Free Fall and Gravity

Acceleration Review 1. A biker is traveling at 12.0 m/sec and speeds up to pass a car to 18.5 m/sec in 1.5 seconds. What is the biker’s acceleration? 2. A car accelerates from rest at a rate of 6.3 m/s 2 for 4.3 seconds. What is the car’s final velocity?

A Little Review…. The force exerted on an object is equal to the product of that object’s mass times its acceleration. The acceleration is in the same direction as the force. Force = mass x acceleration F = m a (force and acceleration are vectors)

What is Free Fall? An object is in free fall if it is accelerating due to the force of gravity and no other forces are acting on it. A dropped baseball is in free fall as soon as it leaves your hand. A ball thrown upward is also in free fall after it leaves your hand.

Galileo Performed experiments to convince others that the acceleration caused by gravity would be the same for all freely falling objects if there was no air to retard their motion. He dropped two heavy metal balls together from the leaning tower. Although one weighed much more than the other, they reached the ground almost at the same time.

Acceleration Due to Gravity On Earth we can’t fall without air resistance, but for normal situations the numbers are realistic. When things fall they constantly accelerate.

Acceleration Due to Gravity If we can ignore air resistance, all objects accelerate at the same rate. 9.8 m/s 2 = g (acceleration due to gravity on Earth at sea level)

Say What? When most of the air is removed from a container, feathers and apples fall almost side- by-side, their speeds changing at almost the same rate. If all the air was removed, they would accelerate downward at exactly the same rate.

Example of Calculating Free Fall Speed 1. A cannon ball is dropped from a tall building. Calculate the speed of the ball after 2.25 seconds.

Upward Launches If a ball is thrown upwards… The ball will slow down as it moves upward, come to a stop for an instant, and then fall back down. As it moves upwards: Speed decreases by 9.8 m/s every second until it reaches zero. At zero, it reverses direction! As it moves downward: Speed increases by 9.8 m/s every second.

Video Clips app.discoveryeducation.com/search?Ntt=free+fall

Free Fall and Distance Using average speed to find distance:

Example: 1. A rock falls off a cliff and splashes into a river 5.00 seconds later. What was the rock’s average speed during its fall? How high, in meters, was the cliff?

Using time to find distance: d = 1/2 g·t 2  This formula only works for objects in free fall close to the surface of the Earth.  Check first example using this formula.

Examples: An apple falls from the top branch of a tree and lands 1.38 seconds later. How tall is the tree? Calculate the final speed and distance of free fall for a skydiver who waits only 4.17 seconds to open his parachute.

Air Resistance The opposing force on a moving object due to the friction of air. Increases with speed The size and shape of an object affect the force of air resistance. Surface area to weight ratio.

Terminal Velocity The maximum speed reached by an object in free fall. The speed at which the forces of gravity and air resistance are equal. After object reaches terminal velocity, its speed is constant. Dependent on the ratio of an object’s weight to its air resistance.