Download Chapter 6 Notes - Northern Highlands

Chapter 6 Notes
Projectile Motion:
Motion in the X-Direction:
 Forces (F x ) = __________; no forces in the x-direction
 Velocity (V x ) = _______________
 Acceleration (a x ) = ___________
 Distance (x) = the object will move ___________ distances in the
________________ direction because it is not ________________.
Motion in the Y-Direction:
 Forces (F y ) = __________; only one force in the y-direction
 Velocity (V y ) = _______________
 Acceleration (a y ) = ___________
 Distance (y) = the distance the object moves each second will
_______________ because it is __________________.
Symbol
Vx
Vy
dx
dy
G
∆t
Name
Unit
Equations for Projectile Motion:
d x = V x (t)
Vx = dx / t
t=dx/Vx
dy = vi + ½ g t 2
t =  2 dy / g
V y = V i + g (t)
g = 9.8 m/s2
Projectiles Launched Horizontally: Practice Problems
1. Rich rolls a ball off a table that is 10 m high.
a. How long will it take the ball to hit the ground?
Given:
y = ___________ m
a = ____________ m/s2
Unknown:
t = ___________ s
b. If the ball lands 15 m away, what horizontal velocity does the ball leave
the table with?
Given:
x = ___________ m
Unknown:
V x = ___________ m/s
2. A stone is thrown horizontally at 15 m/s from the top off a cliff 44 m high?
a. How far (x) from the base of the cliff does the stone hit the ground?
Given:
y = ___________ m
V x = ___________ m
a = ___________ m/s2
Unknown:
t = ___________ s
x = ___________ m
3. You take a running leap off a high-diving platform. You were running at 2.8 m/s
and hit the water 2.6 s later. How high was the platform, and how far from the
edge of the platform did you hit the water?
Given:
V x = ________ m/s
a y = g = ________ m/s2
t = ________ s
Unknown:
x = _______ m
y = _______ m
4. A stone is thrown horizontally at a speed of 7 m/s from the top of a cliff 78.4 m
high.
a. How long does it take the stone to reach the bottom of the cliff?
b. How far from the base of the cliff does the stone hit the ground?
5. A toy car runs off the edge of a table that is 1.225 m high.
a. If the car lands 0.4 m from the base of the table, how long did it take the
car to fall?
b. How fast was the car going on the table?
Projectiles Launched at an Angle
But V i is at an angle We must break it into V x & V y components!
On the way up:
 Vy =
 ay =



At the Top:
vy =
ay =
On the way Down:
vy =
ay =
dy =
dy is ____at peak
dy =
Vx =
Vx =
Vx =
dx =
dx =
dx =
**Symmetrical Path**
time up =__________
2(∆t up ) = total time in air
When the angle = _____ the range is a maximum
When the angle = _____ the height is a maximum
Complimentary angles that create the same horizontal distance are:
30
____
20
____
*they must add up to ____
40
____
Circular Motion, Acceleration, and Centripetal Force
 RotationEx. Earth rotates around its axis once every 24 hours
 RevolutionEx. Earth revolves around the sun once every 365.25 days
 Frequency:
f = # of revolutions
1 second
f = _1_
T
Unit:
T = # of seconds
1 revolution
T = _1_
f
Unit:
 Period:
Period & Frequency Practice:
1. A car tire makes 95 rotations every 2.0 minutes.
a. Calculate the frequency of the tire.
b. Calculate the period of the tire.
2. Matt spins in his chair with a frequency of 0.5 Hz.
What is the period of Matt’s spinning?
Linear speedDistance = circumference =
Velocity (speed) = distance / time =
aka Linear Velocity- V =
 Linear velocity depends on how far away you stand from the center of
the circle (this is the ____________)
 At Center, tangential velocity = ______ m/s
 As you move away from the center, your radius ____________, so
your linear velocity ______________.
** Linear speed and rotational speed are ___________ proportional.
- The faster it turns (faster angular velocity), the __________ your
linear speed is.
- Rotational speed is constant no matter where you stand because your
“distance traveled” is really the angle you cover.
