Transcript Unit 6 Momentum

Momentum
Momentum
• A measure of how hard it is to
stop a moving object.
• Related to both mass and
velocity.
• Possessed by all moving
objects.
Calculating Momentum
• For one particle
p = mv
• For a system of multiple
particles
P = pi = mivi
• Momentum is a vector!
Which has the most
momentum?
Impulse (J)
The product of an external
force and time, which results
in a change in momentum
J=Ft
J = p
•Units: N•s or kg•m/s
Impulse (J)
F(N)
3000
2000
area under curve
1000
0
0
1
2
3
4
t (ms)
Law of Conservation of
Momentum
pi = pf
If the resultant external force on
a system is zero, then the vector
sum of the momenta of the
objects will remain constant.
Collisions
• Collisions are governed by Newton's
laws.
• Newton’s Third Law tells us that the
force exerted by body A on body B in a
collision is equal and opposite to the
force exerted by body B on body A.
Collisions
During a collision, external forces are
ignored.
The time frame of the collision is very
short.
The forces are impulsive forces (high
force, short duration).
Collision Types
• Elastic (hard, no deformation)
– p is conserved, KE is conserved
• Inelastic (soft; deformation)
– p is conserved, KE is NOT conserved
• Perfectly Inelastic (stick together)
– p is conserved, KE is NOT conserved
Inelastic Collisions
• Only momentum is conserved.
• Kinetic Energy is not conserved.
• Some deformation of the object(s) will
occur.
• Perfectly inelastic collision is when the
objects actually “stick” together.
• Examples are: automobile crashes,
catching a ball, recoil of a gun.
Perfectly Inelastic Collision #1
An 80 kg roller skating grandma collides
inelastically with a 40 kg kid as shown.
What is their velocity after the collision?
Perfectly Inelastic Collisions #2
A train of mass
4M moving
5 km/hr couples
with a flatcar of
mass M at rest.
What is the
velocity of the
cars after they
couple?
Perfectly Inelastic Collisions #3
A 1.14-kg skateboard
is coasting along the
pavement at a speed
of 3.53 m/s, when a
1.1-kg cat drops from
a tree vertically down
on the skateboard.
What is the speed of
the skateboard-cat
combination?
Explosions and Recoil
• When an object separates suddenly, this is
the reverse of a perfectly inelastic
collision.
• Mathematically, it is handled just like an
ordinary inelastic collision.
• Momentum is conserved, kinetic energy is
not.
• Examples:
– Cannons, Guns, Explosions, Radioactive
decay.
Recoil Problem #1
A gun recoils when it is fired. The
recoil is the result of action-reaction
force pairs. Calculate the Recoil
velocity
Mass of Gun = 2.1 kg
Mass of Man= 75 kg
Mass of Bullet = 0.001 Kg
Muzzle Velocity = 450 m/s
Elastic Collisions
• Momentum and Kinetic Energy are
conserved.
• No deformation of objects occurs.
• Examples are: billiard balls (pool),
particle collisions,
marbles.
  
i
f
KE i  KE f
Elastic Collision #1
• A 7-g marble has a head-on collision
with a 3-g marble, initially at rest on a
playing surface. The speed of the 7-g
marble is reduced from 1.08 m/s to
0.75 m/s in the collision. What is the
speed of 3-g marble after the collision?
Elastic Collision #2
• A 4-gram object moving to the right with a
speed of 3.9 cm/s makes an elastic headon collision with a 6-gram object moving in
the opposite direction with a speed of 6.6
cm/s. Find the velocities after the collision.