IB Physics 12

Mr. JeanSeptember 15th, 2015

The plan:• Video clip of the day

– https://www.youtube.com/watch?v=QcdlGjAP0xs

• Conical Pendulums Investigation• Banked turns with Friction

New IA Criteria:

Conical Pendulum:• http://www.youtube.com/watch?v=5C4RJl

FABic

• http://www.youtube.com/watch?v=h-aStiXBaus

Conical Pendulum Motion:

Conical Pendulum Motion:• T = Tension in Newton's

• T cos θ is balanced by the object's weight, mg.

– Thus T * cos(θ) = mg

Conical Pendulum Motion:• T sin θ that is the unbalanced central force

that is supplying the centripetal force necessary to keep the block moving in its circular path:

– Thus T sin θ = Fc = mac.

– Thus T sin θ = Fc = (mv2) r

• How long does it take for the object to complete one complete circle?

• HINT: v = 2 π r f

Banked Turns with Friction:

Important assumptions for Banked turns with Friction:

• Fnet = Fc = Ff + Fg

• Let’s look at the frictional force first:1. Ff = μ * Fn

2. Ff = μ * Fg * cos (10)

• Ff = μmg cos(Θ)

Let’s look at the gravitational force:1. Fg = Fg * sin(10)

• Ff = μmg sin(10)

Fnet = Fc = Ff + Fg

Banked Curves (with friction)• The Problem: A car with the mass of

1500kg is traveling in uniform circular motion along a circular curve with radius of 50 meters on a road that is banked at 10 degrees. The coefficient of friction is 0.4.

• What is the maximum velocity in which this car can take the curve?

• Finding the sum of all center seeking forces. (Use previous diagram to highlight forces)

Frictional Force:

Gravitational Force:

Centripetal Force:

Chapter #5• If you are wondering where we are:

• Giancoli– P. 117 to 122 Gravitational Constant– P. 122 to 127 Newton & Kepler’s Synthesis

Newton’s Law of Universal Gravitation:

• Fg = force of gravity in newtons (N)

• m1 = first mass in kilograms (Kg)

• m2 = second mass in kilograms (Kg)• r = distance between centers of mass in meters• G = Universal Gravity Constant (***next slide

for units***)

Universal Gravitational Constant:

How to masses act on each other:

• In the case of the Earth-Moon system, the moon is accelerating towards the Earth.

• The moon has a tangential component to its velocity. So it keeps moving in a circle around the Earth.

Kepler’s Empirical Equations:• Johannes Kepler’s (1571 – 1630) was the

famous German astronomer who laid the framework for understanding planetary motion.

Kepler’s First Law:• Planets move in elliptical orbits around the

sun. • As an average these orbits are nearly

circular.

Kepler’s Second Law:• An imaginary line between the Sun and a

planet sweeps out equal areas in equal time intervals.

• K = is a CONSTANT for all planet’s as they travel around the sun .

• r = average distance from sun (m)

• T = period of planet’s revolution around the sun (seconds)

Kepler’s Third Law:

Kepler’s Third Law:

• The squared product of the period for a planet’s revolution around the Sun and the cube of the average distance from the Sun is a constant and the same for all planets.

• r = average distance from sun (m)• T = period of planet’s revolution around

the sun (s)

Satellites in space:

• A satellite in space moves around a heavy body. To keep the satellite from smashing back into the Earth (or planet it is orbiting), scientists set the force of gravity equal to the centripetal force.

• Fg = Fc

Example Question:• You find yourself in space. In fact you are

walking on a large asteroid. Your mass is 70kg, the asteroid has a mass of 8.0 x 105kg and the radius between the two centers of mass is 80 meters.

• What is your weight on the asteroid?

• m1 = 70 (kg)

• m2 = 8.0 x 105 (kg) • r = 80 meters (m)

This weekend: • Please read Giancoli Chapter #5

– P. 117 to 122 Gravitational Constant– P. 122 to 127 Newton & Kepler’s Synthesis