FI1102 Elementary Physics IB

Impulse and Momentum

Khairul Basar

khairulbasar@itb.ac.id
Momentum
• Concept of Work and Energy can be used to analyze the
dynamics of an object.
• However, when including interaction between objects,
another important concept is needed
• It is another constant of motion: momentum
Momentum
• The linear momentum of an object is the product of the
object’s mass m and velocity .
Linear momentum is a
The total linear momentum of vector that points in the
a system of objects is the same direction as the
vector sum of the momenta of velocity.
the individual objects.

• In Newton’s second law, the mass m is assumed to be

constant.

The time rate of change of the linear momentum of a particle

is equal to the net force acting on the particle.

SI unit for momentum: kg.ms-1 = N.s

Impulse
• The impulse of a force is the product of the average force
and the time interval during which the force acts
Impulse is a vector that
points in the same direction
as the average force.
• Impulse as change in momentum

graphically, impulse can be obtained

from area under the curve F(t)
The Impulse-Momentum Theorem
• The impulse–momentum theorem states that when a net
average force acts on an object during a time
interval t , the impulse of this force is equal to the change in
momentum of the object
Example
• A baseball (m = 0.14 kg) has an initial velocity of = -38 m/s
as it approaches a bat. We have chosen the direction of
approach as the negative direction. The bat applies an
average force that is much larger than the weight of
the ball, and the ball departs from the bat with a final velocity
of = +58 m/s.
(a) Determine the impulse applied to the ball by the bat.
(b) Assuming that the time of contact is s,
find the average force exerted on the ball by the bat.
Example
• A model rocket is constructed with a motor that can provide a
total impulse of 29.0 N.s. The mass of the rocket is 0.175 kg.
What is the speed that this rocket achieves when launched
from rest? Neglect the effects of gravity and air resistance.

• A volleyball is spiked so that its incoming velocity of +4.0 m/s

is changed to an outgoing velocity of 21 m/s. The mass of
the volleyball is 0.35 kg. What impulse does the player apply
to the ball?
Example
• An estimated force–time curve for a baseball struck by a bat is
shown in Figure. From this curve, determine
(a) the impulse delivered to the ball,
(b) the average force exerted on the ball
(c) the peak force exerted on the ball.
The Principle of Conservation of Linear Momentum
• Consider a system consists
of two object. The objects
interact each other with
interaction forces which
obeys Newton’s third law

The interaction force is an internal force

in the system
The Principle of Conservation of Linear Momentum
• External forces are those forces that agents external to the
system exert on objects within the system.
• An isolated system is one for which the vector sum of the
external forces acting on the system is zero. If total external
forces equal zero States that the rate of
linear momentum equal
zero, which means
conservation of linear
momentum

The total momentum of

the system do not
change by time

• The total linear momentum of an isolated system remains

constant.
The Principle of Conservation of Linear Momentum
• For a two-body system, which is interact with the force
obeying action-reaction forces, the conservation of linear
momentum can be written as

• Example interaction: collision, explosion, nuclear reaction

Example
• High-speed stroboscopic photographs show that the head of a
golf club of mass 200 g is traveling at 55.0 m/s just before it
strikes a 46.0-g golf ball at rest on a tee. After the collision,
the club head travels (in the same direction) at 40.0 m/s. Find
the speed of the golf ball just after impact.
Energy during a collisions
• Usually when two macroscopic objects collide the total kinetic
energy after the collision is generally less than that before the
collision.
• Kinetic energy is lost mainly in two ways:
(1) converted into heat because of friction
(2) it is spent in creating permanent distortion or damage
• With very hard objects, the permanent distortion suffered
upon collision is much smaller than with softer objects and,
consequently, less kinetic energy is lost
• However conservation of (total) energy is always valid
Energy during a collision (elastic and inelastic
collision)
• An elastic collision is one in which the total kinetic energy of
the system after the collision is equal to the total kinetic
energy of the system before the collision. Kinetic energy
remains constant
• An inelastic collision is one in which the total kinetic energy
of the system is not the same before and after the collision.
• If the objects stick together after the collision, the collision is
said to be completely inelastic.
Example
• A ballistic pendulum can be used to
measure the speed of a projectile, such
as a bullet. The ballistic pendulum
shown in Figure consists of a stationary
2.50-kg block of wood suspended by a
wire of negligible mass. A 0.0100-kg
bullet is fired into the block, and the
block (with the bullet in it) swings to a
maximum height of 0.650 m above the
initial position. Find the speed with
which the bullet is fired, assuming that
air resistance is negligible.
What is the lost of kinetic energy
during the collision
Collisions in 2D
• Note that momentum is a vector quantity
Center of Mass
• In analyzing the dynamics of
many objects it is important
to discuss about “average
location” of total mass
• This “average location”
known as center of mass

• Many objects (more than 2)

Motion of Center of Mass
• If the objects move, the position of CM changes. The velocity
and acceleration of CM can be describe as

total external forces

act on system of
particles equal total
mass multiply by
acceleration of CM
total momentum of system of particles
equal total mass multiply by velocity of
CM
Motion of CM
• If no external forces act on the system of particles

• If no external forces act on the system of particles then the

center of mass of the system moves with constant velocity
Example
• A rocket is fired vertically upward. At the instant it reaches an
altitude of 1000 m and a speed of 300 m/s, it explodes into
three fragments having equal mass. One fragment continues
to move upward with a speed of 450 m/s following the
explosion. The second fragment has a speed of 240 m/s and is
moving east right after the explosion. What is the velocity of
the third fragment right after the explosion?

• Romeo (77.0 kg) entertains Juliet (55.0 kg) by playing his

guitar from the rear of their boat at rest in still water, 2.70 m
away from Juliet, who is in the front of the boat. After the
serenade, Juliet carefully moves to come to Romeo. How far
does the 80.0-kg boat move toward the shore it is facing?
Example
• Two particles are moving along the x axis. Particle 1 has a mass m1
and a velocity v1 = 14.6 m/s. Particle 2 has a mass m2 and a
velocity v2 = 26.1 m/s. The velocity of the center of mass of these
two particles is zero. Find the ratio m1/m2 of the masses of the
particles.
• The drawing shows a sulfur dioxide
molecule. It consists of two oxygen
atoms and a sulfur atom. A sulfur atom is
twice as massive as an oxygen atom.
Using this information and the data
provided in the drawing, find (a) the x
coordinate and (b) the y coordinate of
the center of mass of the sulfur dioxide
molecule. Express your answers in
nanometers (1 nm = 10-9 m).
References
• John D. Cutnell, Kenneth W. Johnson, David Young, Shane
Stadler, PHYSICS 10Th EDITION, Wiley
• Raymond A. Serway, John W. Jewett, PHYSICS FOR SCIENTIST
AND ENGINEERS, 2006
• David Halliday, Robert Resnick, Jearl Walker, FUNDAMENTALS
OF PHYSICS 10TH EDITION, 2013