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1.2 Falling Balls
Ideas for today:
- Weight
- Acceleration due to gravity
- Falling objects
- Horizontal and vertical motion Recap
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)
a = F / m Mass is a measure of inertia
Recap, continued
Animation (link):
simulation of 1 - d forces
Physics Education Technology
(Carl Wieman’s project at CU)
Courtesy of:
Clicker Question:
Suppose that I throw a ball upward into
the air. Right after the ball leaves my
hand, is there any force pushing the ball
upward?
(A) Yes
(B) No
Galileo, age 60 , drawn by Ottavio Leoni in 1624. Galileo was the first to analyze motion in terms of measurements and mathematics. He described acceleration, which is the rate of change of speed : (should be velocity…)
acceleration = final^ speed^ –^ initial^ speed
time required
Important!
- Galileo did not use vectors
- Really:
acceleration = final^ velocity^ –^ initial^ velocity
time required
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 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.
- Experiment repeated MANY times
- Led by a thought experiment (brick that splits in two) Important for Scientific Method :
The nature of science*:
*according to me
- Physics is about predicting the future
- There is always a limit to accuracy
- Verified by experiment
- Experiments must be reproducible
- Scientific knowledge is constantly
evolving, and is always a little wrong (but
can still predict well enough)
A tennis ball and a golf ball dropped side-by-side in air. The tennis ball is affected more by the air’s resistance than the golf ball. The larger the object is, and the faster it is falling, the greater the air’s resistance to its motion, as skydivers all know… 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.
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
The yellow ball’s
horizontal speed is not
affected by gravity,
which acts only in the
vertical direction.
Clicker question: When is Matt falling?
A. When Matt getting onto the concrete slab B. When Matt is getting off of the concrete slab C. Both when Matt is getting onto and off of the slab D. While Matt is on the slab E. During the whole video
His downward acceleration is g, and his
upward velocity is shrinking
Notice: Matt is not in contact with the
ground!
a=g v
What’s Matt’s acceleration now?
What are the horizontal and vertical
components of his velocity?
v v v Cannonballs shot horizontally with different speeds from the ship travel different distances. But each cannonball drops the same distance in the same amount of time, since the vertical acceleration is the same for each. A simulated strobe illustration of a plane flying horizontally with constant speed dropping a cannonball package of food and medical supplies, ignoring air resistance.
The cannonball package of food and medical supplies initially has the same horizontal speed of the airplane. Neglecting air resistance, it keeps that horizontal speed as it falls, so it stays beneath the airplane. Another example of “packages of food and medical supplies” being dropped by a WWII bomber !!! Note the streamlined packages. Allowances are made for air drag. Note also the acceleration.
Weight is a type of force
It is the earth’s gravitational force on an object
Weight and Mass
- An object’s weight is proportional to its mass weight = g · mass
- On the Earth’s surface, that constant, g, is
- 8 Newtons/kilogram = 9. 8 meters/second^2 ( 9. 8 is approximately 10 ) 32 feet/second^2
- g is called the acceleration due to gravity
- 1 Newton! 1 kilogram · meter/second^2
- A Newton is a unit of force, like pounds. A Newton is about # pound, about the weight of a medium apple
Acceleration Due to Gravity
On Earth’s surface, all falling objects accelerate downward at the acceleration due to gravity, g!
- force = mass x acceleration, or F=ma (Newton’s 2 nd law)
- weight = m g = force
m g = m a
g = a
Don’t think that this is quite so simple…
m g = m a
Why should gravitational and inertial masses be the same?
Einstein’s
equivalence
principle – still
being tested!
U. Washington
