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Unit 4: Newton’s Laws
Forces
Force:
There are four fundamental forces that make up all of
the forces in the universe:
1)
2)
3)
4)
The units of force are:
Force of Gravity
Force of Gravity:
The formula for force of gravity is:
Mass (kg):
Where:
Weight (N):
m=
g =
Mass is ____________ throughout the universe but
weight ____________ depending on where you are.
g varies depending on…
=
Determine your weight on Earth, the moon and Jupiter
(in Newtons)
Your Mass: ___________ kg (1 kg = 2.2 lbs)
! On Earth at sea level, g =
Weight on Earth:
Fg = mg
=
! On the moon, g =
Weight on the Moon:
For Example:
! On Jupiter, g =
! On the sun, g =
Weight on Jupiter:
Activity:
Jumping on the Moon
Purpose: To determine how high you could jump on the surfaces of the Moon and the Sun.
Procedure:
1. Have your lab partner measure your best vertical on Earth.
2. Determine the initial velocity of your jump. We will assume that your initial jump velocity will be the
same on the Moon and the Sun.
3. Find your vertical and hang time on the moon using an acceleration = -1.60 m/s2.
4. Find your vertical and hang time on the Sun using an acceleration = -274 m/s2.
Moon
Earth
Sun
Vertical: ____________
vo = _____________
dmax: _______________
dmax: _______________
t = _________________
t = _________________
A Quick Aside on G-Forces
“G-forces” are actually a measurement of acceleration experienced by an object. It is related to the supporting
reaction force that an object experiences due to acceleration. While at rest on Earth you are experiencing 1 g.
1 g = 9.80 m/s2
For Example:
A car accelerates at 4.9 m/s2, how many g’s is that?
During lift-off a shuttle will accelerate at 28 m/s2. How many g’s are experienced by the astronaut?
A normal human can withstand 4.0 g’s, while a fighter pilot can withstand up to 9.0 g’s. What acceleration would
cause each to pass out?
Unit 4: Newton’s Laws
Newton’s 1st Law
Imagine that you are racing around
a track on a go-kart. List three times
when you notice your inertia.
Newton’s 1st Law:
An object in motion will…
and an object at rest will…
unless…
1)
This is also referred to as the Law of Inertia.
2)
Inertia:
3)
Another way of thinking of Newton’s 1st Law is that if there is no net force on an object then it will stay at a
constant velocity.
If it is not moving then it has a constant velocity of zero!!!
Ex. Imagine a book sitting on a table. There is a
force of gravity pulling down on the book, but there
is also a supporting (normal) force pushing up on
the book.
Ex. If I drop the book from 2 m, there is only a
downwards, gravitational force acting on it. Now
that the forces on it are unbalanced, what does
the book do?
Examples:
1) While riding a skateboard (or chuckwagon or unicycle, whatever), you fly forward off the board when hitting a curb or
rock or other object which abruptly halts the motion of the skateboard.
2) The head of a hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard
surface.
3) While you are sitting in the back seat of the car, it makes a hard right turn. You squish your sister against the side
door (CORNERS!!!).
4) Headrests are placed in cars to prevent whiplash injuries during rear-end collisions.
Unit 4: Newton’s Laws
Newton’s 2nd Law
Newton’s 2nd Law:
Ex. A 5.0 kg block is pushed to the right along a
frictionless track with a force of 10.0 N. What is
its acceleration?
Stated as a formula:
Note that…
Ex. A 650 kg car accelerates at 4.0 m/s2 south. What
is the net force acting on it?
Ex: A 1500 kg ice cream truck accelerates from
rest to a top speed of 45 km/h in 8.0 s. What was
the net force acting on the truck?
To find Fnet when two forces work together …
To find Fnet when many forces act on an object:
Ex. Stan and Kyle are pushing a 75 kg sled along a
frictionless ice rink. Stan pushes with 55 N and Kyle pushes
with 45 N. Find the sled’s acceleration.
Ex: The Batmobile exerts a force of 8.50x103 N east, while
friction pulls back on it with a force of 1500 N. If it has a
mass of 1250 kg, what is its acceleration?
