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Review: Newton’s 1st & 2nd Laws
• 1st law (Galileo’s principle of inertia)- no
force is needed to keep an object moving
with constant velocity
• 2nd law (law of dynamics) – a force is
needed to change the velocity (i.e.,
accelerate) of an object, how much:
F(N) = m(kg) × a(m/s2)
Acceleration due to gravity
• w=m×g
weight, w
• F=m×g=m×a Æ
Problem -1
Problem 2
• Two forces act on a 4 kg object. A 14 N
force acts to the right and a 2 N force acts
to the left. What is the acceleration of the
object?
• Net force = 14 N − 2 N = 12 N (to the right)
• F = m a Æ 12 N = 4 kg x a
• Æ a = 3 m/s2 Î the object accelerates to
the right at 3 m / s2.
Problem: down the
track (no friction):
find the acceleration,
a, of the blocks
M
2 kg
Friction force = 2 N
• A 2 kg box is pushed by a 10 N force while a 2 N
friction force acts on the box. What is the
acceleration of the box?
• Net force = 10 N – 2 N = 8 N to the right
• acceleration = Force / mass = 8N / 2 kg = 4 m/s2
to the right.
Î acceleration is in the direction of the NET Force
T
T
W = Mg
Push = 10 N
a = mg/ (m+M) ≈ (m/M)g
Ftable
M
a = g for any m
m
• Net Force on system = total mass × a
• mg = (m + M) a → a=mg/ (m+M) ≈ (m/M)g,
if M is much bigger than m
• the force on m is applied to M through the
string tension
w = mg
m= 20g
M (g)
m = 40g
a
(m/s2)
M (g)
a (m/s2)
294
0.67
294
1.33
600
0.33
600
0.65
852
0.23
852
0.46
If Galileo had done this experiment, Newton’s Second Law
would be Galileo’s Second Law
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3rd Law
Newton’s third law (lecture 7)
(deals with the interaction of 2 objects)
For every action there is an
equal and opposite reaction.
discuss collisions, impulse,
momentum and how airbags protect
you in a crash
Example
• What keeps the box
on the table if gravity
is pulling it down?
• The table exerts an
equal and opposite
force upward that
balances the weight
of the box
• If the table was flimsy
or the box really
heavy, it would fall!
You can move the earth!
• The earth exerts a
force on you
• you exert an equal
force on the earth
• The resulting
accelerations are
not the same
• Fon earth = - Fon you
• MEaE = myou ayou
• If object A exerts a force on object B, then
object B exerts an equal force on object A
in the opposite direction.
B
A
BÆA
AÆB
The bouncing ball
• Why does the ball
bounce?
• It exerts a downward
force on ground
• the ground exerts an
upward force on it
that makes it bounce
Action/reaction forces always
act on different objects
• A man tries to get the donkey to pull the cart but
the donkey has the following argument:
• Why should I even try? No matter how hard I
pull on the cart, the cart always pulls back with
an equal force, so I can never move it.
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Friction is essential to movement
The tires push back on the road and
the road pushes the tires forward. If
the road is icy, the friction force
between the tires and road is reduced.
Demonstrations
physics
professor
• Bouncy and nonbounce ball
• Dropping the beakers
• Stunt man jumping off
of a building
What is impulse?
• If a force F acts for a time t, then the
impulse is the Force × time = F × t
• Since force is measured in Newtons and
time in seconds, impulse will be measured
in Newton-seconds.
•
IMPULSE = F × t
You can’t walk without friction
You push on backward on the ground and the
ground pushes you forward.
Impulse
• When two objects
collide they exert forces
on each other that last
only a short time
• We call these short
lasting, but usually
strong forces
IMPULSIVE forces.
• For example when I hit
a nail with a hammer, I
exert an impulsive force
Momentum
• The term momentum is used quite often in
everyday conversation about many things.
• For example, you may hear that one team
has the momentum, or that a team has
lost its momentum.
• Momentum is a physics term that has a
very definite meaning. If an object has a
mass m and moves with a velocity v, then
its momentum is mass × velocity = m × v
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Momentum = m × v
Knock the block over
• In physics, if something has momentum, it
doesn’t loose it easily and if it doesn’t have
it, it doesn’t get it easily – something has
to happen to an object to change its
momentum
• Impulse can change momentum, in fact
change in momentum = impulse
• If an object gets an impulse, F × t, then
its momentum changes by exactly this
amount
Elastic and inelastic Collisions
(bouncy)
(non-bouncy)
Which ball experiences the largest upward
force when it hits the ground?
Force on
The ball
Force on
The ball
Physics explains it!
• Beakers dropped from
same height so then
have the same velocity
(and momentum) when
they get to the bottom.
• One falls on a hard
surface
• The other falls on a
cushion.
hard
soft
The bouncy side knocks
the block over but not the
non-bouncy side
Bouncing ball
• The force that the ball exerts on the
ground is equal to and in the opposite
direction as the force of the ground on the
ball.
• The ball that bounces back not only must
be stopped, but must also be projected
back up.
• The ground exerts more force on the ball
that bounces than the ball that stops.
• Why prevents the beaker that falls on the
cushion from breaking?
• First, what causes anything to break?
• If an object experiences a large enough
FORCE then it might break.
• Why does the beaker that falls on the
cushion experience a smaller force?
• Both beakers have the SAME change in
their momentum – they both hit the bottom
with the same speed and both end up with
zero velocity.
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• The beaker that shatters comes to rest
more quickly than the one that gently slows
down on the cushion Å this is the key point!
• According to the impulse-momentum
relation:
Impulse = Force × time (F × t)
= change in momentum
• F × t is the same for both. Since the one on
the cushion takes longer to slow down the
force on it is less, t is biggerÆ F smaller
Air bags
• The same thing is true for airbags
• They protect you by allowing you to come
to rest more slowly, then if you hit the
steering wheel or the dash board.
• Since you come to rest more slowly, the
force on you is less.
• You will hear that “airbags slow down
the force.” this is not entirely accurate
but it is one way of thinking about it.
Momentum and Collisions
Conservation of Momentum
• The concept of momentum is very useful
when discussing how 2 objects interact.
• Suppose two objects are on a collision
course. AÎ ÍB
• We know their masses and speeds before
they hit
• The momentum concept helps us to see
what can happen after they hit.
• One consequence of Newton’s 3rd law is
that if we add the momentum of both
objects before the collision it MUST be the
same as the momentum of the two objects
after the collision.
• This is what we mean by conservation:
when something happens (like a collision)
something doesn’t change – that is very
useful to know because collisions can be
very complicated!
Elastic and inelastic Collisions
(bouncy) (non-bouncy)
Read more about it
http://www.physicsclassroom.com/Class/momentum/U4L1c.html
http://www.geocities.com/thesciencefiles/homerun/homerun.html
http://www.k12.nf.ca/gc/Science/Physics3204/Projects2003/SlotA/P
rojectA2/index1.htm
Force on
The ball
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