Kinematics - Vertical Motion

Ideas for today: Objectives for today: Falling objects Vertical motion Acceleration due to gravity Objectives for today: Understand that falling objects accelerate downwards due to gravity Understand that tossed objects also accelerate downwards due to gravity Use the kinematics formulas to calculate motion of falling objects

What do you think? Do heavier objects fall faster than lighter ones when starting from the same position? _______________________________________ Does air resistance matter?_______________ If the free fall motion has a constant acceleration, what is this acceleration? _______________________________________ How do we solve problems involving free fall?__________________________________

A tennis ball and a golf ball dropped side-by-side in air A tennis ball and a golf ball dropped side-by-side in air. The tennis ball is affected more by air resistance than the golf ball.

Important for Scientific Method: Experiment repeated MANY times Galileo did 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 slow their motion. He dropped two heavy metal balls together from the leaning tower of Pisa. They hit the ground at almost the same time. Demo: heavy ball and marble Important for Scientific Method: Experiment repeated MANY times

Coin and Feather 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. Demo: feather and coin

Constant Acceleration In free fall problems, the acceleration is constant. The acceleration is always constant at ____________________ for vertical motion on Earth!!

Observations About Falling Balls A dropped ball: Begins a rest, but soon acquires downward speed Covers more and more distance each second A tossed ball: Rises to a certain height Comes briefly to a stop Begins to descend, much like a dropped ball Demonstration: Drop Ball Demonstration: Toss Ball

Dropped Ball: Falling Downward velocity = initial velocity + acceleration × time vf = vi + aΔt position=initial position + initial velocity × time + ½ acceleration × time2 df = di + vi Δt + ½ a Δt2 Δd = vi Δt + ½ aΔt2 Demo: ball drop with hand timer Demo: inclined plane and bowling ball

Tossed Ball: Falling Upward

Example 1: Free Fall How far did the ball fall? A ball is dropped from rest from the top of a building. It hits the ground after 23.4 seconds. How far did the ball fall? What is the velocity of the ball when it hits the ground?

Example 2: Free Fall on the Moon A hammer is dropped on the moon. It reaches the ground 1s later. If the distance it fell was 0.83m: Calculate the acceleration due to gravity on the surface of the moon. Calculate the velocity with which the hammer reached the ground and compare to the velocity it would have, if it was dropped on the earth’s surface.