Worksheet 4.1 Newton’s 2nd Law 1) For each of the following diagrams determine the magnitude and direction of the net force. FN = 100 N
FN = 600 N
T = 400 N
Fapp = 20 N Ff = 20 N Fapp = 250 N
Ff = 75 N Fg = 100 N Fg = 150 N Fg = 600 N FN = 200 N
FN = 200 N
FN = 150 N
Fapp = 60 N Fapp = 120 N
Ff = 80 N Ff = 55 N Fapp = 60 N
Fg = 150 N Fg = 200 N
Fg = 200 N
2) Use the information given for each diagram to fill in all missing blanks. FN = 300 N FN = _____
FN = _____
Ff = 20 N Fapp = 70 N Ff = 20 N
Fapp = 20 N
Fapp = 240 N
Ff = 80 N Fg = ______
Fg = 300 N m = 5 kg a = _______ m/s2 m = 12 kg
a = _______ m/s2 Fg = _____ m = _________
a = 4 m/s2 right FN = 500 N
FN = _____
FN = 160 N Ff = ______
Fapp = 200 N
Ff = 125 N Fg = _____ m = 8 kg a = _______ m/s2 Fg = ______
m = 40 kg
a = 4 m/s2 right Fg = ______
m = ______ a = _______ m/s2 Unit 4: Newton’s Laws - FBDs
Force
Description
Ex 1: A box is pushed across a rough floor at a
constant velocity.
Ex 2: A hockey player glides on frictionless ice at a
constant velocity.
1. A book is at rest on a table top.
2. A girl is suspended motionless from a bar which
hangs from the ceiling by two ropes.
3. An egg is free-falling from a nest in a tree.
Neglect air resistance.
4. A plane flies at a constant velocity (Note: there
will be an applied force generated by the engines as
well as a lift force provided by the wings).
5. A rightward force is applied to a book in order to
move it across a desk with a rightward acceleration.
Consider frictional forces. Neglect air resistance.
6. A rightward force is applied to a book in order to
move it across a desk at constant velocity. Consider
frictional forces. Neglect air resistance.
7. A college student rests a backpack upon his
shoulder. The pack is suspended motionless by one
strap from one shoulder.
8. A skydiver is descending with a constant
velocity. Consider air resistance.
9. A force is applied to the right to drag a sled
across loosely-packed snow with a rightward
acceleration.
10. A football is moving upwards towards its peak
after having been booted by the punter.
11. A car is coasting to the right and slowing down.
Diagram the forces acting upon the car.
Unit 4: Newton’s Laws
Newton’s 3rd Law
Newton’s 3rd Law:
1) You hit a baseball with a bat.
2) A sprinter starts running.
Any interaction involves two forces that we call…
3) A fish swims through water.
Imagine a bug hitting the windshield of a semi trailer.
What force pair occurs?
Which force is bigger?
Which object has a greater acceleration?
Example 1: Recoil
Example 2: Bricks
Example 3: Rockets
Unit 5: Forces Force of Friction Friction is created whenever… On the microscopic level… Friction is given by the equation: Where: FN = = µ = = = Static Friction: Kinetic Friction: Frictionstatic Frictionkinetic μ static μkinetic Ex 1: A 3.75 kg block is pushed along a tabletop with a force of 45.0N. The coefficient of friction is 0.65. a) Find the force of friction. b) Find the acceleration. Ex 2: A 0.200 kg puck is pushed along a sheet of ice with a force of 0.240 N. If it moves at a constant velocity, find the coefficient of friction. Ex 3: A 1.1 kg textbook is held against a vertical wall with a force of 45 N. What is the coefficient of friction between the book and the wall? Worksheet 5.3 ‐ Force of Friction 1) A 7.6 kg object is resting on a horizontal surface. What is the normal force on the object? 2) A 7.6 kg object is pulled along a horizontal surface. If the coefficient of friction is 0.20, what is the force of friction? 4) A 9.6 kg object is pulled along a horizontal surface. If the coefficient of friction is 0.11 what is the force of friction? 5) A 20.0 N object is pulled along a horizontal surface at a constant velocity by a 3.0 N force, what is the coefficient of friction? 6) A 16.2 kg object is pulled along a frictionless surface by an applied force of 10.2 N, what is the normal force acting on it? 7) A 6.2 kg object is pulled along a horizontal surface by a force of 22.0 N. If its acceleration is 1.1 m/s2, what is the coefficient of friction between the two surfaces? 8) A 1250 kg car traveling at 60.0 km/h comes to a sudden stop in 35 m. What is the coefficient of friction acting on the brakes? 9) A 950 kg car traveling at a constant velocity of 28 m/s, has a coefficient of friction of 0.125 acting on its axle. How much force is required by the engine to maintain its speed? 10) A 1425 kg dragster exerts 13900 N of force and accelerates from 0 to 100.0 km/h in 3.25 s. What is the coefficient of friction acting on the car? 1) 74 N 2) 15 N 3) 137 N 4) 10. N 5) 0.15 6) 159 N 7) 0.25 8) 0.40 9) 1200 N 10) 0.123
