Units covered: 14 -16, bit of 17, 19, and 20. Today’s Slides This set of slides covers some physics – Newton’s Laws of Motion, Law of Gravitation, Tides, Conservation Laws Units covered: 14 -16, bit of 17, 19, and 20.

Isaac Newton (1642-1727) Isaac Newton discovered the fundamental laws that govern the motion of all (large) bodies. Had to invent his own mathematics (Calculus) to do it. His work is used even today in calculating everything from how fast a car stops when you apply the brakes, to how much rocket fuel to use to get to Saturn. And he did most of it before his 24th birthday…

Mass and Inertia Mass is the amount of matter an object contains. Mass is different from weight – weight requires gravity (or some other force) to exist. Example: while swimming, you may feel somewhat weightless because your body floats. Your mass, however, stays the same. Inertia is the tendency of mass to stay in motion or at rest.

The Law of Inertia Newton’s First Law is sometimes called the Law of Inertia: A body continues in a state of rest, or in uniform motion in a straight line at a constant speed, unless that state is changed by forces acting on it. Or, a body maintains the same velocity unless some force changes it. It does NOT take force to make a (moving) object move; it only takes force to CHANGE its motion. A ball rolling along a flat, frictionless surface will keep going in the same direction at the same speed, unless something pushes or pulls on it.

Another View of Newton’s First Law If an object’s velocity is changing, there must be force(s) present. Dropping a ball. Applying the brakes in a car. If an object’s velocity is not changing, either there are no forces acting on it, or the forces are balanced and cancel each other out. Holding a ball… Driving down the road a constant speed in straight line…

What’s a Vector, Victor? A vector is a physical quantity that requires both a magnitude (or size) and a direction to fully define it. Force, velocity, momentum, angular momentum, and acceleration are all examples of vector quantities. A scalar is a physical quantity that can be fully defined by magnitude (or size) only. Length, area, volume, temperature, energy, are all examples of scalar quantities.

Acceleration The term acceleration is used to describe the change in a body’s velocity. Stepping on the gas pedal of a car accelerates the car – it increases the speed. Stepping on the brake accelerates (decelerates) the car – it decreases the speed. BUT, a change in an object’s direction is also acceleration. Turning the steering wheel of a car makes the car go left or right – this is an acceleration. Force(s) must be present if there is any acceleration.

Circular Motion A string tied to a ball and swung around your head. Law of Inertia says that the ball should go in a straight line. Ball goes in a circle – there must be force(s). Where’s the force? It’s the tension in the string that is changing the ball’s velocity. If the string breaks, the ball will move off in a straight line (while falling to the ground.)

Centripetal Force This force that causes circular motion is sometimes referred to as the centripetal force, a force directed towards the center of the system. The tension in the string provides this force. Newton determined that this force can be described by the following equation:

Newton’s Second Law The net force (F) acting on an object equals the product of its acceleration (a) and its mass (m) F = m  a We can rearrange this to: a = F/m For an object with a large mass, the acceleration will be small for a given force. If the mass is small, the same force will result in a larger acceleration. Though simple, this expression can be used to calculate everything from how hard to hit the brakes to how much fuel is needed to go to the Moon.

This works for everything, Newton’s Third Law When two bodies interact, the forces between them are always equal and oppositely directed. If two skateboarders have the same mass, and one pushes on the other, they both move away from each other at the same speed but in opposite directions. If one skateboarder has more mass than the other, the same push will send the smaller person off at a higher speed, and the larger one off in the opposite direction at a smaller speed. This works for everything, planets, too.

Masses from Orbital Speeds We know that for planets, the centripetal force that keeps the planets moving on an elliptical path is the gravitational force. We can set FG and FC equal to each other, and solve for M. This M is the mass of the center object (the larger object.) If we know the orbital speed of an object orbiting a much larger one, and we know the distance between the two objects, we can calculate the larger object’s mass.

Newton’s Modification of Kepler’s 3rd Law Newton applied his ideas to Kepler’s 3rd Law, and developed a version that works for any two massive bodies. Here, MA and MB are the two object’s masses expressed in units of the Sun’s mass. This expression is useful for calculating the mass of binary star systems, and other astronomical phenomena.

There are two possible causes of weightlessness. No (or little) gravity. Possible if far enough out in space. A state of freefall. How so? Standing on a scale, in an elevator… Accelerating upward… Accelerating downward… The cable breaks… A state of freefall is equivalent to a state of weightlessness.

Orbital Motion and Gravity Newton’s Thought Experiment Imagine a cannon on top of a mountain that fires a cannonball parallel to the ground. The cannonball leaves the cannon and is pulled toward the ground by gravity. If the ball leaves the cannon with a low velocity, it falls to the ground near the mountain. If the cannonball has a higher velocity, it falls farther from the mountain.

