Transcript Lecture 8: Forces & The Laws of Motion

Lecture 14:
Collisions & Momentum
Questions of Yesterday
A 50-kg object is traveling with a speed of 100 m/s and a 100-kg
object is traveling at a speed of 50 m/s.
1a) Which object has more momentum?
1b) Which object has more kinetic energy?
a) 50-kg object
b) 100-kg object
c) they are equal
2) Would a head-on collision between two cars be more damaging to
the occupants if the cars stuck together or if the cars rebounded upon
impact?
a) if the cars stuck together
b) if the cars rebounded
c) both collisions would be equally damaging
d) it depends on the relative masses of the cars
Collisions
MOMENTUM of an object is CONSERVED if Fnet = 0
What happens in a collision?
If no net external force acts on a system of objects…
The total momentum of the system remains constant in time
pi = pf
mvi1 + mvi2 = mvf1 + mvf2
Kinetic Energy Conservation
Is the total kinetic energy conserved in a collision?
Is it possible to lose kinetic energy? How?
Kinetic Energy
Sound, Heat,
Deformation,
Kinetic Energy
Kinetic energy is generally NOT conserved in a collision
Types of Collisions
INELASTIC Collisions
ELASTIC Collisions
Momentum is Conserved
Momentum is Conserved
Kinetic Energy is NOT Conserved Kinetic Energy IS Conserved
pi = pf
KEi > KEf
pi = pf
KEi = KEf
PERFECTY INELASTIC Collisions
Momentum is Conserved
Kinetic Energy is NOT Conserved
Objects stick together
vf1 = vf2
Perfectly Inelastic Collisions
Momentum is Conserved
Kinetic Energy is NOT Conserved
Objects stick together
vf1 = vf2
pi1 = m1vi1
pi2 = m2vi2
Perfectly Inelastic Collisions
Momentum is Conserved
Kinetic Energy is NOT Conserved
Objects stick together
vf1 = vf2
vf
pi1 = m1vi1
pi2 = m2vi2
pi = p f
Perfectly Inelastic Collisions
pi = p f
m1vi1 + m2vi2 = (m1 + m2)vf
vf
pi1 = m1vi1
vf =
m1vi1 + m2vi2
(m1 + m2)
pi2 = m2vi2
Perfectly Inelastic Collisions
pi = p f
m1vi1 + m2vi2 = (m1 + m2)vf
Vector Equations!
Velocities must be in same direction!!
Equations for 1D collisions!
In general: pix
vf =
= pfx AND piy = pfy
m1vi1 + m2vi2
(m1 + m2)
Perfectly Inelastic Collisions
How much Kinetic Energy is lost in a
perfectly inelastic collision?
pi = pf
m1vi1 + m2vi2 = (m1 + m2)vf
DKE = KEf - KEi
KEf =
(1/2)(m1 + m2)vf2
KEi = KEi1 + KEi2 =
(1/2)m1vi12 + (1/2)m2vi22
Perfectly Inelastic Collisions
A 10.0 g bullet is fired horizontally into a 100-g wooden block that
is initially at rest on a frictionless horizontal surface and
connected to a spring having spring constant 100 N/m. The bullet
becomes embedded in the block.
If the bullet-block system compresses the spring by a maximum of
100 cm..
What was the initial speed of the bullet at impact with the block?
Elastic Collisions
Momentum is Conserved: pi
= pf
Kinetic Energy IS Conserved: KEi = KEf
m1vi1 + m2vi2 = m1vf1 + m2vf2
(1/2)m1vi12 + (1/2)m2vi22 = (1/2)m1vf12 + (1/2)m2vf22
2 equations -> Can solve for 2 unknown quantities
How do the final velocities of the objects compare with
the initial velocities?
vi1 - vi2 = -(vf1 - vf2)
Elastic Collisions
A 10-kg object moving to the right at 20.0 m/s makes an elastic
head-on collision with a 20.0-kg object moving in the opposite
direction at 30.0 m/s.
What is the velocity of each object after the collision?
What is the change in the kinetic energy of each object?
What is the change in kinetic energy of the system?
2D (Glancing) Collisions
Momentum is a VECTOR
In 2 Dimensional collisions…
momentum in EACH direction is conserved!
x-component: m1vi1x + m2vi2x = m1vf1x + m2vf2x
y-component: m1vi1y + m2vi2y = m1vf1y + m2vf2y
Kinetic Energy is a SCALAR quantity
Only the speeds of the objects are important
(1/2)m1vi12 + (1/2)m2vi22 = (1/2)m1vf12 + (1/2)m2vf22
2 Dimensional Collisions
A 0.5 kg puck, initially at rest on a frictionless horizontal surface,
is struck by a 0.25-kg puck that is initially moving along the x-axis
with a velocity of 2.0 m/s. After the collision the 0.25-kg puck has
a speed of 1.0 m/s at an angle of 30o to the positive x-axis.
What is the velocity of the 0.5-kg puck after the collision?
Is this collision elastic?
If not, what is the fraction of kinetic energy lost in the collision?
Questions of the Day
1) A piece of clay traveling north with speed v collides perfectly
inelastically with an identical piece of clay traveling east with
speed v. What direction does the resultant piece of clay travel?
a) north
b) east
c) 45o N of E
d) 45o S of W
2) If Ball 1, moving with an initial speed v, collides with Ball 2 which is
initially at rest, which scenario is not possible following the
collision?
a) Both balls are moving
b) Ball 1 is at rest and Ball 2 is moving
c) Ball 2 is at rest and Ball 1 is moving
d) Both balls are at rest