Homework #2  Due today at 6PM  Covers Chapters 1, 2, and 3  Estimated time to complete: 1 hour 10 minutes (so don’t wait until the last minute!)  Read chapters, review notes before starting  Make sure you have finished all parts of all questions!  Due today at 6PM  Covers Chapters 1, 2, and 3  Estimated time to complete: 1 hour 10 minutes (so don’t wait until the last minute!)  Read chapters, review notes before starting  Make sure you have finished all parts of all questions!

Homework #3  Due Thursday, September 17, 6PM  Covers Chapters 4 and 5  Estimated time to complete: 1 hour (so don’t wait until the last minute!)  Read chapters, review notes before starting  Due Thursday, September 17, 6PM  Covers Chapters 4 and 5  Estimated time to complete: 1 hour (so don’t wait until the last minute!)  Read chapters, review notes before starting

Office Hours Tomorrow 11:00am-noon (instead of the usual 10:00am-noon)

 Realized the same physical laws that operate on Earth also operate in the heavens  one universe  Discovered laws of motion and gravity  Much more: experiments with light, first reflecting telescope, calculus…  Realized the same physical laws that operate on Earth also operate in the heavens  one universe  Discovered laws of motion and gravity  Much more: experiments with light, first reflecting telescope, calculus… Sir Isaac Newton (1642–1727) How did Newton change our view of the universe?

Not bad!  1665: develops calculus (for gravitation, tides)  1667: laws of optics  1670ish: laws of gravitation This would be like one person discovering bacteria, penicillin, and DNA in the same 5-7 year period.  1665: develops calculus (for gravitation, tides)  1667: laws of optics  1670ish: laws of gravitation This would be like one person discovering bacteria, penicillin, and DNA in the same 5-7 year period.

What are Newton’s three laws of motion? Newton’s first law of motion: An object moves at constant velocity unless a net force acts to change its speed or direction. In other words, objects in motion stay in motion, objects at rest stay at rest – unless a force acts on it. Newton’s first law of motion: An object moves at constant velocity unless a net force acts to change its speed or direction. In other words, objects in motion stay in motion, objects at rest stay at rest – unless a force acts on it.

Newton’s second law of motion: Force = mass * acceleration

Newton’s third law of motion: For every force, there is always an equal and opposite reaction force. The rocket moves upward not because the exhaust pushes on the ground beneath it, but to obey Newton’s third law (and to conserve linear momentum).

Is the force that Earth exerts on you larger, smaller, or the same as the force you exert on it? A) Earth exerts a larger force on you. B) You exert a larger force on Earth. C) Earth and you exert equal and opposite forces on each other. A) Earth exerts a larger force on you. B) You exert a larger force on Earth. C) Earth and you exert equal and opposite forces on each other.

Is the force that Earth exerts on you larger, smaller, or the same as the force you exert on it? A) Earth exerts a larger force on you. B) You exert a larger force on Earth. C) Earth and you exert equal and opposite forces on each other. A) Earth exerts a larger force on you. B) You exert a larger force on Earth. C) Earth and you exert equal and opposite forces on each other. For every force, there is an equal and opposite force. However, you and the Earth experience very different accelerations, since you and the Earth have very different masses.

Basic Types of Energy  Kinetic (motion)  Radiative (light)  Potential (stored)  Kinetic (motion)  Radiative (light)  Potential (stored) Conservation of Energy: Energy can change type, but cannot be created or destroyed. Important concept!

1) Kinetic Energy A) Energy of motion (large, macroscopic objects) B) Thermal energy (atomic and molecular motion)

Energy of Motion Energy = ½ * m * v 2 where m = mass v = velocity Any time an object is moving, it has kinetic energy.

Temperature Scales Kelvin scale is the preferred measure of temperature in astronomy. Kelvin = Celsius degrees Absolute zero (Kelvin) = temperature at which all molecular movement ceases

Thermal Energy: the collective kinetic energy of many atomic/molecular particles (for example, molecules in a rock, in air, in water) Thermal energy is a form of kinetic energy. Thermal energy is related to temperature but it is NOT the same. Temperature is the average kinetic energy of the many particles in a substance – a measure of how fast the molecules of a substance are moving (vibrating). Velocity of moving (vibrating) molecules is dependent on their temperature  hotter objects have more thermal energy than cooler objects (at the same density)

Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends both on temperature AND density. Example: Which would you least want to put your hand into? Note: a typical sauna has a temperature of 160° – 210° F

Don’t Confuse Temperature and Thermal Energy The Sun possesses a very low- density corona with a temperature of 1 million degrees Kelvin. But the heat in the corona is not enough to warm up a cup of coffee. Why? There are so few particles per volume that energy can not be easily transferred from the corona to an object in the corona. High temperature does not automatically imply high kinetic (thermal) energy! (Think hot air vs. hot water).

2) Radiative Energy Energy in the form of light or other form of electromagnetic radiation (more on this in Chapter 5).

3) Potential Energy A) Gravitational B) Chemical C) Mass-energy

Gravitational Potential Energy  On Earth, depends on:  object’s mass (m)  strength of gravity (g)  distance object could potentially fall  On Earth, depends on:  object’s mass (m)  strength of gravity (g)  distance object could potentially fall

Gravitational Potential Energy  In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts.  A contracting cloud converts gravitational potential energy to thermal energy.  In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts.  A contracting cloud converts gravitational potential energy to thermal energy.

