AP Physics unit 4 linear momentum

Linear momentum

a vector quantity, magnitude & points in the same direction as velocity

P=

mv

p=

kg*m/s

9000kg bus moving at 16m/s

1.44 ×10^5 kg*m/s

A bus is at rest while a truck is moving. Which vehicle has more inertia?

Both vehicles have inertia because they both have mass

A bus is at rest while a truck is moving. Which vehicle has more momentum?

The truck. The bus’s velocity is 0, which means its momentum is 0.

change in momentum equation

The change in momentum = impulse,

change in p = p_f - p_i or change in p = F / change in t

F = is the force applied and

change in t = is the time duration of the force.

A 1kg teddy bear moving a 4m/s lands on the floor. What is its change in momentum?

Initial velocity is -4m/s (moving downwards) and final velocity is 0m/s because it is at rest. 0 - (-4) = 4 kg*m/s

A 1kg ball bounces on the floor at 4m/s without losing speed. What is its change in momentum?

The initial velocity is -4m/s (downwards) and the final velocity is 4m/s (upwards). The change in momentum is 4 - (-4) = 8 kg*m/s.

Total momentum of a system is…

the VECTOR SUM of all of the individual objects. Can be negative, positive or 0.

KE = ?

p²/2m = (mv)²/2m = mV²/2 = 1/2mv² OR
pv/2 = (mv)(v)/2 = mv²/2

26 degrees to the x axis is…

26 degrees north of east

relationship between newton’s second law & impulse

Fnet = ma = m(v/t) = (mv/t) = (mv/t) = p/t, where impulse is the change in momentum.

impulse real life application

crumble zone of a car
bike helmet

crumble zone increases _______ and therefore decreases the ________ acting on the object,

time
force

Mechanical energy

ME = KE + PE
kinetic energy & potential energy

Mechanical energy of a closed system…

remains constant, as energy is conserved in the absence of external forces.

impulse is

the change in momentum of an object

force over time

elastic collision

total kinetic energy and momentum are conserved
example: two billiard balls collide on a table

what is a billiard ball?

ball used to play pool

nearly elastic collision

when two separate bodies meet and energy is lost to heat or sound
example: kicking a soccer ball

perfectly inelastic

when two separate objects becomes one mass
example: a car crash

force between two collisions in N equation

(mv_f - mv_i)/change in time

20N of force applied over 5 seconds

F*T
100

given initial and final momentum

you can find impulse:
final momentum - initial momentum

why are there arrows above velocity, momentum, and impulse?

because they are a vector, with direction and magnitude,

equation for elastic collisions

is reversible

begins with 1/2mv²
v_1i + v_1f = v_2f + v_2i

ball a: initial and final momentum
ball b: only initial momentum
what is final momentum of ball b?

v_1i + v_1f = v_2f + v_2i

nearly elastic collision equation

momentum changes because some is lost due to heat
m₁v_1i + m₂v_2i = m₁v_1f + m₂v_2f

perfectly inelastic collision

m₁v_1i + m₂v_2i = (m1 + m2)v_f