Transcript PHY081 – Lecture 3

PPMF102– Lecture 3
Linear Momentum
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Linear momentum (p)
Linear momentum = mass x velocity
p = mv
 SI unit: kgm/s
 It is a vector quantity.
 The direction of p is the same as the
direction of v.
 A body at rest has zero momentum.

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Illustrations
1. What is the momentum of a 5.0 kg
body that moves at 10 m/s?
 p = mv
= (5.0)(10)
= 50 kg m/s
 2. What is the momentum of a 1500 kg
car moving at 110 km/h?

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Conservation of linear momentum

The total momentum of an isolated
system of bodies remains constant
Total momentum before collision = Total
momentum after collision
 pbefore = pafter


m1u1 + m2u2
=
m1v1 + m2v2
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Momentum is
conserved in
collisions
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Eg. 1 Railroad cars collide
momentum conserved
A boxcar traveling 24.0 m/s strikes a second car
initially at rest. The two stick together after the
collision. If the two boxcars have the same mass,
what is their final velocity?
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Elastic collision
•Total
momentum is conserved.
•pbefore = pafter
•In
an elastic collision, total kinetic energy is
also conserved.
•Total
kinetic energy before collision = Total
kinetic energy after collision
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Inelastic collision
Total momentum is conserved.
 pbefore = pafter

In an inelastic collision, some kinetic energy is
lost.
 Total kinetic energy before collision > Total
kinetic energy after collision
 With inelastic collisions, some of the initial kinetic
energy is lost to thermal or potential energy.
 In a completely inelastic collision, the two objects
stick together after the collision.

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Inelastic Collisions
Example 2: Ballistic pendulum.
The ballistic pendulum is a device
used to measure the speed of a
projectile, such as a bullet. The
projectile, of mass m, is fired into a
large block of mass M, which is
suspended like a pendulum. As a
result of the collision, the pendulum
and projectile together swing up to a
maximum height h. Determine the
relationship between the initial
horizontal speed of the projectile, v,
and the maximum height h.
Eg. 2

A 10-kg wheelbarrow moves with a
constant speed of 2.0 m/s. An additional
6.0 kg load is dropped into the
wheelbarrow. What then will be its speed?
Assume no friction.
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Eg. 3

A 0.012-kg bullet traveling 190 m/s hits a
2.0-kg block of wood and embedded in it.
If the block is stationary on a frictionless
surface when hit, how fast does it move
together with the bullet?
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Impulse
Impulse = change in linear momentum
J = p = mv – mu
Since the time involved in a collision is
usually short, average force can be used.
Impulse = Average Force x time
J = Ft
Unit for impulse is kgm/s; same unit as
momentum
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