Unit 4: Newton’s Laws Tension Tension occurs within a material that is being… __ _________ along a rope (string, chain, etc) in _____ ____________. It is an internal force that acts ___ ___
Consider two carts attached by a rope b
being pulled along a flat surface. (Friction is n
negligible.) If m1 is pulled to the right by a force of 4
40.0 N find: a) The acceleration of the carts. NOTE: tension… b) The tension in the string connectting them. NOTE: Since it cancels out of the total Fnet equation, we will only consider the forcess acting... NOTE: Since tension acts on both masses eq
qually we can use… Consider two equal masses hanging fro
om a pulley. e system. Diagram the forces acting on the entir
With pulley problems it is sometime ea
asier to “unfold” the rope as shown. Ex: The two masses shown hanging fro
om a frictionless pulley are released at rest. FFind a) The acceleration of the system. b) The tension in the string. NOTES: 1. When solving for acceleratiion of the whole system we consider ______
________ 2. When finding T we only use
e ______ __________. Ex: A mass on a frictionless table is att
ached to a hanging mass over a frictionless p
pulley as shown. Find: a) The acceleration of the massess. b) The tension in the rope. Ex2: If the same system has a friction f
force of 25 N acting on the 8.0 kg mass find:
a) The acceleration of the massess. b) The tension in the rope. Dynamics Notes
1 – Newton’s Laws
Newton’s 1st Law:
An object…
and an object…
unless…
Newton’s 2nd Law:
Newton’s 3rd Law:
For every…
As a formula:
As a formula:
Free Body Diagrams: (Draw one for EVERY force question)
1) Represent the object as a box and,
2) Represent all forces as arrows
• The arrows are vectors so their direction is critical
• Start in the center and draw outwards
• The size of the arrow represents the magnitude of the force
1. A puck slides along frictionless ice.
2. A dragster accelerates from rest.
Ex. A student pulls straight upwards with a force of 650
N on their 15 kg backpack. What is the backpack’s
acceleration?
3. A block of wood slides
down an incline
Ex. A 1200kg car accelerates at 5.85 m/s2. If the
coefficient of friction acting on the car is roughly
0.24, how much force does the engine exert?
Dynamics Notes
2 – Forces in 2-D
As with any vectors, forces must be resolved with consideration to both their ____________ and ____________.
Ex
Two students push a crate across a frictionless surface.
Student A pushes with 75 N East and Student B
pushes with 48 N South.
What is the resultant force acting on the box?
If there are more than two forces then it is best to solve for the resultant using the...
Ex
Resolve these force vectors into their x and y components
50o
F1 = 35 N
F2 = 45 N
F3 = 65 N
20o
Ex 2 - Determine the resultant force if all three forces in the
last example are applied to a single body.
F3
F1
F2
FR
Ex 3: Two children pull a third child on a toboggan
(shown from the top, assume up is north). Assuming
that they pull on ropes that are parallel to the ground
determine the magnitude of the force exerted on the
toboggan.
Dynamics Notes
3 – Inclines
A ball sitting on a level surface will not roll because the
forces on it are balanced (Fnet = 0).
Although the Fg pulls straight down at all times…
However, when the ball is
placed on an inclined
plane it will roll down the
plane.
For inclined plane questions our first step should always be
to resolve the object’s Fg into two components:
FN is always…
Two important things to notice:
1) Only the ___________________ ___________________________ pulls down the ramp.
