Transcript Part II

Newton’s Second Law (Lab)
Inertia & Mass
• Inertia  The tendency of an object to
maintain its state of rest or motion.
• MASS: A measure of the inertia of an object
– Quantity of matter in a body
– Quantify mass by having a standard mass =
Standard Kilogram (kg)
(Similar to standards for length & time).
– SI Unit of Mass = Kilogram (kg)
• cgs unit = gram (g) = 10-3 kg
• Weight: (NOT the same as mass!)
– The force of gravity on an object (later in the chapter).
Newton’s Second Law
• 1st Law: If no net force acts on it, an object
remains at rest or in uniform motion in straight line.
• What if a net force does act? Do Experiments.
• Find, if the net force ∑F  0  The velocity v
changes (in magnitude, in direction or both).
• A change in the velocity v (Δv)
 There is an acceleration a = (Δv/Δt)
OR
A net force acting on a body produces an
acceleration!! ∑F  a
• Experiment: The net force ∑F on a body
and the acceleration a of that body are related.
• HOW? Answer by EXPERIMENTS!
– Thousands of experiments over hundreds of
years find (for an object of mass m):
a  ∑F/m (proportionality)
• We choose the units of force so that this is not
just a proportionality but an equation:
OR:
a  ∑F/m
(total!)
 ∑F = ma
• Newton’s 2nd Law:
∑F = ma
∑F = the net (TOTAL!) force acting on mass m
m = the mass (inertia) of the object.
a = acceleration of the object.
a is a description of the effect of ∑F
∑F is the cause of a.
• To emphasize that the F in Newton’s 2nd Law is the
TOTAL (net) force on the mass m, your text writes:
∑F = ma
Vector Sum of all
Forces!
∑ = a math symbol meaning sum (capital sigma)
• Newton’s 2nd Law: Based on experiment!
Not derivable
∑F = ma mathematically!!
A VECTOR equation!!
Holds component by component.
∑Fx = max, ∑Fy = may, ∑Fz = maz
ONE OF THE MOST
FUNDAMENTAL & IMPORTANT
LAWS OF CLASSICAL
PHYSICS!!!
Summary
Newton’s 2nd law is the relation between
acceleration & force. Acceleration is proportional to
force and inversely proportional to mass.
It takes a force to change either the direction
of motion or the speed of an object.
More force means more acceleration; the same
force exerted on a more massive object will yield
less acceleration.
Now, a more precise definition of force:
Force = an action capable of accelerating an object.
Force is a vector & is true along each coordinate axis.
The SI unit of force is the
Newton (N)
∑F = ma, unit = kg m/s2
 1N = 1 kg m/s2
Note The pound is a unit of
force, not of mass, & can
therefore be equated to Newtons
but not to kilograms!
Examples
Example: Estimate the net force needed to accelerate
(a) a 1000-kg car at (½)g (b) a 200-g apple at the same rate.
Example: Force to stop a car.
What average net force is required to bring a 1500-kg car
to rest from a speed of 100 km/h (27.8 m/s) within a
distance of 55 m?
Example 5.1: Accelerating Hockey Puck
A hockey puck, mass m = 0.3 kg,
slides on the horizontal, frictionless
surface of an ice rink. Two hockey
sticks strike the puck
simultaneously, exerting forces F1
& F2 on it. Calculate the magnitude
& direction of the acceleration.
Steps to Solve the Problem
1. Sketch the force diagram (“Free Body Diagram”).
2. Choose a coordinate system.
3. Resolve Forces (find components) along x & y axes.
4. Write Newton’s 2nd Law equations x & y directions.
5. Use Newton’s 2nd Law equations & algebra to solve for
unknowns in the problem. x & y directions.
Example
Find the resultant force FR
Example
Find the resultant force FR
FR = [(F1)2 + (F2)2](½) = 141 N
tanθ = (F2/F1) = 1, θ = 45º
Example
Find the resultant force FR
If the boat moves with
acceleration a,
∑F = FR = ma
FRx = max, FRy = may
Sect. 5.5: Gravitational Force & Weight
• Weight  Force of gravity on an object. Varies
(slightly) from location to location because g varies.
