1. Velocity, Acceleration, and Mechanical Energy
Pgs of INB

2. Velocity Distance vs. displacement Speed vs. Velocity
Distance is amount traveled
Displacement is distance away from starting point
Speed vs. Velocity
Speed is just displacement/Time (Scalar)
Velocity is speed and direction (Vector)
V=Δd/ Δt
Δd=dfinal-dinitial Δt=tfinal-tinitial

3. Acceleration
Acceleration is a change in velocity/ time elapsed (vector)
A= Δv/Δt

4. Mechanical Energy
Transformation of GPE (grav. Potential energy) and KE (kinetic energy)
GPE = mgh
G= 9.8 m/s2
KE = 1 2 𝑚𝑣2
Unit for energy is Joules (𝐽=𝑁×𝑚 or kg×m2/s2)

5. ME (continued..for real…)
ME (bottom) = ME (top)
KE (bottom) + GPE (bottom) = KE (top) + GPE (top)
Conservation of energy – Energy can’t be created or destroyed only transferred.
ME is only true using these calculations if we negate energy lost to sound, friction or any other outside forces (i.e. wind, motors etc.)

6. Equations needed to be put in INB (pg. 50)
V=Δd/ Δt
Δd=dfinal-dinitial
Δt=tfinal-tinitial
GPE = mgh
KE = 1/2mv2
ME (bottom) = ME (top)
KE (bottom) + GPE (bottom) = KE (top) + GPE (top)

7. Take Home Quiz To turn in Thursday…
Answer the Checking up Questions on page 680 and page 693.

8. INB directions
Title pgs 52in table of contents Apparent weight practice and 53 apparent weight notes.
The practice problems from 744 will go on the right hand page 52of your INB.
The notes from the following slides will go on page 53 (Cornell Note style, don’t forget your summary and questions!!).

9. Free-body diagrams (aka Force diagrams)
The arrows represent the direction and the size of the force
The larger/smaller the arrow, the more/less force there is.
Adding up all the arrows will tell you if there is going to be any motion and in what direction.

10. Apparent Weight
When an elevator is at rest, moving up or moving down at CONSTANT velocity, your weight readings are identical.
In other words you do not weigh more when it is moving up or less when it is moving down.

11. Apparent Weight cont.
When the elevator or coaster is ACCELERATING up or down, a change in the amount of force of gravity will cause a change in your weight.
Increasing the force of gravity increases your APPARENT WEIGHT (how heavy you appear to be). So decreasing the force of gravity decreases your apparent weight.
So increasing the apparent weight increases the forces of gravity (G’s). a safe coaster should NEVER exceed 4 G’s

12. Air Resistance
An object in free fall will accelerate at 9.8 m/s2 (gravitational constant). So for every second the speed increases by 9.8 m/s. Air resistance is the force that apposes the motion of the object. Therefore at some point in the motion of the object, the air resistance will balance the force of gravity reaching what is called terminal velocity or the maximum speed an object can reach.
While we usually calculate values up to this point without air resistance, please note that this will give you an incorrect calculation.

13. Apparent weight practice problems
Complete the following questions from your textbook pages on page 52 of your INB.
Pg 744 questions 1 and 2.
Pg 745 question 9.

14. Centripetal Force, Acceleration and Safety of Coaster
You will need your INB and a pencil.
Set up pages for notes.
Your title is Centripetal Force and Acceleration.
Page 53 (R side) is Cornell Notes, page 52 (L side) illustrations/calculations.

15. Centripetal Force and Acceleration
All objects moving in circles are accelerating and require a force toward the center of the circle.
In a roller coaster where the car tilts vertically and the wheels face outside the circle, the force towards the center is the NORMAL FORCE of the track on the wheels.
The normal force is the force acting perpendicular to the surface (review)
(Left side pg. 52)
Horizontal
Vertically

16. Centripetal Force and Acceleration
In a circular motion when the object is moving at a constant speed the force that keeps an object moving in a circle is known as CENTRIPITAL FORCE.
This force is always directed toward the center. Centripetal means “center seeking”.
𝐹 𝑐 = 𝑚 𝑣 2 𝑟
𝐹 𝑐 is the centripetal force
m is the mass
v is the speed (velocity)
r is the radius (of the circle)

17. Centripetal Force and Acceleration
If there is a net force then the object must be accelerating.
When a roller coaster car goes around a curve it is accelerating.
We know from the previous slide that the force is toward the center. In circular motion the acceleration is also towards the center.
CENTRIPETAL ACCELERATION is the acceleration directed toward the center of a circle of an object traveling in a circular motion.
𝒂= 𝒗 𝟐 𝒓
a is the acceleration
v is the velocity
r is the radius

18. Centripetal Force and Acceleration
In a vertical loop the direction of the centripetal force is always changing as the coaster moves through the loop because the force is always towards the center. Pg
(left side pg. 52)

19. Centripetal Force and Acceleration
Angular momentum says that the smaller the loop (circle) the more momentum an object has.
Think of an ice scatter as she pull her arms in. When she does this she will spin faster because more of her mass is closer to the center of her body.

20. Extra Credit
If you are trying to figure out how fast (velocity) your cart is moving remember these important facts:
The GPE top = KE bottom
𝐾𝐸= 1 2 𝑚 𝑣 2
If you know KE and the mass you can solve for the velocity.
𝑣= 𝐺𝐻2
Once you have the velocity going into the loop you can use the centripetal acceleration equation to calculate the acceleration through the loop.

21. Safety
If you experience an acceleration of more than 9 times gravity for a sustained period you will most likely become unconscious.
The acceleration of gravity (or gravitational constant) is 9.8 𝑚 𝑠 2 (or rounded to 10 𝑚 𝑠 2 ). This is equal to 1G. Therefore, free fall is equal to 1G.
Safety on a roller coaster requires that the acceleration be under 4Gs or 4𝐺 9.8 𝑚 𝑠 2 = 𝑚 𝑠 2
More information and equation examples on pgs

22. Safety
Acceleration through a loop can be calculated with the following equation:
𝑎= 𝑣 2 𝑟

23. Centripetal force practice
Complete and turn in (on a separate sheet of paper) the checking up pg , and the following:
What is the centripetal force of the following:
A mass of 25kg a speed of 2m/s and a radius of 5m.
A mas of 10kg and speed of 12m/s and radius of 7m.
What is the acceleration of the following:
A velocity of 2m/s and a radius of 5m.
A velocity of 12m/s and a radius of 7m.

24. Roller coaster safety practice
Are the following examples safe or not safe?
A speed of 19m/s and a loop of 15 m
A speed of 4m/s and loop of 1 m
A speed of 15m/s and a loop of 10m.
A speed of 38m/s and a loop of 8m.