- Double angular speed  you double linear speed
Merry-go-round Example:
Hannah (H) and Rebecca (R) are on the merry-go-round. Hannah is on a horse close to
the center and Rebecca is on a horse near the outer edge.
1. Is Hannah’s linear speed greater than, less than,
or the same as Rebecca’s linear speed? Why?
2. Is Hannah’s rotational speed greater than,
less than, or the same as Rebecca’s rotational
speed? Why?
Tangential and Rotational Velocity Practice:
1. A racecar rounds a track in 5 min. The radius of the track is 20 m.
a. What distance does the car travel?
Given:
r = _______ m
Unknown:
C = _______ m (circumference)
b. What is the velocity of the racecar?
Given:
C = _______ m
t = ________ s (convert min to s)
Unknown:
v = _______ m/s
2. Jon, Donny, and Anthony ride on the Superman rollercoaster in Great Adventure.
They go around a loop with a velocity of 50 m/s. It takes them 3 s to complete
this revolution.
a. What distance (circumference) do the boys travel?
Given:
v = _______ m/s
t = _______ m/s
Unknown:
C = _______ m
b. What is the radius of the loop? What is the diameter?
Given:
C = _______ m
Unknown:
r = _______ m
Diameter = _______ m
3. Robbie swings a ball in a complete circle, the radius is 3 m.
a. What is the circumference of the circle made by the ball?
b. Robbie accidentally lets go of the ball after 5 s.
With what velocity does the ball fly away (v t )?
Centripetal Acceleration
Def:
a c = v2
r
 The direction is
Units:
towards the ______________ of the circle!
Centripetal Acceleration Practice:
1. A yo-yo is swung overhead in a circle with a velocity of .5 m/s. If the rope is .25
m away, what is the centripetal acceleration of the yo-yo?
Given:
v = _______ m/s
r = _______ m
Unknown:
a c = _______ m/s2
2. A runner moving at a speed of 6 m/s rounds a bend with a radius of 15 m.
Calculate the centripetal acceleration of the runner?
Given:
v = _______ m/s
r = _______ m
Unknown:
a c = _______ m/s2
3. A roller coaster goes around a loop with a velocity of 20 m/s. What is the
centripetal acceleration, if the radius of the loop is 16 m?
Given:
v = _______ m/s
r = _______ m
Unknown:
a c = _______ m/s2
4. A stopper is attached to a 0.5 m string and is swung overhead. What is the
centripetal acceleration, if the velocity of the stopper is 1 m/s?
Given:
r = _______ m
v = _______ m/s
Unknown:
a c = _______ m/s2
Centripetal Force (F c ) =
F c = ma c
F c = mv2
r


Units:
The direction is
towards the ______________ of the circle!
F c is NOT an additional vector; it is simply the _______ _____________
that is producing circular motion.
o It could be tension in a string or the wall of a washing machine, or a
seatbelt in a car.
Centrifugal Force=
- Fictitious force;
- An effect of rotation (as seen in rotating system of reference)
- Due to inertia
- Always directed toward the outside (tangent line)
- Not part of an interaction; not a true force
Ex 1: Driving around a curve in a car
Ex 2: Washing machine- spin cycle
Centripetal Force Practice:
1. A 0.1 kg stopper is attached to a 0.5 m string. The stopper swings in a horizontal
circle making one revolution in 1.18 seconds.
a. What is the tangential velocity of the stopper?
Given:
r = _______ m
T = _______ s
Unknown:
v t = _______ m/s
b. Calculate the centripetal acceleration.
Given:
v t = _______ m/s
r = _______ m
Unknown:
a c = _______ m/s2
c. Calculate the centripetal force needed to provide circular motion.
Given:
a c = _______ m/s2
m = _______ kg
Unknown:
F c = _______ N
2. A 40 kg runner moving at a speed of 8.8 m/s rounds a bend with a radius of 25m.
a. Calculate the centripetal acceleration.
Given:
r = _______ m
v t = _______ m/s
m = _______ kg
Unknown:
F c = _______ N
3. Racing on a flat track, a 1500 kg car going 32 m/s rounds a curve with a 56 m
radius.
a. What is the car’s centripetal acceleration?
Given:
v t = _______ m/s
r = _______ m
Unknown:
a c = _______ m/s2
b. What amount of force is created ?