2) The ______________________ __________________________ is equal and opposite to
__________________________.
Ex
An 8.0 kg block slides down the
frictionless inclined plane shown.
What is its acceleration?
35o
Ex
How much force is required to push
an 11 kg block up the frictionless ramp
shown at a constant velocity?
Ex
A 15 kg block sits on an inclined ramp
whose coefficient of friction is 0.21. Find
the block’s acceleration.
58o
40o
Dynamics Notes
4 – Two Objects and Tension
There are a number of common force problems that involve 2 objects, that you will be expected to be able to solve. We
will focus on 3 of these.
Atwood’s Machine: Two masses suspended by a pulley
Both masses have a Fg that pull downwards,
but since they are connected by a pulley those
forces work in ______________
_________________.
Diagram: Include all forces at work on the two masses.
The masses will accelerate so that the…
Since they are attached by a rope the
acceleration of the masses must be
_____________________.
Note that there is a force of TENSION (T) that
exists along the rope. Tension acts the same
as all other forces, with two important
peculiarities:
1) It is an internal force, acting…
2) It cancels out…
The Strategies:
• When solving these problems it is easiest for us to choose
the direction …
•
Remember that the acceleration on the two masses...
•
It can also be easier to conceptualize this problem if we
“unfold” the masses and lay them out in a line, while keeping
all of our forces as they are…I know that sounds weird so,
here’s an example.
Ex
Two masses are suspended from a lightweight rope over a frictionless pulley as shown.
What will their acceleration be once released?
kg
kg
NOTE: When calculating the acceleration we use the _____________ because the Fnet is accelerating the entire system
(both masses)!
Alright that wasn’t too hard, but can you find the tension in the rope?
If we use the same force diagrams and equations as before we hit a
snag. The two tension forces ______________ !!!
Strategy: To solve for tension chop your
diagram in half and only consider one of the
masses. Either one is fine because…
This is because tension is an___________ ____________.
In order to solve for tension we have to consider…
Ex - Find the tension in the rope in the preceding example.
Note: When finding the tension we are only considering half of the equation therefore we only use ___________.
The Hanging Mass: One mass hanging, one horizontal
Ex
Consider the two masses shown. Find their acceleration and the tension in the rope.
8.0
kg
6.0
kg
Because one tricky concept is never enough, I give you…
Ex
Two forces are attached by a rope over a frictionless pulley as shown.
(Assume the incline is frictionless) Determine:
a. The acceleration of the masses.
b. The tension in the rope.
m1 =
m2 =
4.0 kg
6.0 kg
30o
Problem: What direction will they accelerate?
In earlier pulley problems it was obvious, the bigger
mass always wins. When an inclined plane is
involved this is not always the case because for the
mass on an incline only...
So determine the forces on each one separately
and see which one is the winner.
Force 1 =_________
Force 2 = _________
Ex
In the name of physics, a monkey is attached to a sleeping sheep on a ramp. Don’t ask why.
As we all know, the coefficient of friction for a sleeping sheep on a ramp is precisely 0.15. Determine:
a. The acceleration of the system.
b. The tension in the rope.
even
adorabler
sheep
28 kg
adorable
monkey
24 kg
40o
Strategies:
1. Find the forces acting on the two
bodies separately to determine a
winner
2. Determine the friction on the
sheep. Friction can work either
up or down the ramp, because it
always opposes motion, so we
don’t know which direction it is
acting until we know the winner.
3. Based on the winner find the
acceleration using mtotal
4. Choose either body and examine
it separately to determine the
tension in the rope
Ex: A boy pulls his 8.0 kg toboggan by a rope that
angles 32o above the horizontal. If his 36.0 kg sister
sits on the toboggan, how much force does he need to
exert to accelerate them at 2.25 m/s2?
Ex: A 1.12 kg textbook is pushed horizontally against a
wall with a coefficient of friction of 0.465. What is the
least amount of force required to keep the book from
slipping?
Ex: Two blocks (m1 = 2.0 kg and m2 = 3.0 kg) are
connected by a rope as shown. m1 is pulled to the right
with a force of 18 N. What is the tension in the rope
connecting the two masses?
Ex: A 65 kg student stands on a bathroom scale in an
elevator and notices that it reads 520 N.
Determine the magnitude and direction of the
acceleration of the elevator.