1. Roller Coaster Physics

2. Motion

3. Motion
a change in position, or location of a place or object, over a certain amount of time
relies on a frame of reference or something assumed to be stationary
is relative to a frame of reference
i.e. – you may be stationary as you sit in your seat, but you are moving 30 km/sec (≈19 mi/sec) relative to the Sun
Relative Motion Simulation

4. Speed the rate at which an object moves
a measure of how fast something moves, or the distance it moves, in a given amount of time
Formula:
typically expressed in units of m/s
is considered average when taking into account the total distance covered and the total time of travel
is considered constant when it does not change
is considered instantaneous when it represents a specific instant in time
S = d t
00:00. 4 5 3 1 2 6
What is the ball’s speed?
6 meters

5. Interesting Speeds meters/second miles/hour Cockroach Kangaroo Cheetah
1.25
2.8
Kangaroo 15 34
Cheetah 27 60
Sound
(in 200C air)
343
767
Space Shuttle
(getting into orbit)
7,823
17,500
Light
300,000,000
671,080,888

6. Practice Problems - Speed
If you walk for 1.5 hours and travel 7.5 km, what is your average speed?
2. Calculate the speed of a bee that flies 22 meters in 2 seconds.
S = d t
7.5 km
5 km hr
S = =
1.5 hr
22 m
11 m
sec
S = d t
S = =
2 sec

7. The Speed Triangle
S = d t
t = d S
d = S t . d d S t S . t

8. Position (Distance) vs.Time Graph
Shows how speed relates to distance and time 50 40 30 20 10 60 70 80 90
100
Time (seconds)
120
Distance (meters) D
This distance-time graph will show a student’s speed as s/he returns to class after lunch.
What is the speed from C-D ?
What is the speed from B-C ? B C
What is the student’s average speed?
What is the speed from A-B ? A

9. Describe What’s Happening (distance-time graphs)
Constant speed; away from starting point
Constant speed; no movement
Constant speed; toward the starting point

10. Velocity the rate of change of an object’s position
speed in a given direction
is considered constant when speed and direction do not change
changes as speed or direction changes
is a vector
can be combined
Example
If you are walking at a rate of 1.5 m/s up the aisle of an airplane that is traveling north at a rate of 246 m/s, your velocity would actually be m/s north
10 m/s
Does the ball
have a constant
velocity?
What is the formula for calculating velocity?
29 m/s east
29 m/s west
visuals taken from:

11. Acceleration the rate at which velocity changes is a vector
occurs when something is speeding up (+), slowing down (-), or changing direction
Formula:
typically expressed in units of m/s2
is always changing when traveling in a circle - centripetal
10 m/s
Is the ball
accelerating?
a = vf – vi t
Describe the car’s acceleration
Describe the car’s acceleration
a = 0 m/s – 10 m/s = -5 m/s2
2 s
a = 50 m/s – 0 m/s = 10 m/s2
5 s

12. Understanding Acceleration
Time
(sec)
Velocity
(m/s) 1 2 3 4 5
When dropped, the ball will accelerate toward the center of the Earth at a rate of m/s2 because of gravity. What will be the ball’s velocity at each second?
9.8
19.6
29.4
39.2
49.0

13. Practice Problems - Acceleration
Tina starts riding her bike down a hill with a velocity of 2 m/s. After six seconds, her velocity is 14 m/s. What is Tina’s acceleration?
2. A motorcyclist goes from 35 m/s to 20 m/s in five seconds. What was his acceleration?
a = vf – vi t
14 m/s -
2m/s
2 m s2
a = =
6 s
a = vf – vi t
a =
20 m/s -
35 m/s
-3 m s2 =
5 s

14. Describe the student’s acceleration as she travels to class?
Velocity-Time Graph
Shows how acceleration relates to velocity and time 50 40 30 20 10 60 70 80 90
100
Time (seconds) 2 4 6 8 12
Velocity (meters/second)
This velocity-time graph will show a student’s acceleration as she returns to class after lunch.
Describe the student’s acceleration as she travels to class?

