Gravity and Free FallImagine dropping a baseball out of a second-floor window. What happens? Is the speed constant or does the ball accelerate? If it accelerates, at what rate?Do all objects fall at the same rate?

Mass and Weight different!

► Mass is an intrinsic propertyintrinsic property of an object. It is completely determined by the number and type of atoms that make up the object. It does not depend on the environmentenvironment in which the object is located. ► But weight is different. Weight depends on both the object itself, and on some other object that exerts the gravitational force.

So, for example, the mass of an object would be the same on the moon or the Earth; but the weight would be different.

Weight = the force of gravityThe weight of an object is, by definition, the strength of the force of gravity pulling the object downward.

W

m g1 Newton= m/s² X Kg

2.2 lb.= 1.0 kg

Your mass (lbs.) Mass (kg.) Weight (N)

   

Your mass (lbs.) Mass (kg.) Weight (N)

   

Earth: ag= 9.8 m/s2

Saturn: ag= 10.06 m/s2

Introduction to Free Fall• A free-falling object is an object which is

falling under the sole influence of gravity. • That is to say that any object which is moving

and being acted upon only be the force of gravity is said to be "in a state of free fall."

• This definition of free fall leads to two important characteristics about a free-falling object:– Free-falling objects do not encounter air

resistance. – All free-falling objects (on Earth) accelerate

downwards at a rate of 9.8 m/s/s or 32ft/s/s

Freely Falling Body• The acceleration of freely falling

body is so important that physicist called it acceleration due to gravity.

• Denoted by letter g which is equivalent to 32ft/sec2 or 9.8m/sec2.

• Meaning in the 1st second, a falling body accelerates from a stationary position to a velocity of 9.8m/sec2, after 2 seconds, the velocity is doubled to 19.6m/sec2 after 3 seconds it triples to 29.4m/sec2

A simple rule to bear in mind• is that all objects (regardless

of their mass) experience the same acceleration when in a state of free fall.

• When the only force is gravity, the acceleration is the same value for all objects.

• On Earth, this acceleration value is 9.8 m/s/s that it is given a special name - the acceleration of gravity - and a special symbol - g.

Air ResistanceWe just said the acceleration of all objects in free fall is the same. So why does a feather fall slower than a baseball? The answer is that objects on Earth are not truly in free fall because gravity is not the only force acting on falling objects. When something falls through air, the air exerts an additional force. This force, called air resistance, acts against the direction of the object’s motion.

2-6. Air Resistance• Free Fall

– A person in free fall reaches a terminal velocity of around 54 m/s (125mi/hr) which means the person stops acceleratingstops accelerating

– Force of air resistance = gravitational force

– Called terminal velocity (balanced forces)

– With a parachute, terminal velocity is only 6.3 m/s

• Allows a safe landing

Calculating Velocity during Free Fall• If you know the acceleration of

an object in free fall, you can predict its speed at any time after it is dropped.

• The speed of a dropped object will increase by 9.8 m/sec every second If it starts at rest, it will be moving at 9.8 m/sec after one second, 19.6 m/sec after two seconds, 29.4 m/sec after three seconds, and so on.

• To calculate the object’s speed, you multiply the time it falls by the value of g. Because the units of g are m/sec2, the speed must be in m/s.

Calculating velocity during Free Fall Practice

1.) You drop a ball from the edge of a cliff. It lands 4 seconds later. What is the velocity that it hits the ground with?

2.) During a science experiment, your teacher drops a tennis ball out of a window. The ball hits the ground 3 seconds later. What is the velocity of the ball when it hits the ground?

Upward Launches• When an object is in free fall, it accelerates

downward at 9.8 m/sec2. Gravity causes the acceleration by exerting a downward force. So what happens if you throw a ball upward?

1.) The ball will slow down as it moves upward

2.) come to a stop for an instant

3.) then fall back down.

As it moves upward, the speed decreases by 9.8 m/sec every second until it reaches zero. The ball then reverses direction and starts falling down. As it falls downward, the speed increases by 9.8 m/sec every second.

• An object’s direction is importantpositive sign means upward and the negative sign means downward.

Free Fall and distance• Now that you know how to calculate the

velocity at any given moment during free fall, you can calculate the distance that the object falls

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Calculating distance and free fall practice

1.) A sky diver falls for 6 seconds before opening her parachute. Calculate her actual speed at the 6 seconds mark and the distance she has fallen in this time.

2.) Calculate the final speed and distance of a skydiver who waits only 4 seconds to open his parachute.

3.) An apple falls from the top branch of a tree and lands 1 second later. How tall is the tree?

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More Practice Problems…1.) you are walking and an apple from the top of an apple tree falls and hit you on the head. You know that the height of the tree is 28.5 feet.

a.Calculate how many seconds the apple falls before it hits you on the head.

b.What is the speed with which the apple hits you on the head?

2.) A man drops a pencil from the top of Sears tower in New York City. The building is 450 meters tall.

a.Calculate how many seconds the pencil falls before it hits the ground.

b.What is the speed of the pencil when it hits the ground?