Download Sources of Forces

Sources of Forces
Name: _______________________
Date: ___________ Period: _____
I. TYPES OF FORCES
1. As a beginning physics student it is important to know the five most common forces in Newtonian
mechanics: tension, weight, normal, friction, and drag. Read each paragraph below and then draw and
label arrows on each diagram to illustrate that force.
Tension ( ) is the pulling force exerted by a string, cable, or
similar solid object on another object. It is the pull exerted
by a solid trying to restore its original shape. The direction
of tension is always parallel to the string. When two objects
are connected by a string, the tension acts equally upon
both objects, in accordance with Newton’s 3rd law.
Weight ( ) is the gravitational force between two bodies,
typically an object on or near the surface of a planet and
the planet itself. Most often, that planet is Earth. The
magnitude of weight can be found by multiplying the
object’s mass by the planet’s acceleration of gravity. The
direction of weight is always straight down towards the
center of the planet.
Normal ( ) is the force exerted on the object when it
touches a surface. It is a contact force which prevents an
object from penetrating the surface. The direction of the
normal force is always perpendicular to the surface. For
example, a person sitting on a chair feels a normal force
from the surface of the chair and this force is directed
straight up from the flat surface.
Friction ( ) is a force that results from the rubbing together
of two surfaces. When we try to slide an object across
another surface, microscopic bumps along each surface
impede (resist) the motion. The direction of friction is
always such as to oppose the motion which created it. For
example if an object is sliding to the right, friction will point
to the left.
Drag ( ) is a resistive force that acts on an object as it
moves through a fluid (liquid or gas). The magnitude of the
drag force depends on the speed of the object, with the
drag force becoming stronger the faster the object moves
through the fluid. The direction of the drag force is always
such as to oppose the motion of the object.
Fremont Physics ©Kepple 2013
Circular Motion – Page #1
10/7/13
II. SUMMARY TABLE
2. Using the definitions we just reviewed on the previous page, fill in the table below.
Force
What causes it?
Direction
Tension
Weight
Normal
Friction
Drag
III. REAL OBJECTS FOR REAL FORCES
Since force is part of an interaction between two objects, it is important
to remember that all forces are exerted by real objects. Whenever you
draw a force on a force diagram, you must also be able to identify the
source (a real object) associated with that force. For example, a football
flying through the air (shown to the right) is in contact with air only. Only
the earth and air (gravity and drag) exert forces on it; the kicker does not.
3. For each situation below, add arrows to the diagram to show each of the forces acting on the object.
Label each force and indicate which object is associated with that force.
(a) A hockey puck is at rest on frictionless ice.
(b) A hockey puck slides across frictionless ice.
(c) A box is pulled across the floor by a rope.
(d) A sign hangs from two supporting ropes.
(e) A block slides down an inclined plane.
(f) A block slides up an inclined plane.
Linear Speed
Name: _______________________
Date: ___________ Period: _____
I. UNIFORM CIRCULAR MOTION
Suppose an object is moving in a circle at constant speed. Even though the
object has constant speed, it is accelerating because the direction of the
velocity is changing. This means there must be unbalanced force acting on
the object. The direction of the velocity is tangent to the circle and its
magnitude is called the linear speed. The net force acting on the object is
called centripetal force because it points towards the center of the circle.
1. Add arrows to the diagram to show the direction of the velocity and the force acting on the object.
2. What happens when a force is applied
perpendicular to the velocity?
3. A mass tied to a string is moving in a circle.
What happens when the string is cut?
II. LINEAR SPEED FORMULA
Consider an object moving at constant speed along a circular path of radius . The time it takes the
object to travel once around the circle is called the period ( ).
4. How much distance is
traveled in one period?
5. Start with the average velocity formula and then substitute in
the distance and time for one period of circular motion.
III. LINEAR SPEED – EXAMPLE PROBLEMS
7. A boring object takes 2 seconds to move
around a circle of radius 8 m. How fast was the
object moving?
8. An object travels in a circle of radius 5 m with
a speed of 10 m/s. How long does it take to go
around the circle once?
9. At a pony ride you go around in circles. It
takes 60 s to complete 1 circle. If the pony
walks at 1 m/s, what is the radius of the circle?
10. The Earth rotates once every 24 hours
(
s). The radius of Earth is
m.
How fast does the Earth spin?
Fremont Physics ©Kepple 2012
Circular Motion – Page #3
10/9/13
IV. LINEAR SPEED – PRACTICE PROBLEMS
11. A car is doing donuts in the parking lot. The
radius of the donut is 5 m and it takes the car 3
seconds to go around once. What is the speed
of the car?
12. A bicycle loops around a 45 meter radius
race track once every 15 seconds. What is the
linear speed of the bicycle?
13. Eddie, the crazy pit-bull, is chasing his own
tail. If his linear speed is 3 m/s and he turns in a
circle of radius 0.5 m, how long does it take him
to spin around once?