Write as Fg  mg. (Read discussion of difference
between inertial mass & gravitational mass).
• Consider an object in free fall. Newton’s 2nd Law:
∑F = ma
• If no other forces are acting, only Fg  mg acts
(in vertical direction).
∑Fy = may
or
Fg = mg (down, of course)
• SI Units: Newtons (just like any force!).
g = 9.8 m/s2  If m = 1 kg,
Fg = 9.8 N
Newton’s 3rd Law
• 2nd Law: A quantitative description of how
forces affect motion.
• BUT: Where do forces come from?
– EXPERIMENTS find: Forces applied to an object
are ALWAYS applied by another object.
 Newton’s 3rd Law: “Whenever one object exerts a
force F12 on a second object, the second object exerts an
equal and opposite force -F12 on the first object.”
– Law of Action-Reaction: “Every action has an
equal & opposite reaction”. (Action-reaction forces
act on DIFFERENT objects!)
Another Statement of Newton’s 3rd Law
“If two objects interact,
the force F12 exerted
by object 1 on object 2
is equal in magnitude
& opposite in direction
to the force F21 exerted
by object 2 on object 1.”
As in figure
Example: Newton’s 3rd Law
When a force is exerted on an
object, that force is caused by
another object.
Newton’s 3rd Law:
“Whenever one object exerts
a force on a second object,
the second exerts an equal
force in the opposite direction
on the first.”
If your hand pushes against the edge of a desk (the force vector
shown in red), the desk pushes back against your hand (this
force vector is shown in purple, to remind us that this force
acts on a DIFFERENT object).
Newton’s 3rd Law: Alternative Statements
1. Forces always occur in pairs
2. A single isolated force cannot exist
3. The “action force” is equal in magnitude to
the “reaction force” & opposite in direction
a. One of the forces is the “action force”,
the other is the “reaction force”
b. It doesn’t matter which is considered the
“action” & which the “reaction”
c. The action & reaction forces
must act on different objects
& be of the same type
Conceptual Example:
What exerts the force to move a car?
Conceptual Example:
What exerts the force to move a car?
Response
A common answer is that the engine makes the car move
forward. But it is not so simple. The engine makes the
wheels go around. But if the tires are on slick ice or deep
mud, they just spin. Friction is needed. On firm ground,
the tires push backward against the ground because of
friction. By Newton’s 3rd Law, the ground pushes on the
tires in the opposite direction, accelerating the car forward.
Helpful notation: On forces, the 1st subscript is the object
that the force is being exerted on; the 2nd is the source.
Action-Reaction Pairs act on
Different Objects!
Action-Reaction Pairs: Act on Different Objects
The key to correct the application of
Newton’s 3rd Law is:
The forces are exerted on
different objects.
Make sure you don’t use them as if
they were acting on the same object.
Example: When an ice skater pushes
against the railing, the railing pushes
back & this reaction force causes
her to move away.
Conceptual Example
Michelangelo’s assistant has been assigned the task of moving a block of
marble using a sled. He says to his boss, “When I exert a forward force on the
sled, the sled exerts an equal and opposite force backward. So how can I ever start
it moving? No matter how hard I pull, the backward reaction force always equals
my forward force, so the net force must be zero. I’ll never be able to move this
load.” Is he correct?
Action-Reaction Pairs
Act On Different Objects
• Forces exerted BY an object DO NOT (directly)
influence its motion!!
• Forces exerted ON an object (BY some other
object) DO influence its motion!!
• When discussing forces, use the words “BY” and
“ON” carefully.
Rocket propulsion can be explained using
Newton’s Third Law:
Hot gases from combustion spew out of the tail of the rocket at high
speeds. The reaction force is what propels the rocket.
Note:
The rocket doesn’t need
anything to “push”
against.