Understanding Gravity and Falling Objects: Mass, Weight, and Acceleration, Slides of Physics

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Falling Stuff

Do Falling Objects Accelerate?• It sure seems like it!– Starts from rest, goes faster and faster....• What about a feather, though?– Air resistance, drag– Terminal velocity– What if we could get rid of the air?• What’s responsible for the downwards force?– If it’s accelerating, then a force is acting:^ F^ = m a

Acceleration Due to Gravity• At the earth’s surface, all objects experience thesame acceleration from gravity!^2 2 “ g ”= 9.8m/s^ = 32 ft/s• If the acceleration due to gravity is indeeduniversal, then...Since^ F^ = m a , the gravitational force must beproportional to mass.

Golf Ball vs. Bowling Ball• Which one is more massive?• Which one experiences more gravitational force?• Which one is most reluctant to accelerate?• How do they respond to a gravitational force?

How Do We Know the Accelerations are the Same?Experimental tests show theUniversality of Free Fall isthe same for differentmaterials to within0.00000000001%

Said Another Way....

-^ Gravitational force is proportional to mass•^ F^ = m a^ gives an object’s responding acceleration•^ Divide both sides of the equation by “

m ”

-^ a^ =^ F /m •^ Both numerator and denominator are proportionalto “ m ”, if force is gravity•^ SO....acceleration is the same, regardless of themass•^ We’ll return to this point when we considerGeneral Relativity!

Falling Objects

Accelerate

-^ Ignoring air resistance, falling objects near thesurface of the Earth experience a constantacceleration of 9.8 m/s

-^ That means if you drop something it goes fasterand faster, increasing its speed downwards by9.8 m/s in each passing second.

An Example of the Reductionist Approach• By breaking the motion into independent parts,analysis is simplified!• The horizontal and vertical motions

are

independent

Components of Motion• Break the motion into 2 aspects, “components”– Horizontal– Vertical• Is there a force acting in the horizontal direction?• Is there a force acting in the vertical direction?• Does the ball accelerate in the horizontaldirection?– Does its horizontal velocity change?• Does the ball accelerate in the vertical direction?– Does its vertical velocity change?

Some Exercises

-^ A ball falls from rest for 4 seconds. Neglecting air resistance,during which of the 4 seconds does the ball’s speed increasethe most?•^ If you drop a ball from a height of 4.9 m, it will hit the ground1 s later. If you fire a bullet exactly horizontally from a heightof 4.9 m, it will also hit the ground exactly 1 s later. Explain.•^ If a golf ball and a bowling ball (when dropped from the sameheight) will hit your foot at the same speed, why does one hurtmore than the other?

Doing the Numbers• Imagine dropping an object, and measuring how fastit’s moving over consecutive 1 second intervals• The vertical component of velocity is changing by9.8 m/s in each second, downwards• Let’s approximate this acceleration as 10 m/s

TimeAcceleration^2 Interval(m/s^ down)

InitFinalAverageVelocityVelocity(m/s down)(m/s down) 0 – 1 s^10

0 ^10

1 – 2 s^10

10 ^20

2 – 3 s^10

20 ^30

3 – 4 s^10

30 ^40

4 – 5 s^10

40 ^50

Starting from rest, letting go:

The average velocity inthe interval is justV= ½(vavg^

• v^ )initial^ final^ For the 1 – 2 s interval,v = 10 m/si^ v = 20 m/sf^ So v = ½ (10+20) m/savg = 15 m/s Docsity.com

TimeAcceleration^2 Interval(m/s^ down)

FinalAverageVelocityVelocity(m/s down)(m/s down)

Dist.FinalPositionmoved(m down)(m down)

0 – 1 s^10

1 – 2 s^10

2 – 3 s^10

3 – 4 s^10

4 – 5 s^10

Starting from rest, letting go:

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