14. The largest Ferris wheel in the world is The
Star of Nanchang in China. It has a radius of 90
meters and takes 1800 seconds to turn once.
What is the linear speed of this Ferris wheel?
15. In the Simpsons Movie, Homer takes the
“Ball of Death” challenge, where he must ride a
motorcycle in a vertical circle around a
spherical cage at 25 m/s. If Homer loops around
the cage once every 1.2 seconds, what is the
radius of the cage?
16. In Superman: The Movie, Superman flies
around the Earth (radius
m) until his
speed reaches the speed of light (
m/s).
How long does it take Superman to go around
the Earth once?
Answers: 11)
m/s; 12)
m/s; 13)
s; 14)
m/s; 15)
m; 16)
s
Name: _______________________
Centripetal Force
Date: ___________ Period: _____
I. CENTRIPETAL FORCE FORMULA
An object moves counter-clockwise at constant speed along a circular path of radius .
1. Follow each step to add to the diagram below.
a) Draw arrows to show the velocity at
each position, label them .
b) Indicate the radius of the circle at
each position, label it .
c) Mark the angle the object has
moved through, label it .
d) Draw a line to show the distance
between the two points, label it .
2. The arrows to the right side of the circle are the same arrows you just drew in part 1a for the
velocity. They should point in the same direction, label both of these arrows .
a) Connect these two velocity arrows with an
line that points towards the center of the circle.
Label this arrow .
b) Notice that the angle between the velocity
vectors is the same as the angle between the
radius vectors. Label this angle .
3. What is the change in speed formula?
4. What do we need to find acceleration?
5. Determine
6. Determine by using the distance formula.
by using similar triangles.
7. Plug parts 5 and 6 into part 3, solve for .
8. Check to make sure this is a true expression
for by plugging in the units.
9. How can we relate acceleration to force?
10. Plug part 7 into part 9.
Fremont Physics ©Kepple 2011
Circular Motion – Page #3
10/11/12
II. EXAMPLE PROBLEM
11. A centrifuge is used to test a pilot’s ability to withstand the centripetal forces involved when flying
a fighter jet at high speeds. A typical human centrifuge has a radius of about 8 meters.
(a) The linear speed of the centrifuge is 12 m/s,
what acceleration does the pilot experience?
(b) If the mass of a pilot is about 100 kg, how
much force is impressed upon the pilot?
III. PRACTICE WORD PROBLEMS
12. I saw a Force commercial where they attached an F-150 to a 9 m radius centrifuge and spun it
around in circles. This was supposed to show the strength of the truck’s “two closed loop two hooks”.
(a) If the centrifuge was spinning at 30 m/s,
what acceleration did the truck experience?
(b) An F-150 truck has mass 2,000 kg, how
much force did the two hooks withstand?
13. A cool way to create artificial gravity in space is by making a
circular space station and rotating it. The centripetal force acting on
the passengers will mimic the feeling of gravity!
(a) The “floor” of the space station is actually the outer edge, or the
walls. In this case, what is the source of the centripetal force?
(b) Suppose the radius of the station was 40
meters, how quickly would it need to rotate to
simulate gravity as the surface of Earth?
(c) At this speed, what would be the centripetal
force acting on a person with mass of 75 kg?
Answers: 12a) 𝑎 = 100 m/s ; 12b) 𝐹 = 200 kN; 13a) normal force; 13b) 𝑣 = 20 m/s; 13c) 𝐹 = 750 N
2
Proportionality
Name: _______________________
Date: ___________ Period: _____
I. WHAT IS PROPORTIONALITY?
You have been conditioned your entire life to do math in one way, today we are going to learn a new,
more useful way to do math. The math you are familiar with uses what is called an equality, which
shows what a quantity is equal to, it is represented using an equal sign: =. Today we are going to learn
about a proportionality, which shows how a quantity changes, it is represented by the symbol: . Here
are two examples, to make this difference more clear.
Equality
Proportionality
N
“The force is equal to 2 newtons.”
“The force is doubled.”
1. PRACTICE: Write out the meaning of each expression.
(a)
(b)
N
(a)
(b)
II. WHY DO WE NEED PROPORTIONALITY?
In physics proportionalities make it possible to solve problems with missing information. However, you
must realize that proportionality is only the means to answer, not the actual answer! Remember, the
proportionality tells you how a quantity changes, not what the quantity is equal to.
2. EXAMPLE: A 100 N force causes an object to accelerate at 4 m/s². If the force is doubled, what will
be the new acceleration of the object?
(a) Solve using equality:
(b) Solve using proportionality:
III. MATHEMATICAL RELATIONSHIPS
Since proportionality shows how a quantity changes, it very useful for expressing how two quantities
depend upon one other, or in other words their “mathematical relationship.” The two most basic
mathematical relationships are direct and inverse. A direct proportionality is when two physical
quantities change in conjunction which each other, which means they change in the same way: if A
increases then B increases. An inverse proportionality is when two physical quantities change in
opposition, which means they change in the opposite way: if A increases then B decreases.
