PHYSICS UNIT 4: ENERGY & MOMENTUM

WORK & KINETIC ENERGY Work, W: using a force, F, to

displace an object a distance, d unit: Joule (1 J = 1 Nm)

W = Fd W < Fd W = 0

WORK & KINETIC ENERGY Work done by any force: W = Fd

can be positive, negative, or zero

Ex: sled sliding down a hillgravity does positive workfriction does negative worknormal force does no work

d

WORK & KINETIC ENERGY Power, P: the time rate at which work

is done P = W/t unit: Watt, W (1 W = 1 J/s = 1 Nm/s) english unit: horsepower, hp (1.00 hp =

746 W) What happens to power with twice work? What happens to power with ½ the time?

WORK & KINETIC ENERGY Kinetic Energy, K: energy of motion

energy: the ability to do work K = ½mv2 unit: Joule scalar quantity – amount only –

direction doesn’t matter If velocity doubles what happens to K?

WORK & KINETIC ENERGY

WORK & KINETIC ENERGY Work – Kinetic Energy Theorem:

Work done on an object is equal to the total change in kinetic energy of the object Wnet = Kf – Ki

Fnetd = ½mvf2 – ½mvi

2

WORK & KINETIC ENERGY net work determines the change in an object’s

motion positive work = increase in kinetic energy (speed

up) Ex: throwing a ball

negative work = decrease in kinetic energy (slow down)

Ex: catching a ball zero work = no change in kinetic energy

Ex: weightlifting

POTENTIAL ENERGY & CONSERVATION

Potential Energy, PE: stored energy gravitational: energy of position due to

gravity force Grav. PE = mgh

h: height - measured from origin (reference point)

unit: Joule, J can be positive, zero, or negative

depending on choice of origin

POTENTIAL ENERGY & CONSERVATION

Potential Energy, PEspring: energy of position elastic: energy of position due to elastic

force PEspring = ½kx2

k: spring constant, x: stretch/compress distance

unit: Joule can only be positive or zero

Energy 101

POTENTIAL ENERGY & CONSERVATION

Conservation of Mechanical Energy: a system's total mechanical energy (K+U) stays constant if there is no friction Ki + Ui = Kf + Uf if there is friction, some K will be turned

into other energy forms - heat, sound, etc. mechanical energy is not conserved total energy is still conserved

PHYSICS

UNIT 4: ENERGY & MOMENTUM

MOMENTUM & IMPULSE Impulse, J: change in momentum

produced by a force J = change in P, = Ft unit: kg m/s

MOMENTUM & IMPULSE Bouncing vs. Sticking in an impact

ex: a 1000 kg car going +10 m/s hits a wall J = pf-pi

sticking: pi = +10,000 kgm/s, pf = 0 J = –10,000 kgm/s bouncing: pi = +10,000 kgm/s, pf = –

10,000 kgm/s J = –20,000 kgm/s bouncing off at impact has up to twice the

force of sticking

MOMENTUM & IMPULSE angular momentum, L: amount of

“rotation” an object has L = I

: angular velocity, rad/s I: rotational inertia, resistance to rotation (due to mass and its distribution - same mass further from center has more I), kgm2

unit: kgm2/s

MOMENTUM & IMPULSE Law of Conservation of

Momentum: total momentum of a system of objects is constant if no outside forces act mivi = mfvf if mass

increases, velocity decreases (and vice versa)

MOMENTUM & IMPULSE Law Conservation of Angular

Momentum: total angular momentum of a system of objects is constant if no outside torques act Iii= Iff

MOMENTUM & IMPULSE

if rotational inertia increases, angular velocity decreases (and vice versa)

PHYSICS

UNIT 4: ENERGY & MOMENTUM

QUIZ 4.4 A 2000 kg car going 30 m/s hits a

brick wall and comes to rest. (a) What is the car’s initial momentum? (b) What is the car’s final momentum? (c) What impulse does the wall give to the car? (d) If the impact takes 0.5 seconds, what force is exerted on the car?

60,000 kgm/s

-120,000 N

-60,000 kgm/s0 kgm/s

PHYSICS

UNIT 4: ENERGY & MOMENTUM

COLLISIONS inelastic collision: objects collide

and stick (or collide and deform)

momentum is conserved, kinetic energy is not

m1v1 + m2v2 = Mv3 (M = m1 + m2)

be sure to include + or – for velocity’s direction

COLLISIONS Ex: An 8000 kg truck going 10 m/s

N collides with a 1000 kg car going 5 m/s S and their bumpers lock. How fast are the truck & car going after the collision?

COLLISIONS propulsion or explosion: total initial

momentum is zero; separated pieces receive equal & opposite momentums, so total final momentum is zero

0 = m1v3 + m2v4 or m1v3 = –m2v4

ex: rocket propulsion, gun recoil

COLLISIONS Ex: A 4 kg rifle fires a 0.050 kg

bullet, giving the bullet a final velocity of 300 m/s east. What is the recoil velocity of the rifle?

COLLISIONS elastic collision: objects collide and

bounce off with no loss of energy

santa elastic.IP

both momentum and kinetic energy are conserved

m1v1 + m2v2 = m1v3 + m2v4

½m1v12 + ½m2v2

2 = ½m1v32 +

½m2v42

QUIZ 4.4 A 1 kg soccer ball going 8 m/s hits a

player’s 4 kg head (which is not moving before the hit). The soccer ball bounces back in the opposite direction (-) at 8 m/s. There is no loss of energy. (a) What kind of collision is this? (b) What conservation of momentum equation applies? (c) What is the velocity of the player’s head after the collision?

PHYSICS

UNIT 4: ENERGY & MOMENTUM

UNIT 4 REVIEW Ki + Ui = Kf + Uf

Ug = mgh Ue = ½kx2

K = ½mv2

W = Fdcos Wnet = Kf – Ki

P = W/t 1.00 hp = 746 W

p = mv J = pf – pi = Ft

L = I Iii = Iff

m1v3 = –m2v4

m1v1 + m2v2 = Mv3

m1v1 + m2v2 = m1v3 + m2v4