Chemical Potential Energy  Energy in an unlit match is stored chemical potential energy.  Energy in food (breaking apart chemical bonds of starches, carbohydrates, etc.)  Energy in an unlit match is stored chemical potential energy.  Energy in food (breaking apart chemical bonds of starches, carbohydrates, etc.)

Mass-Energy E = mc 2 Energy (potential) mass speed of light Einstein’s theory of special relativity says that mass and energy are equivalent, and can be converted back and forth into each other. In other words, mass is a form of (potential) energy.

Mass-Energy E = mc 2 A small amount of mass can release a great deal of energy Concentrated energy can spontaneously turn into particles (for example, in particle accelerators) Amount of energy in a 1 kg rock could power all cars in the United States for a week. 0.1 kg of material

Summary of Types of Energy Kinetic Radiative Potential Energy of motion (moving objects) Thermal energy (energy of vibrating atoms/ molecules at temperature T) + Light (Chapter 5) Gravitational (potential to fall in a gravitational field) + Chemical (matches, energy stored within food) + Mass-energy (E = mc 2 ) – convert mass to pure energy, and back

Conservation of Energy  Energy can be neither created nor destroyed.  It can change form or be exchanged between objects.  The total energy content of the Universe was determined in the Big Bang and remains the same today. Important concept!  Energy can be neither created nor destroyed.  It can change form or be exchanged between objects.  The total energy content of the Universe was determined in the Big Bang and remains the same today. Important concept!

Conservation of Energy At top of arc, ball has lots of gravitational potential energy and little kinetic energy. Just before the ball hits the table, it has less gravitational potential energy, but more kinetic energy (it is moving faster). Conservation of energy tells us that sum of kinetic energy + gravitational potential energy of ball is the same at all times. At top of arc, ball has lots of gravitational potential energy and little kinetic energy. Just before the ball hits the table, it has less gravitational potential energy, but more kinetic energy (it is moving faster). Conservation of energy tells us that sum of kinetic energy + gravitational potential energy of ball is the same at all times.

Near the Sun, planet has less gravitational potential energy and more kinetic energy (it is moving faster), than when planet is far away from the Sun (but PE + KE always a constant). This is just Kepler’s 2nd law of planetary motion! Same concepts apply to space!

Suppose you step off a cliff, and landed on a trampoline. Your kinetic energy is greatest _________, while your gravitational potential energy is greatest _________. A) when you jump; just before you land on the trampoline. B) half way down; half way down. C) just before you land on the trampoline; when you jump D) actually neither your kinetic nor gravitational energy vary during the process A) when you jump; just before you land on the trampoline. B) half way down; half way down. C) just before you land on the trampoline; when you jump D) actually neither your kinetic nor gravitational energy vary during the process

Suppose you step off a cliff, and landed on a trampoline. Your kinetic energy is greatest _________, while your gravitational potential energy is greatest _________. A) when you jump; just before you land on the trampoline. B) half way down; half way down. C) just before you land on the trampoline; when you jump D) actually neither your kinetic nor gravitational energy vary during the process A) when you jump; just before you land on the trampoline. B) half way down; half way down. C) just before you land on the trampoline; when you jump D) actually neither your kinetic nor gravitational energy vary during the process

Newton’s Second Law and Gravity The Universal Law of Gravitation: 1.Every mass attracts every other mass. 2.Attraction is directly proportional to the product of their masses. 3.Attraction is inversely proportional to the square of the distance between their centers. The Universal Law of Gravitation: 1.Every mass attracts every other mass. 2.Attraction is directly proportional to the product of their masses. 3.Attraction is inversely proportional to the square of the distance between their centers. G = Gravitational constant of Nature

Gravity (An Example) Suppose M 1 doubles in mass, and the distance between the two masses is doubled. What happens to the gravitational force between them? New Force F g = G * (2M 1 )(M 2 )/(2d) 2 = G * 2M 1 M 2 /4d 2 = 2/4 G* M 1 M 2 /d 2 = ½ G* M 1 M 2 /d 2 = ½ Old Force F g Gravitational force would be diminished by a factor of 2. Now, new mass_1 = 2M 1, new mass_2 = M 2, and new distance = 2d

Clicker Question Suppose M 1 and M 2 have their masses cut in half, and the distance between the two masses doubles. What happens to the gravitational force between them? A) It remains the same. C) It is cut in half. B) It doubles. D) It decreases by a factor of 16.

Clicker Question Suppose M 1 and M 2 have their masses cut in half, and the distance between the two masses doubles. What happens to the gravitational force between them? New Force F g = G * (½M 1 )*(½M 2 )/(2d) 2 = G * ¼ M 1 M 2 /4d 2 = 1/16 G* M 1 M 2 /d 2 = 1/16 Old Force F g Force decreases by a factor 16 (Answer D)

The Acceleration of Gravity  All falling objects accelerate at the same rate (not counting friction of air resistance) because of gravity at a rate g.  On Earth, g ≈ 10 m/s 2 : speed increases 10 m/s with each second of falling for all objects, regardless of mass.  All falling objects accelerate at the same rate (not counting friction of air resistance) because of gravity at a rate g.  On Earth, g ≈ 10 m/s 2 : speed increases 10 m/s with each second of falling for all objects, regardless of mass. Of course, value of g is different if you go to the Moon, Jupiter, etc.