Transcript Mass and Acceleration

Mass and Acceleration
Mass

Matter has substance.
• Solids, liquids or gases
• Subatomic particles
• Planets and stars



We feel the weight of different objects.
We will see that weight is not mass, but mass can
have weight.
Mass measures the amount of matter in an object.
Mass Units

Mass is measured in kilograms.
• 1 kg = 1000 g
• 1 atomic mass unit (about the mass of one hydrogen atom) =
1.66 x 10-27 kg

Mass is a scalar.
• Mass times a vector gives another vector


• For instance, momentum: p  mv
Force and Acceleration

With force there is acceleration.

The amount of acceleration
depends on the mass.

 F
a
m

The direction of the force and
acceleration are the same.


F  ma
Force Units

Force is mass times acceleration.

The dimensions of force are M(L/T2).

In SI units a newton (N) = 1 kg m / s2.
Law of Action
2


The change in motion is proportional to the force and
the change is made in the same direction as the
force.
A force gives rise to action by acceleration.
Force = mass x acceleration (Newton’s second law).
Initial
velocity
Final
velocity:
changed by
the force
Rocket:
has mass
Force:
becomes
acceleration
Accelerating a Mass

A loaded 747 jet has a
mass of 3.6 x 106 kg
and four engines.

The distance and final velocity
are used to get the acceleration.
2

v  v0   x
v  v0 
x
v
2a
It takes 1700 m at
constant thrust (force) to
reach a takeoff speed of
86 m/s (310 km/h).

What is the force per
engine?

0
a
0
v2

2a
The acceleration and mass give
the force.
mv2
F  ma 
2x
F = (7.8 x 106 N)/4 = 2.0 x 106 N.
Vector Force

A 1000 kg satellite in
space is moving at 5 km/s
when a rocket fires with a
thrust of 5 x 103 N at 60°
to the direction of motion.
The rocket fires for 1
minute. Where does it
move after firing?

x


The force and acceleration are
vectors.
Pick x in the direction of initial
motion.

 F F
F
a   (cos  )iˆ  (sin  ) ˆj
m m
m

The new velocity is
  
Ft
Ft
v  at  v0  ( cos  v0 )iˆ  ( sin  ) ˆj
m
m

vx = 5.1 km/s, vy = 0.26 km/s.
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