Given:
m = _______ kg
a c = _______ m/s2
Unknown:
F c = _______ N
4. A merry-go-round makes on revolution in 90.0 s. Its radius is 4.0 m.
a. Find the velocity of the ride.
Given:
r = _______ m
T = _______ s
Unknown:
v t = _______ m/s
b. What is the centripetal acceleration if you are standing on the outside?
Given:
v t = _______ m/s
r = _______ m
Unknown:
a c = _______ m/s2
Law of Universal Gravitation
4 Different Forces (unified at the beginning of the universe)
1. Gravitational Force-______________ force that exists between all objects
a. Earth on moon holds moon in orbit
b. Sun on Earth holds Earth in orbit
c. Moon on Earth causes tides
d. Weakest of all the 4 forces
2.
Electromagnetic Force- gives materials their ___________, their ability to
bend, squeeze, stretch, or shatter.
a. Results from electric charge
b. Large compared to gravitational force
3.
Strong Nuclear Force- holds particles in the ___________of an ________
together; Strongest of all 4 forces
4. Weak Nuclear Force- A form of electromagnetic force;
Involved in radioactive decay
The Gravitational Force:
Ex: The Apple & the Earth
-
Newton reasoned that if an apple that fell from rest to the ground it must be acted
upon by some force
Since it fell to the Earth, the _________ exerted a __________ on the apple.
Based on Newton’s ______ Law: The Apple also exerted a force on the Earth.
Newton concluded that there exists a force between any _______ _________.
Law of Universal Gravitation
Every mass feels an ________________ force from every other one.
Objects Influenced by gravity:
Newton’s Law of Universal Gravitation
“Every particle in the universe attracts every other particle with a force
that is directly proportional to the product of the masses and inversely
proportional to the square of the distances between their centers.”
Fg = G m1m2
d2
G: universal gravitation constant =
m 1 and m 2 :
d:
Since gravity is the _______________ of all the 4 fundamental forces, we
can only sense its effects when masses like that of the earth are involved
- force between two classmates is too weak to notice
- force of attraction between you and earth = _________
Relationship between Force & Mass:
Force is _____________ proportional to the product of the masses.
Fg 
Suppose one mass is doubled: F g  2m 1 m 2  the force is ___________
Suppose both masses are doubled: F g  2m 1 2m 2  the force is __________
Relationship between Force & Distance:
Force is ________________ proportional to the square of the distance.
F
If the distance is doubled: F  __1___
(2d)2  the force is _____ as large
If the distance is tripled: F 
 the force is _____ as large
** The relationship between force and distance is called the
_________________ _________________ _________.**
Universal Gravitation Practice
F = G m1 m2
d2
G = 6.67 x 10-11 Nm2/kg2
m earth = 5.97 x 1024 kg
R earth = 6.38 x 106 m
1. Calculate the force of gravity of a 50 kg person standing on earth. Use the
universal gravitation formula.
Given:
m 1 = __________ kg
m 2 = __________ kg
d = ___________ m
G = __________ Nm2/kg2
Unknown:
F g = __________ N
2.
Tom has a mass of 70.0 kg and Sally has a mass of 50.0 kg. Tom and Sally are
standing 20m apart on the dance floor. Find the gravitational force between them.
Given:
m 1 = __________ kg
m 2 = __________ kg
d = ___________ m
G = __________ Nm2/kg2
Unknown:
F g = __________ N
3. Two balls have their centers 2.0 m apart. One ball has a mass of 8.0 kg.
The other has a mass of 6.0 kg.
a. What is the gravitational force between them?
Given:
m 1 = __________ kg
m 2 = __________ kg
d = ___________ m
G = __________ Nm2/kg2
Unknown:
F g = __________ N
b. If the mass of one of the balls is doubled, how will the force compare?
4. If the mass of Mars is 6.42 x 1023 kg, and the mass of the sun is 1.99 x 1030 kg .
The distance between Mars and the Sun is 2.278 x 1011 m. Calculate the amount
of gravitational force between them.
Given:
m 1 = __________ kg
m 2 = __________ kg
G = __________ Nm2/kg2
d = __________ m
Unknown:
F g = __________ N