Orbits and Weightlessness Newton’s Thought Experiment Continued… What if the cannonball is traveling so fast, that for every foot it falls, the Earth curves away from the cannonball by one foot? The cannonball will be forever falling, and never landing! The cannonball will be in orbit! Being in orbit is being in a state of freefall! Astronauts on the space shuttle, in orbit, are in freefall, and are thus in a state of weightlessness.

Gravity in Space? There’s still plenty of gravity for the astronauts in orbit. Has to be, otherwise the spacecraft wouldn’t stay in orbit. At the altitude of the space shuttle in orbit (for example), the strength of gravity is 90% of that on the surface of earth. The same cannonball explanation is valid for every planet, moon, comet, asteroid, satellite in orbit around some other body.

Mass versus Weight Even in a state of weightlessness, an object STILL HAS MASS. Mass is a measure of the amount of “stuff” there is in an object. Mass is not a measure of how much space something takes up. That’s volume. Mass is a measure of the amount of inertia an object has. Mass doesn’t depend on location. Mass is measured with a balance. Units: grams, kilograms, slugs Weight is a measure of the gravitational force on an object. It varies depending on the planet or moon that you are on. Weight is measured with a spring scale. Units: lbs, newtons, tons

Newton’s Universal Law of Gravitation Every mass exerts a force of attraction on every other mass. The strength of the force is proportional to the product of the masses divided by the square of the distance between their centers of mass. Simply put, everything pulls on everything else. Larger masses have larger gravity. Objects close together pull more on each other than objects farther apart. This is true everywhere, and for all objects. The Sun and the planets exert a gravitational force on each other. You exert a gravitational force on other people in the room!

Surface Gravity Objects on the Moon weigh less than objects on Earth. This is because surface gravity is less. The Moon has less mass than the Earth, so the gravitational force on surface is less. We use the letter g to stand for the acceleration of a body (in freefall) due to gravity. Fgravity = weight = mg On Earth, g = 9.8 m/s2 g on the Moon is around 1/6 as much as on the Earth.

The Origin of Tides The Moon exerts a gravitational force on the Earth, and the water in the oceans. The effect of the various forces acting together causes the water to create tidal bulges both beneath the Moon and on the opposite side of the Earth (from the Moon.)

High and Low Tides As the Earth rotates beneath the Moon, the water on the surface of the Earth experiences high and low tides. Note the high tides exist on two sides of the Earth at the same time (as do the low.)

The Sun Also Effects the Tides The Sun is much more massive than the Moon, so one might think it would create far larger tides. However, the Sun is much farther away, so its tidal forces are smaller, but still noticeable. When the Sun and the Moon line up, higher tides, call “spring tides” are formed. When the Sun and the Moon are at right angles to each other smaller “neap tides” result.

The Law of Conservation of Energy The energy in a closed system may change form, but the total amount of energy does not change as a result of any process. Energy can be neither created nor destroyed but only changed in form. Technically, it’s the law of conservation of mass/energy…

Kinetic Energy Kinetic Energy is the energy of motion. Both mass (m) and speed (V) contribute to kinetic energy: Imagine catching a thrown ball. If the ball is thrown gently, with low speed, it hits your hand with very little pain. If the ball is thrown very hard, at high speed, it hurts to catch.

Thermal Energy Thermal energy is the energy associated with heat. It is the energy of the random motion of individual atoms or molecules within an object. What you perceive as heat on a stovetop is the energy of the individual atoms in the heating element transferring to your finger. Really, it’s a form of kinetic energy.

Potential Energy You can think of potential energy as stored energy. Better: it’s energy due to position. Gravitational potential energy is the energy an object has due to its position in a gravitational field. PE = mgh Potential energy is released when the object is put into motion, or allowed to fall. Forms of Potential Energy: chemical, electrical, elastic, gravitational

Conversion of Forms of Energy Example: A bowling ball is lifted from the floor onto a table. Converts chemical energy in your muscles into potential energy of the ball The ball is allowed to roll off the table. As the ball accelerates downward toward the floor, gravitational potential energy is converted to kinetic energy When the ball hits the floor, it makes a sound, and the floor trembles. Kinetic energy of the ball is converted into sound energy in the air and floor, as well as some heat energy as the atoms in the floor and ball get knocked around by the impact.

Definition of Angular Momentum Linear momentum: p = m x V. If no external forces are acting on an object, then its linear momentum is conserved. Angular momentum is the rotational equivalent of linear momentum. For an object in orbit, can be expressed mathematically as the product of the object’s mass, orbit velocity, and radius. If no external forces (torques) are acting on an object, then its angular momentum is conserved, or a constant:

Conservation of Angular Momentum Since angular momentum is conserved, if either the mass, size or speed of a spinning object changes, the other values must change to maintain the same value of momentum. As a spinning figure skater pulls her arms inward, she decreases her value of r in angular momentum. Mass cannot increase, so her rotational speed must increase to maintain a constant angular momentum Works for stars, planets orbiting the Sun, satellites orbiting the Earth, etc…