3. What is a direct proportionality?
Fremont Physics ©Kepple 2012
4. What is an inverse proportionality?
Circular Motion – Page #5
10/16/14
IV. FORMULAS AND RELATIONSHIPS
You can use a formula to determine the relationship between two quantities. This is because formulas
are made from proportionalities! First change the equality to a proportionality and remove any
coefficients from the formula. The formula is now showing only how things change, not what they are
equal to. Since we only care about how two of the quantities are changing, make all the other
quantities in the proportionality go to 1. Remember, proportional to 1 means the quantity is
unchanged! Use algebra to rearrange the quantities and what you have left is the relationship between
the two quantities.
5. In the linear speed formula, what is the relationship between…
(a) and ?
(b) and ?
(c) and ?
V. EXAMPLE PROBLEMS
6. An object moving in uniform circular motion has a period of 60 seconds. If the linear speed of the
object were halved what would be the new period of motion?
(a) Find the proportionality.
(b) Solve the proportionality.
(c) Calculate the period.
7. An object is moving at constant speed along a circular path of radius 40 meters. If the speed of the
object were doubled, and the force held constant, what would be the new radius of the circular path?
(a) Find the proportionality.
(b) Solve the proportionality.
(c) Calculate the radius
V. PRACTICE PROBLEMS
8. An object moves around a circular path of radius 10 meters at constant speed. If the speed of the
object were doubled – without changing the period – what would be the new radius of the circle?
(a) Find the proportionality.
(b) Solve the proportionality.
(c) Calculate the radius.
9. An object moving in a circle has a force of 200 N acting on it. What force would be required to give
the object twice as much speed around this same circle?
(a) Find the proportionality.
(b) Solve the proportionality.
(c) Calculate the force.
Circular Motion Practice Test
Name: _______________________
Date: ___________ Period: _____
I. VOCABULARY
If the underlined word is used incorrectly, cross it out and replace it with the correct word.
1. An object moves in a circle, the acceleration is tangent and the displacement is centripetal.
2. The force of gravity is called friction and the force from a string or rope is called weight.
3. When force and velocity are perpendicular the speed changes and the direction is constant.
4. Linear motion requires the application of a constant force directed to the outside of the circle.
5. An accelerating object can have a constant speed if the magnitude of velocity is changing.
II. CIRCULAR MOTION DRAWINGS
6. Draw the force and
7. Apply a force that changes
velocity of the object.
direction but not speed.
8. Indicate the direction the object will
move when the string is cut.
v
III. MULTIPLE CHOICE
9. An object is in uniform circular motion, which
of the following is true?
A
B
C
D
the acceleration is zero.
the velocity points to the center.
the force points to the center.
velocity is constant.
IV. WORD PROBLEMS
13. A car makes a turn of radius 25 m while
traveling at a constant speed of 15 m/s. What
acceleration was required to make this turn?
Fremont Physics ©Kepple 2011
Circular Motion – Page #6
10. What is the force required to keep a 10kg
model train moving in a circle of radius 10m if
the train has a linear speed of 0.5 m/s?
A 0.02 N
B 0.25 N
C 1N
D 2.5 N
14. A race car moves around a circular turn at
60 m/s. If the radius of the turn is 300 m what
is the period?
Answers: 1) velocity, force 2) weight, tension 3) direction, speed 4) circular, force,
center 5) constant, direction 6-8) See Quiz, 9) C, 10) B, 11) 9m/s², 12) 30s
Circular Motion Study Guide
MAJOR CONCEPTS:
 Period ( ) is the time it takes to complete
one revolution (cycle).
 When force and velocity are perpendicular,
the object changes direction but not speed.
 In uniform circular motion, the velocity is
tangent to the circle and the force is
centripetal. They are perpendicular!
 An object in uniform circular motion moves
at constant speed in a circle. The object is
accelerating because the direction changes!
 Circular motion requires a centripetal force.
Without a force, the object goes STRAIGHT!
 Centripetal is a direction. it means:
“directed to the center of a circle.”
MATHEMATICAL RELATIONSHIPS
DIRECT
INVERSE
when two
variables change
in conjunction
(the same)
when two
variables change
in opposition
(opposite)
CIRCULAR MOTION DRAWINGS
𝐹
𝑣
The velocity ( ) points TANGENT to the circle.
if
doubles then
is doubled.
if
doubles then
is halved.
The force ( ) is CENTRIPETAL (to the center).
Don’t forget: They are perpendicular! (90)
if is one half
then is halved.
if is one half
then is doubled.
EXAMPLE WORD PROBLEMS
Ex1. A race car speeds around a 150 m radius
circular race in 15 seconds. What is the speed
of the racecar?
𝑣
𝜋𝑟
𝑇
𝑣
( )( 5 )
( 5) 1
𝑣
𝑣
6 m/s
10
Ex2. During a windmill dunk, Vince Carter
moves the basketball in a circle at 30 m/s with
acceleration of 1000 m/s². How long is his arm?