15. Describe What’s Happening (velocity-time graphs)
Constant, positive velocity; away from starting point
Constant, zero velocity
Constant, negative velocity toward the starting point
What do all of these velocity – time graphs have in common?
How do these relate to the distance – time graphs? D T D T D T

16. Applying What You Have Learned
Describe what’s happening in the graphs. How would it look on a distance-time graph? T D T D T

17. Momentum p = mv Formula: a measure of mass in motion is a vector
the product of an object’s mass and velocity
Formula:
typically expressed in units of kg·m/s
is in the same direction as the velocity
makes an object harder to stop or change direction as it increases
can be transferred
is conserved
p = mv
20 kg
Which object has more momentum – the curling rock or the hockey puck? Explain your reasoning.
Describe the scenario where the puck would have more momentum than the curling rock?
0.17 kg

18. Practice Problems - Momentum
What is the momentum of a 7.3 kg bowling ball moving at 8.9 m/s?
2. At a velocity of 8.5 m/s, Tim moves down a hill on an inner tube. If his mass is 59 kg, how much momentum does he have?
p = mv
p =
(7.3 kg)
(8.9 m/s) =
65 kg·m/s
p =
(59 kg)
(8.5 m/s)
p = mv =
502 kg·m/s

19. Momentum vs. Intertia
What is the difference between momentum and inertia?
– Momentum is a physically calculable property, while inertia cannot be calculated using a formulae.
– Inertia is just a concept to help us understand and define mechanics better.
– While, momentum comes in the forms of linear momentum and angular momentum, the inertia comes only in one form.
– Momentum is conserved in some cases. Momentum conservation can be used to solve problems. Inertia doesn’t have to be conserved in any case.

20. Energy

21. Energy the ability to do work or cause change
typically expressed in units of joules (J)
can be transferred from one object to another
two general types:
Potential
Kinetic

22. Potential Energy (PE)
stored energy that an object has due to its position or chemical composition
Types:
Gravitational – results from vertical position or height
Formula: PE = mgh
Elastic – results from stretching or compressing
0.45 kg
Which soccer ball has more gravitational
potential energy? Explain your reasoning.
The types listed are not all-inclusive

23. Kinetic Energy (KE) energy of motion depends on mass and velocity
Formula: KE = ½ mv2
increases as mass or velocity increases and decreases as mass or velocity decreases
What is the difference between speed and velocity?
2 m/s
3 m/s
0.45 kg
Which soccer ball has more kinetic energy? Explain your reasoning.

24. Relationship Between PE and KE

25. Practice Problems
A diver weighing 46 kg is preparing for a dive from the 10 meter diving platform. How much gravitational potential energy does the diver have?
A cheetah weighing approximately 50 kg was seen chasing a gazelle at a speed of 32.4 m/s. What is the kinetic energy of the cheetah?
PE = mgh
Earth’s
Gravity
P.E. =
(46 kg)
(9.8 m/s2)
(10 m)
= 4,508 J
KE = 1mv2 2
(1)_____________ 2
(50 kg)
(32.4 m/s)2
K.E. =
= 26,244 J

26. Law of Conservation of Energy
states that energy can be neither created nor destroyed
the total amount of energy in a closed system is the same
energy can be changed from one form to another, but all of the different forms of energy add up to the same total amount of energy
PE = 24 J
KE = 0 J
PE =
KE =
12 J
12 J
A seagull steals a sandwich and drops it from a height of 7 m before eating it. What would be the sandwich’s approximate PE and KE as it falls to the ground if air resistance is negligible?
PE =
KE =
0 J
24 J

27. Efficiency = energy output x 100
Energy Efficiency
comparison of the amount of energy before a conversion with the amount of useful energy after a conversion
the closer the energy (work) output is to the energy (work) input, the more efficient the conversion is
more efficient conversions  less waste
Formula:
Sample Problem
A particular cell phone charger uses joules per second when plugged into an outlet, but only 1.31 joules per second actually goes into the cell phone battery. The remaining joules are lost as heat. That’s why the battery feels warm after it has been charging for a while. How efficient is the charger?
1.31 J
Efficiency = energy output x 100
energy input
= ____ x 100
4.83 J
= 27.1%
Sample Problem taken from:

