Buoyancy

Momentum/Impulse Angular Momentum

Torque

Newton’s Third Law Problem:

How can a horse pull a cart if the cart is pulling back on the horse with an equal but opposite force?

NO!!!

Aren’t these “balanced forces” resulting in no acceleration?

Newton’s Third Law

forces are equal and opposite but act on different objects

they are not “balanced forces”

the movement of the horse depends on the forces acting on the horse

Explanation:

Rocket Propulsion In a rocket engine, burning fuel produces hot gases.

The rocket engine exerts a force on these gases and causes them to escape out the back of the rocket.

By Newton’s third law, the

gases exert a force on the

rocket and push it forward.

Momentum A moving object has a property called momentum that

is related to how much force is needed to change its motion.

The momentum of an object is the product of its mass and velocity

Momentum is given the symbol p and can be calculated with the following equation:

Momentum Momentum

quantity of motion p = mv

p: momentum (kg·m/s) m: mass (kg) v: velocity (m/s) m

p

v

• Use the unit kg·m/s

Force and Changing Momentum By combining these two relationships, Newton’s

second law can be written in this way:

In this equation mvf is the final momentum and mvi is the initial momentum

Newton’s Third Law Action-Reaction Pairs

Both objects accelerate.

The amount of acceleration depends on the mass of the object.

aF

m

Small mass more acceleration

Large mass less acceleration

Conservation of Momentum

Law of Conservation of Momentum

The total momentum in a group of objects doesn’t change unless outside forces act on the objects.

pbefore = pafter

Conservation of Momentum

Elastic Collision

KE is conserved

Inelastic Collision KE is not conserved

Momentum Find the momentum of a bumper car if it has a

total mass of 280 kg and a velocity of 3.2 m/s.

GIVEN:

p = ?

m = 280 kg

v = 3.2 m/s

WORK:

m

p

v

Momentum The momentum of a second bumper car is 675

kg·m/s. What is its velocity if its total mass is 300 kg?

GIVEN:

p = 675 kg·m/s

m = 300 kg

v = ?

WORK:

m

p

v

Conservation of Momentum A 5-kg cart traveling at 1.2 m/s strikes a stationary

2-kg cart and they connect. Find their speed after the collision.

BEFORE

Cart 1: m = 5 kg v = 4.2 m/s

Cart 2 : m = 2 kg v = 0 m/s

AFTER

Cart 1 + 2: m = 7 kg v = ?

p = 21 kg·m/s

p = 0

pbefore = 21 kg·m/s pafter = 21 kg·m/s

m

p

v v = p ÷ m v = (21 kg·m/s) ÷ (7 kg) v = 3 m/s

Impulse = Momentum

F = ma

3-15

Angular Momentum L = mvr

L = angular momentum, m = mass, v = velocity, and r = distance to center of motion

L1 = L2

m1v1r1 = m2v2r2

Section 3.6

3-16

Angular Momentum

Mass (m) is constant. As r changes so must v. When r decreases, v

must increase so that m1v1r1 = m2v2r2 Section 3.6

3-17

Torque

Torque is a twisting action that produces rotational motion or a change in rotational motion.

Torque = rF

Section 3.6

Copyright © Houghton Mifflin

Company. All rights reserved. 3-18

Conservation of Angular Momentum

Rotors on large helicopters rotate in the opposite direction

Section 3.6

3-19

Conservation of Angular Momentum Figure Skater – she/he starts the spin with arms out at

one angular velocity. Simply by pulling the arms in the skater spins faster, since the average radial distance of the mass decreases.

m1v1r1 = m2v2r2

m is constant; r decreases;

Therefore v increases

Section 3.6

3-20

Buoyancy Upward force exerted by a fluid

Archimedes’ principle: An object immersed wholly or partially in a fluid experiences a buoyant force equal in magnitude to the weight of the volume of fluid that is displaced.

An object will float in a fluid if its average density is less than the density of the fluid

An object will sink it is average density is greater than the density of the fluid.

Section 3.6

3-21

Discussion People can easily float in the Great Salt Lake in Utah.

Why is that?

Section 3.6

3-22

Chapter 3 - Important Equations

F = ma (2nd Law) or w = mg (for weight)

F1 = -F2 (3rd Law)

F = (Gm1m2)/r2 (Law of Gravitation)

G = 6.67 x 10-11 N-m2/kg2 (gravitational constant)

g = GM/r2 (acc. of gravity, M=mass of sph. object)

r = mv (linear momentum)

Pf = Pi (conservation of linear momentum)

L = mvr (angular momentum)

L1= m1v1r1=L2 = m2v2r2 (Cons. of ang. Mom.)

Review