Transcript m/s 2 - mrhsluniewskiscience

Objectives
• Investigate the relationship between mass,
force, and acceleration.
• State Newton’s second law and give examples
to illustrate the law.
• Solve problems involving force, mass, and
acceleration.
Warm-up
•
•
•
•
Find the weight in Newtons for:
10 kg = _____ N
100 kg = _____ N
1 kg = _____ N
Everything in the world does
one of two things:
Or……
Demo
• http://www.youtube.com/watch?v=iwP4he
WDhvw
Exploring Newton’s Second Law
• Demonstration
– What do you observe?
– What can you measure?
– What can you change?
• Design two separate data collection
strategies to determine how two factors
affect the acceleration of the system: the
net force on the system and the total mass
of the system.
Activity
• Computer Activity on Exploring Forces
Newton’s Second Law of Motion
The relation between acceleration and
force. Acceleration is proportional to force
and inversely proportional to mass.
“sigma” symbol means summation
If there is only one force present,
then you can leave it out.
Force is vector
Acceleration is a vector
Newton’s Second law
• Fnet = ma
(N) = (kg) (m/s2)
Force problems always must use
these units!
• If you prefer triangles
Fnet
a
• “net” means “the total sum”
or you can use the symbol Σ
m
Newton’s Second Law
• Force = Mass x Acceleration
• Force is measured in Newtons
ACCELERATION of GRAVITY(Earth) = 9.8 m/s2
• Weight (force) = mass x gravity (Earth)
Moon’s gravity is 1/6 of the Earth’s
If you weigh 420 Newtons on earth,
what will you weigh on the Moon?
70 Newtons
If your mass is 41.5Kg on Earth
what is your mass on the Moon?
Newton’s Second Law
• WEIGHT is a measure of the
gravity on the
force of ________
mass of an object
Newtons
• measured in __________
4-4 Newton’s Second Law of Motion
Force is a vector, so
each coordinate axis.
is true along
The unit of force in the SI
system is the newton (N).
Note that the pound is a
unit of force, not of mass,
and can therefore be
equated to newtons but
not to kilograms.
Newton’s Second Law
One rock weighs 5 Newtons.
The other rock weighs 0.5
Newtons. How much more
force will be required to
accelerate the first rock
at the same rate as the
second rock?
Ten times as much
nd
2
Law: Fnet = m a
• The acceleration an object undergoes is
directly proportion to the net force acting on it.
• Mass is the constant of proportionality.
• For a given mass, if Fnet doubles, triples, etc.
in size, so does a.
• For a given Fnet if m doubles, a is cut in half.
• Fnet and a are vectors; m is a scalar.
• Fnet and a always point in the same
direction.
• The 1st law is really a special case of the 2nd
law (if net force is zero, so is acceleration).
What is Net Force?
F1
F2
F3
Fnet
When more than
one force acts on a
body, the net force
(resultant force) is
the vector
combination of all
the forces, i.e., the
“net effect.”
Net Force & the 2nd Law
For a while, we’ll only deal with forces that
are horizontal or vertical.
When forces act in the same line, we can
just add or subtract their magnitudes to
find the net force.
32 N
15 N
2 kg
10 N
Fnet = 27 N to the right
a = 13.5 m/s2
Units
Fnet = m a
1N
= 1 kg
2
m/s
The SI unit of force is the Newton.
A Newton is about a quarter pound.
1 lb = 4.45 N
Graph of F vs. a
In the lab various known forces are
applied—one at a time, to the same mass—
and the corresponding accelerations are
measured. The data are plotted. Since F
and a are directly proportional, the
relationship is linear.
F
a
Slope
Since slope = rise / run = F / a, the slope
is equal to the mass. Or, think of y = mx
+ b, like in algebra class. y corresponds
to force, m to mass, x to acceleration,
and b (the
y-intercept) is zero.
F
F
a
a
W = mg
• Weight = mass  acceleration due to gravity.
• This follows directly from F = m a.
• Weight is the force of gravity on a body.
• Near the surface of the Earth,
g = 9.8 m/s2.
Two Kinds of Mass
• Inertial mass: the net force on an object
divided by its acceleration. m = Fnet / a
• Gravitational mass: Compare the
gravitational attraction of an unknown
mass to that of a known mass, usually
with a balance. If it balances, the
masses are equal.
?
m
Balance
Einstein asserted that
these two kinds of
masses are equivalent.
Inertial Mass =Gravitational Mass
Video
• http://science360.gov/obj/video/58e62534e38d-430b-bfb1-c505e628a2d4/sciencenfl-football-newtons-second-law-motion
Forces & Kinematics
To solve motion problems involving
forces:
1. Find net force (by combining vectors).
2. Calculate acceleration (using 2nd law).
3. Use kinematics equations:
vf = v0 + a t
1
x = v0 t + 2 a t2
vf2 – v02 = 2 a x
Example: Pushing a Box on Ice.
• A skater is pushing a heavy box (mass m =
100 kg) across a sheet of ice (horizontal
& frictionless). He applies a force of 50
N toward the right. If the box starts at
rest, what is its speed v after being
pushed for a time t = 5 s ? v = ?
F = 50 N
m
d=?
Newton 2, Slide 25
t=5s
a=?
Example: Pushing a Box on Ice...
• Start with Fnet = ma.
– a = Fnet / m.
– a = (50 N)/(100 kg) = 0.5 N/kg = (0.5 kg
m/s2)/kg
– a = 0.5 m/s2
– Recall that vf = vi+ at (from definition of a)
– So v = (0.5 m/s2) (5 s)
v = 2.5 m/s
– v = 2.5 m/s
F = 50 N
m
Newton 2, Slide 26
d=?
t=5s
a = 0.5 m/s2
Example: Pushing a Box on Ice...
• Now, what distance will the block travel
during the 5 seconds?
– d = ½ a t2
– d = (0.5)(0.5m/s2)(5 s)2
– d = 6.25 m
v = 2.5 m/s
F = 50 N
m
Newton 2, Slide 27
d=?
t=5s
a = 0.5 m/s2
Sample Problem A
Goblin
400 N
Ogre 1200 N
Treasure 300 kg
Troll 850 N
A troll and a goblin are fighting with a big, mean ogre
over a treasure chest, initially at rest. Find:
1. Fnet = 50 N left
2. a = 0.167 m/s2 left
3. v after 5 s = 0.835 m/s left
4. x after 5 s = 2.08 m left
Problem 1
• What average force is required to stop an
2100-kg car in 12.0 s if the car is traveling
at 95 km/h?
Problem 2
• What average force is needed to
accelerate a 7.00-gram pellet from rest to
125 m/s over a distance of 0.800 m along
the barrel of a rifle?
Newton 2 Slide 30
#11 in book
• A particular race car can cover a quartermile track (402 m) in 6.40 s starting from
a standstill. Assuming the acceleration is
constant, how many “g’s” does the driver
experience? If the combined mass of the
driver and race car is 485 kg, what
horizontal force must the road exert on
the tires?
Newton 2 Slide 31
Application of Newton’s 2nd Law
• http://science360.gov/obj/video/58e625
34-e38d-430b-bfb1c505e628a2d4/science-nfl-footballnewtons-second-law-motion
• Other examples of applications of
Newton’s 2nd Law.
Newton 2 Slide 32
Homework Chapter 4
• Questions on page 97 #s 3, 4, and 13
• Problems #s 1, 3, and 9
Closure
• If a loaded truck that can accelerate at 1
m/s2 loses its load and has three-fourths of
the original mass, what acceleration can it
attain from the same driving force.
• Kahoot
34