Mass and Motion
Mass

Matter has substance.
• Solids, liquids or gases
• Subatomic particles
• Planets and stars


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

© R. Rathe, NIST
Pounds measure weight (a
force) not mass.
Force and Acceleration

With force there is acceleration.

The amount of acceleration
depends on the mass.

Mass is a scalar.
• Mass times a vector gives another
vector.
• The direction of the force and
acceleration are the same.

 F
a
m


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.
Second Law: Law of Acceleration
2


The change in motion is proportional to the net force
and the change is made in the same direction as the
net force.
Net force gives rise to acceleration.
Force = mass x acceleration (Newton’s second law).
Initial
velocity
Final
velocity:
changed by
the force
Rocket:
has mass
Force:
becomes
acceleration
Vector Force


A 1000 kg satellite in
space is moving at 5.0
km/s when a rocket fires
with a thrust of 5.0 x 103 N
at 60° to the direction of
motion.
The rocket fires for 1
minute. Where does it
move after firing?
F = 5000 N
q = 60
x

Identify the quantities in the
problem:
•
•
•
•

Mass, m = 1000 kg
Initial velocity, v0 = 5 x 103 m/s
Force, F = 5 x 103 N at 60°
Time, t = 1 min = 60 s
Force and velocity are vectors
• Pick x in the direction of initial
motion: vx = v0 .
• Fx = F cosq
• Fy = F sinq
Change in Velocity


A 1000 kg satellite in
space is moving at 5.0
km/s when a rocket fires
with a thrust of 5.0 x 103 N
at 60° to the direction of
motion.
The rocket fires for 1
minute. Where does it
move after firing?
v

The force gives acceleration.
• ax = Fx /m = (F/m) cosq
• ay = Fy /m = (F/m) sinq

The change in velocity is due to
this acceleration.
• vx = v0 + ax Dt
•
= v0 + (F t / m) cosq
• vy = ay Dt = (F t / m) sinq

The final velocity is
• vx = 5200 m/s = 5.2 km/s
• vy = 260 m/s = 0.26 km/s.
v0
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