Download Relative Motion

Relative Motion

You are swimming across a 50m wide river in
which the current moves at 1 m/s with respect
to the shore. Your swimming speed is 2 m/s
with respect to the water.
You swim across in such a way that your path
is a straight perpendicular line across the river.
– How many seconds does it take you to get across?
a) 50 2  25s
b) 50 1  50s
c) 50
3  29s
d) 50
2  35s
2m/s
50m
1m/s
What Causes Acceleration?

Group 1 Go on the internet and find newtons laws.
Physicsclassroom.com might be good. Be prepare
to discuss them.
 Group 2 Devise an experiment to test what is
important in horizontal acceleration. You have a
bowling ball, and tennis ball as equipment. (don't
drop the bowling ball) List the things that effect
the acceleration as you push a ball.
 Group 3 Discuss moving the contents of your
house what would you least like to move and why?
 Group 4 Push against the wall. Tell me all the
things that are pushing and being pushed. (Their
are more than you think.)
The Laws of Motion

Isaac Newton (1642 - 1727) published Principia
Mathematica
in 1687. In this work, he proposed three “laws” of motion:
Law 1:
An object at rest tends to stay at rest and object
in motion tends to stay in motion.
Law 2:
For any object, FNET = F = ma
Law 3:
Forces occur in pairs: FA ,B = - FB ,A
(For every action there is an equal and opposite reaction.)
Force


We have an idea of what a force is from everyday life.
Physicist must be precise.
– A force is that which causes a body to accelerate.
(See Newton’s Second Law)
– A Force is a push or a pull.
– A Force has magnitude & direction (vector).
– Adding forces is like adding vectors
a
a
F1
FNET = ma
F1
FNET
F2
F2
Force …

We will consider two kinds of forces
 Contact force: (physical contact between objects)
– This is the most familiar kind.
– Kicking a ball
– I push on the desk.
– The ground pushes on the chair...

Field Forces (Non-Contact): (action through “empty”
space)
– Moon and Earth
– Gravity
– Electricity

On a microscopic level, all forces are non-contact
(Hun????)
Contact forces:

Objects in contact exert
forces.

Convention: Fa,b means
“the force acting on a due
to b”.
Fhead,thumb

So Fhead,thumb means “the
force on the head due to
the thumb”.
An Example
Consider the forces on an object undergoing
projectile motion
FB,E = - mB g
FB,E = - mB g
FE,B = mB g
FE,B = mB g
EARTH
Action at a distance

Gravity:
We’ll come back to this
later. Just remember you
don’t have to touch to push
Mass

We have an idea of what mass is from everyday
life.

Physicist must be precise.
– mass (for this class) is a quantity that specifies how
much inertia an object has.
(See Newton’s First Law)

Mass is an inherent property of an object.

Mass and weight are different quantities.
weight is a force.
Newton’s First Law
An object subject to no external forces moves with
a constant velocity if viewed from an inertial
reference frame.
– If no forces act, there is no acceleration.

The above statement can be thought of as the
definition of inertial reference frames.
– An IRF is a reference frame that is not accelerating
(or rotating) with respect to the “fixed stars”.
– If one IRF exists, infinitely many exist since they are
related by any arbitrary constant velocity vector!
Newton’s Second Law
The acceleration of an object is directly
proportional to the net force acting upon it. The
constant of proportionality is the mass.

Units
The units of force are kg m/s2 = Newtons (N)
The English unit of force is Pounds (lbs)

Ex: weight is a force W=mg
Mass vs. Weight

An astronaut on Earth kicks a bowling
Ouch!
ball and hurts his foot. A year later, the
same astronaut kicks a bowling ball on the
moon with the same force.
His foot hurts...
(a)
more
(b)
less
(c)
the same
Mass vs. Weight
 THE
SAME!!!!
If I stand on earth and hit
myself in the head with a
hammer it hurts. If I do
the same thing in space I
think you can imagine that
it would still hurt.
Ouch!
Mass vs. Weight Wow!
That’s light

However the weights of the bowling
ball and the astronaut are less:
W = m gMoon

gMoon < gEarth
Thus it would be easier for the
astronaut to pick up the bowling ball on
the Moon than on the Earth.
Newton’s Second Law...

Components of F = ma :
FX = maX
FY = maY

Suppose we know m and FX , we can solve for aX and apply the things
we learned about kinematics over the last few weeks:
1
x = x0 + v 0 x t + ax t 2
2
v x = v 0 x + ax t
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 50N in the i direction. If the box starts at rest,
what is its speed v after being pushed a distance d=10m ?
v=0
F
m
a
i
Force and acceleration

A force F acting on a mass m1 results in an acceleration a1.
The same force acting on a different mass m2 results in an
acceleration a2 = 2a1.
m1
F

a1
m2
F
a2 = 2a1
If m1 and m2 are glued together and the same force F acts
on this combination, what is the resulting acceleration?
F
(a)
2/3 a1
m1
m2
(b) 3/2 a1
a=?
(c)
3/4 a1
Newton’s Second Law
A constant force is exerted on a cart that is initially at rest on
an air table. The force acts for a short period of time and
gives the cart a certain final speed.
Force
Cart
Air Track
For a second shot, I can apply a force only half as large (I’m
getting tired). To reach the same final speed, for how long
must I apply the force ?
A) 4 x as long B) 2 x as long C) Same time
D) 1/2 as long E) 1/4 x as long
Talk about Quadratic and
linear relationships
1 2
x = x0 + v 0 x t + ax t
2
v x = v 0 x + ax t
Newton’s 3rd Law

For every action there is an equal and
opposite reaction
Newton’s Third Law
A fly gets smushed onto the windshield of a speeding bus.

The force exerted by the bus on the fly is,
A) greater than
B) the same as
C) less than
that exerted by the fly on the bus.