28. Forces

29. Force a push or pull acting on an object
typically measured in Newtons (kg•m/s2)
is a vector
can be combined to predict motion net force
Soccer Simulation

30. Types of Forces Contact Forces Non-Contact Forces Applied Normal
Friction
Air Resistance
Tension
Spring
Non-Contact Forces
Gravity
Electromagnetic

31. Applied Force
any push or pull on an object created from another source (person, animal, another object, etc.)

32. Normal Force
the support force exerted on an object directly related to weight (gravity)
consequence of Newton’s 3rd Law
is always perpendicular to the surfaces in contact
Gravity
900
Gravity
900
Box
Box
Friction
Normal
Force
Normal
Force

33. is the force (friction)
exerted by a surface as an object moves across it or attempts to move across it
opposes the motion of an object
depends on the type of surfaces and the normal force (weight)
Types
Kinetic
Static
In which direction
is the force (friction)
vector pointing?
Motion
Friction

34. Air Resistance friction due to air molecules
acts upon objects as they travel through the air
opposes the motion of an object
most noticeable for objects traveling at fast speeds
Examples
Space shuttle re-entry
Meteorite in Freehold
Meteor over Russia

35. Minimizing Air Resistance (Drafting)
used in variety of competitive events (bicycle and car racing, swimming, etc.) to reduce air resistance
Notice how the second biker experiences less air resistance because he is shielded by the first biker.
Image taken from:
Although it does not work
exactly the same way, where
is these seen in nature?

36. Gravity natural force of attraction between any two objects factors:
distance – increased distance  less gravitational pull or vice versa
mass – increased mass  more gravitational pull or vice versa
Why does the force of gravity have more of an impact on holding our solar system together compared to holding the parts of an atom together?

37. G-Force??? Not an actual force!
Any time that an object changes its velocity faster than gravity can change it, the forces will be greater than one g.
Formula is g=(gravity+acceleration)/9.8m/s2
Ex. (9.8m/s2+ 2.2m/s2)/9.8m/s2= 1.22 g
At zero g, you would feel weightless.
And past 100g, you’re almost certainly dead.
Forces that intense can crush bones and squash organs.

39. Laws
Newton’s 1st Law
Newton’s 2nd Law
Newton’s 3rd Law

40. Newton’s 1st Law
objects at rest remain at rest, and objects in motion remain in motion with the same velocity, unless acted upon by an unbalanced force
also considered the Law of Inertia
How is this illustrated when riding in a car? Can you think of other
experiences where this is illustrated?

41. Inertia
the resistance of an object to a change in the speed or the direction of its motion
directly related to mass

42. Newton’s 2nd Law
the acceleration of an object increases with increased force and decreases with increased mass
the direction in which an object accelerates is the same as the direction of the force
Formula: F = ma (or a = F/m)
Shopping Cart Simulation

43. In this case, the force of the
Centripetal Force
any force that keeps an object moving in a circle
directed toward the center of the circle
In this case, the force of the
ball as it accelerates around the circle is pointing inward, toward the center.

44. Practice Problems - Force
What net force is needed to accelerate a 24 kg dogsled to a rate of 3 m/s2?
2. A 1.5 kg object accelerates across a smooth table at a rate of 0.5 m/s2? What is the unbalanced force applied to it?
72 kg·m/s2
or 72 N
F = ma
F =
(24 kg)
(3 m/s2) =
F =
(1.5 kg)
(0.5 m/s2)
F = ma =
0.75 kg·m/s2
or 0.75 N

45. Newton’s 3rd Law
states that every time one object exerts a force on another object, the second object exerts a force that is equal in size and opposite in direction back on the first object.
How was this illustrated during the Scooter Games competition? Can you think of other experiences where this is illustrated?