Free Fall Galileo’s experiments showed that all objects fall at the same speed no matter what their weight Regardless of their mass, all objects fall with the same acceleration (ignoring air resistance) Moon Drop Myth Busters
Free Fall When gravity acts on an object we call this gravitational acceleration or g. Scientists have found that the average gravitational acceleration on Earth is Would the value of g be the same on the moon or on Mars? -9.81 m/s 2
Free Fall For free fall problems we will use the kinematic equations with g plugged in for a: g is just a special kind of acceleration. d =v O t+ ½ gt 2 v f =v O + gt v f 2 = v 0 2 + 2gd
Free Fall Remember, velocity and acceleration are not the same thing.
Free Fall 3 types of objects in freefall 1.an object dropped v 0 = 0 m/s and d is negative 2.an object thrown down d is negative 3.an object thrown up at the top v f = 0 m/s, for the whole path d = 0 m
Free Fall Problems If a ball is dropped off a high building, calculate the distance it has traveled and its velocity after 3 seconds. Distance:d = ½ gt2Distance:d = ½ gt2 = ½ (-9.81) (3) 2 =-44.1 m Velocity: v f = gt = (-9.81) (3)=-29.4 m/s v i = t= a= 3s0m/s -9.81 m/s 2
How high does it go? An upward object’s velocity slows down as it goes up until it is zero at the highest point. To calculate the time to maximum height: 1.Calculate the time it takes to reach the highest point using: v f =v i + at v i = v f =a= t= (v f -v i )/a = t=0.61 s 2.Use this time to calculate the distance of the highest point using: d=v i t +1/2 at 2 d=1.83 m Example: A referee tosses a coin up at 6m/s. What is the time it takes to reach the maximum height and what is the max height of the coin? 6.00m/s0 m/s-9.81m/s 2 (0-6)/-9.81 =6 (.61) +.5 (-9.81) (.61) 2 To calculate just for the max height, solve v f 2 =v i 2 +2ad for d
How long is it in the air? The time it takes an object to go up is equal to the time it takes to go down. So, the total time is equal to 2 times the time it takes to reach its max. height. Proof: If we assume the coin is caught in the referee’s hand the total displacement is? We can solve d= v i t +1/2at 2 for t where d=0. (Solve using quadratic formula.) t=?
Equal Speeds For a given displacement along the motion path, the upward speed of the coin is equal to its downward speed, but the two velocities point in opposite directions. Mathematically, v f 2 =v i 2 + 2ad v i = 6.00m/s and d = 1.50 m v f 2 =6 2 + 2(-9.8)(1.5) v f =±2.57 m/s
Which ball hits the ground with the greatest speed? Ball A is thrown upward with a velocity of 30m/s; ball B is thrown downward with a velocity of 30m/s Both balls hit the ground with the same speed.