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Chapter 4: Lesson 4 - Math and Terminal Velocity
Chapter 4: Lesson 4 - Math and Terminal Velocity
Equations
Equations
We are going to expand our available math equations now. It will be helpful to have your equation sheet ready. A copy of the equation sheet is under resource materials on this website and on google classroom. It can also be found HERE.
Chapter 4 Math
Chapter 4 Math
The math in chapter 4 comes from Newton's Second Law of Motion. Click here to see the paper that I used in the video to review the math.
As you watch this video, pause it and try the math on your own. When you have your answer, start the video and see if you are right. It is important to know where YOU make your mistakes so you can correct them for next time!
Remember there are more practice math problems under Chapter 4 Resources. Practice the math and see if your answer matches my answer.
Before the Next Class Period:
Before the Next Class Period:
Practice these Math Problems Before Class!
Practice these Math Problems Before Class!
Click on the picture to take you to the practice problems that I will be going over the next time we have class. Remember, you need to try the problems on your own to see where you make your mistakes if you want to learn how to do the math problems on your own.
Apparent Weight
Apparent Weight
An object's apparent weight is the force an object experiences as a result of all the forces acting on it.
The term weightlessness does not mean that an object's weight is actually zero. It just means that there are no contact forces pushing up on the object and the object's acceleration is zero. You feel like you have no weight because nothing is pushing on you.
This is a girl standing in an elevator. The the left picture, the acceleration is zero, she is either not moving or moving at a constant velocity. Her weight appears normal on the scale that she is standing on.
If the elevator is accelerating upwards, there is a force pushing up on her feet, so her feet have to counter that force by pushing down. This makes the scale reading appear that she weighs more. If you were to stand on a scale and pull up on a counter next to you, the reading on the scale would increase. This is the same principle.
In the third picture from the left, the elevator is accelerating down, so there is a force going down. It is harder for the girl's feel to press on the floor, so the scale reads that as less weight pushing down. This would be the same principle if you were to push down on a counter next to you while standing on the scale. Some of your weight would be transferred to the counter so the scale would read less.
In the picture all the way to the right, the girl is in free fall because the cable broke on the elevator. Her acceleration is equal to the acceleration due to gravity (9.8 m/s2) so there is no force on the scale. She doesn't even feel any forces, so she is weightless. Again, this doesn't mean that she is without weight. It means that she can't feel any contact forces on her.
Air Resistance
Air Resistance
Air resistance depends on the speed of an object as well as its cross-sectional area.
TRY IT AT HOME:
TRY IT AT HOME:
Take two pieces of paper that are the same size and mass. Crumple one of the papers up into a small ball. Both papers still have the same mass, but now the crumpled up one has a smaller surface area. Drop both papers from the same height. Which one reaches the ground first?
Terminal Velocity
Terminal Velocity
The constant velocity that is reached when the drag force (in this case air resistance) is equal to the force of gravity is called terminal velocity.
Look at the picture of the guy jumping out of a helicopter. Diagram A is taken RIGHT when he jumps out of the plane. The only force acting on him right now is his weight, which is 833 N.
In diagram B, the air resistance starts to increase. Air resistance is 350N pointed up and his weight is still 833 N down. His net force is 483 N down, so he is still accelerating downward and his speed is increasing.
In diagram C, the air resistance is still increasing, right now it is 700N up. Since his weight is still 833 N, the net force is now 133 N down. He is still accelerating downward and his speed is increasing.
In diagram D, the air resistance has now increased to 833 N. The guy's weight is 833 N. The net force on this guy is 0 N. He is in equilibrium. Since there is no net force, (because of F=ma) his acceleration is also 0 m/s2. He has stopped accelerating and has reached the final speed that he will have, his terminal velocity.
Look at this animation. You can see the math behind what was discussed above. When the parachute is pulled, the acceleration is directed upwards because the air resistance is suddenly greater than the weight of the skydiver. When this happens, you slow down. That is why parachutes are so important!
Without Air Resistance
Without Air Resistance
Without air resistance, the feather and the elephant fall at the same rate, 9.8 m/s2.
With Air Resistance
With Air Resistance
With air resistance, the feather reaches its terminal velocity MUCH faster than the elephant, who has more weight. The elephant has a much higher final velocity than the feather and reaches the ground in a shorter time than the feather.
Physics of Skydiving
Physics of Skydiving
When a skydiver pulls his/her parachute, what happens? Do you think that they move up?
When they are falling and pull their parachute, they do not move upwards. It appears that they do because they slow down VERY quickly and to the camera moves down faster than they do.
Watch this fun video on the physics of skydiving to see what happens when you skydive.
You have finished Lesson 4!
You have finished Lesson 4!
Be sure to head over to google classroom and fill out the exit pass.
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