Unit 2 Summary

In this unit, we focused solely on how things fall. Appropriate for the season...

FREE FALL-THINGS FALLING STRAIGHT DOWN

Free fall is when objects fall due to the acceleration of gravity. There is no air resistance, and hence, weight has no affect.

Say you throw a penny off a cliff, and you want to know how far it will have fallen after 3 seconds.

You would use the formula d=1/2at²

Plug in 10 (acceleration of gravity) for a, and 3 for t

d=1/2 (10X3²)

d=45 meters

If you want to know how fast the penny fell…

Use the formula v=at

V=10X3

V=30m/s

FREE FALL-THROWING THINGS STRAIGHT UP

We already know that objects accelerate at a rate of 9.8 m/s squared. So if you throw a ball upwards, every second it's speed will decrease by 10m/s, which as stated above, is the force of gravity. Similarly, when objects fall, their speed will increase by 10m/s

Use this diagram to help you visualize...

 

To find the balls height at 2 seconds, you would find the total height that it traveled, and subtract that by it’s height at 2 seconds

d=1/2at²

d=1/2 (10X3²⁾

d=45 meters

d=1/2 (10X2²)

d=20 m

45m-20m= 15 meters high at 2 seconds

FREE FALL-FALLING AT ANGLES

Lets say an airplane is delivering supplies to an army base. The pilot needs to know how far ahead he should drop the package so that it lands in the right spot.

(Please excused my poor attempt at drawing an airplane. Prime example of why we can't have nice things) 

 

To determine when he should drop the package, use the formula v=d/t as shown below

You can also find how long the package has been falling using d=1/2at²

So the package of supplies needs to be dropped 480 meters before the designated spot.

Also, you might want to find the velocity of the falling object at any given place in it’s path. To do this, you use the formula v=at

THROWING THINGS UP AT AN ANGLE

Say you are throwing a baseball across the field (120 meters), and you know that the ball is in the air for 4 seconds.

In order to find the horizontal velocity, you would use the formula v=d/t

v=d/t

v=120/4

v=30 m/s

The vertical velocity is 20m/s, because the ball is in the air 4 seconds

Now that we know the horizontal (30 m/s) and vertical velocities (20m/s), we can use this information to find the true velocity…

The path of the two velocities create a triangle, and use can use the Pythagorean Theorem to find the balls true velocity

 

NEWTON’S SECOND LAW

a=f/m

Mass is Inversely proportional to Acceleration

Force is Directly proportional to Acceleration

Use this helpful pneumonic device to remember…

MIA FDA

Another helpful formula to know is w=mg

Say you have an object with a mass of 30 newtons…what is it’s weight?

w=30X10

w=300 kg

During the lab we did in class we used a cart, a hanger, some weights, and a track, and experimented with Newton's Second Law. 

Trial A

Mass increased, force stayed constant

àacceleration decreased

y=   m    x

a=  1/m   f

Trial B

Force increased, mass stayed constant (weight transferred)

àacceleration increased

THINGS FALLING WITH AIR RESISTANCE- SKYDIVING

Since net force decreases as you fall, your F weight and F Air will eventually equal each other, and your F Net will become zero. This is called terminal velocity, where you will begin to move at a constant velocity.

Parachutes

Once you are through skydiving, you will want to slow down to ensure that you don't hit the ground with extreme speed, for obvious reasons. You can use a parachute to do this. 

àonce you open the parachute, your air resistance will increase for a brief moment, then immediately begin decreasing.

àvelocity decreases because you are accelerating in the opposite direction

àyou will enter a second terminal velocity, which has a slower velocity due to the higher surface area

Don't try this at home kids.

THINGS FALLING WITH AIR RESISTANCE

Have you ever crumpled up a piece of paper, and tossed it into your trashcan? I usually miss, but that’s not the point. Anyways, moving on…

If you drop a balled up piece of paper (A) and a flat sheet of paper (B), you will notice that the compressed paper hits the ground first.

Paper A has a faster velocity, because it has to accelerate longer to reach terminal velocity

Paper B has a slower velocity because with it’s extra surface area, it has initial F Air and does not have to accelerate for as long.

Similarly, if you drop a golf ball and a ping pong ball from a high enough point, the golf ball hits the ground first. This is because it has a greater F weight, and therefore a greater F Air in order to push it towards the ground. The ping pong ball has less F Weight and F Air, thus, will take longer to fall.