5 m/s2. Find the distance required to stop such a car from the moment a curve is seen when the initial velocity is (a.) 30 km/h (b.) 50km/h