Impulse, Momentum and Collisions

AP Physics B

IMPULSE AND MOMENTUM The impulse F t is a vector quantity equal in magnitude to the product of the force and the time interval in which it acts. Its direction is the same as that of the force.

F t Units: newton.second (N.s)

The momentum p of a particle is a vector quantity equal in magnitude to the product of its mass m and its velocity v.

p = m v Units: (kg.m/s)

7. A 3 N baseball moving toward the batter with a velocity of 15 m/s is struck with a bat which causes it to move in a reversed direction with a velocity of 30 m/s. Find the impulse and the average force exerted on the ball if the bat is in contact with the ball for 0.01 s.

Fg = 3 N

v0 = - 15 m/s

vf = 30 m/s

t = 0.01 s

30.31 kg

9.8gFmg

m = 0.31 kgv0 = - 15 m/s

vf = 30 m/s

t = 0.01 s

FΔt = mΔv =m(vf - v0)

=0.31(30-(-15)) = 13.95 Ns

0( )fm v vF

t

0.31(30 ( 15))

0.01

= 1395 N

CONSERVATION OF LINEAR MOMENTUM According to the law of conservation of linear momentum, when the vector sum of the external forces that act on a system of bodies equals zero, the total linear momentum of the system remains constant no matter what momentum changes occur within the system.

Although interactions within the system may change the distribution of the total momentum among the various bodies in the system, the total momentum does not change. Such interactions can give rise to two general classes of events:

a. explosions, in which an original single body flies apart into separate bodies

b. collisions, in which two or more bodies collide and either stick together or move apart, in each case with a redistribution of the original linear momentum.

For two objects interacting with one another, the conservation of momentum can be expressed as:

 v1 and v2 are initial velocities, and are final

velocities

m v m v m v m v1 1 2 2 1 1 2 2 ' '

v1' v2

'

ELASTIC AND INELASTIC COLLISIONS If the Kinetic energy remains constant in a collision, the collision is said to be completely elastic. If the colliding bodies stick together and move off as a unit afterward, the collision is said to be completely inelastic. In inelastic collisions only the momentum is conserved.

In elastic collisions no permanentdeformation occurs; objects elasticallyrebound from each other.In head-on elastic collisions betweenequal masses,velocities are exchanged.

Inelastic collisions are characterized by objects sticking together and permanent deformation.

8. A 12-g bullet is fired into a 2-kg block of wood suspended from a cord. The impact of the bullet causes the block to swing 10-cm above its original level. Find the velocity of the bullet as it strikes the block.

m1 = 0.012 g

m2= 2 kg

h = 0.1 m

KE0 = PEf

m1v1= ( m1+m2 )v'

m1 = 0.012 g

m2= 2 kg

h = 0.1 m

KE0 = PEf

m1v1= ( m1+m2 )v'

21 2 1 2

1

2m m v m m gh

2v gh

2(9.8)(0.1) = 1.4 m/s

1 21

1

( ) 'm m vv

m

(0.012 2)1.4

0.012

= 234.7 m/s