Gravity

Galileo’s Physics Inertia: A moving object will stay in motion unless acted upon by a force. Rate of falling: Gravity accelerates all objects, regardless of weight, by the same amount

Speed Example: a car moving at 60 miles/hour

Velocity Velocity refers to not only how fast an object is moving but its direction as well. Example: a car moving 60 miles/hour due west.

Acceleration Acceleration refers to any rate of change in the velocity of an object. An acceleration can mean a speeding up, a slowing down, or simply a change in the direction of motion with no change in speed.

Units of acceleration

Example A car accelerates from a stop light at 10 m/sec2 following a straight path. So, at time t = 0 the car’s speed is 0 m/sec. After one second of acceleration, the car’s speed is 10 m/sec (velocity 10 m/sec south). After two seconds, the car’s speed is 20 m/sec.

Discussion After one minute of accelerating at 10 m/sec2 at what speed is the car moving?

Discussion If I had two identical inclined planes placed so that they faced each other and I rolled a ball down one of the planes. How high up the second inclined plane will the ball get before it stops rolling? Explain.

Discussion What if the second inclined plane is replaced by one which is half as steep as the first inclined plane. How high will the ball reach on this plane?

Law of falling objects In the absence of air resistance, all objects fall with the same constant acceleration regardless of the objects mass.

Newton

Newton’s first law of motion The Law of inertia A body remains at rest or moves in a straight line at a constant speed unless acted on by a net external force. Inertia is the tendency of an object to resist a change in velocity.

Discussion Using Newton’s first law of motion why is it a good idea to be wearing a seatbelt in case of an car accident?

Newton’s second law of motion Force = mass  acceleration If the same force is applied to an object with half the mass, the acceleration of that object will be twice as much.

Discussion Using Newton’s 2nd law of motion, explain why you can throw a baseball farther than a shot-put.

Discussion If I pull on either side of the a pen as hard as I can, what is the net force I exert on the pen?

Discussion Which will do more damage to your car. Hitting a brick wall at 60 miles per hour which does little damage to the brick wall. A head on collision with another car traveling at 60 miles per hour in the opposite direction with the same mass such that both cars immediately come to rest.

Newton’s third law of motion For any force there is always an equal and opposite reaction force.

Example: Walking In order to walk, you have to push with your foot back on the ground. The Earth pushes your foot with an equal and opposite force. While the forces are equal and opposite the response to that force is not, because the masses are very different.

Discussion If I put my car in neutral and try to push it with a force F, according to Newton’s third law my car pushes back with the same force. Therefore, the car should never move. Is Newton wrong? Why or why not?

Discussion Your on a space walk outside the space station using Nasa’s jetpack to move around when it breaks down leaving you stranded 500 feet from safety. All you have is a bag of tools. How do you get back to the space station.

Discussion Consider an object in uniform circular motion. That is, an object traveling in a circle with a constant speed. Is there a force acting on this object? Why or why not?

Discussion Consider an object in uniform circular motion. That is, an object traveling in a circle with a constant speed. How is the velocity of the object changing and how must the force on the object be directed to change its velocity in this way?

Discussion Is there a force acting on the Moon? How can you tell?

Speed and distance The faster you throw something, the farther is goes before it hits the ground.

The Moon is falling The nearly circular orbit of the Moon is constantly accelerating toward the Earth. The Moon is constantly falling toward the Earth.

Discussion Newton’s third law tells us that the force of the Sun on the Earth is the same as the force of the Earth on the Sun. Why then does the Earth orbit the Sun instead of the other way around?

The Sun is more Massive The force of the Earth on the Sun is the same as the force of the Sun on the Earth. But, the Sun is 333,000 times more massive than the Earth. From Newton’s second law the Earth will be accelerated 333,000 time more than the Sun.

Orbits Because of Newton’s third law, it is not exactly correct to say that the Earth orbits the Sun or the Moon orbits the Earth. Instead, both objects, the Earth and the Sun or the Moon and the Earth, orbit a common point called the center of mass.

Discussion If two stars with equal mass are held together by gravity, describe their orbit.

Newton’s Universal Law of Gravity Every mass attracts every other mass through a force called gravity The force is directly proportional to the product of their masses The force is inversely proportional to the square of the distance between them

Newton’s law of gravity

Discussion Consider the gravitational force between two objects with mass M1 and M2 separated by a distance d. How would the gravitational force change if the distance between them increases to 3  d. How will it change in the distance in decreased to 0.1  d?

Discussion Suppose a new planet is discovered out in the Kuiper belt. This planet has twice the mass of the Earth but is also twice the size. Is the surface gravity of this new planet greater than, less than or the same as the surface gravity of the Earth?

Gravitational forces between spherical masses d The distance to use is the distance between the two spheres centers.

Discussion You dig a very deep mine shaft. As you get closer to the center of the Earth, does your weight increase or decrease? Why? (Hint: consider what the force of gravity will be at the very center of the Earth.)

Where does it come from? For a planet to orbit the Sun, it must constantly accelerate toward the Sun, otherwise it would fly off in a straight line at a constant velocity.

Discussion If I drop two balls at exactly the same time and from exactly the same height, with each ball exactly same shape and size but very different masses, which ball hits the ground first?

Discussion If I drop two balls at exactly the same time and from exactly the same height, with each ball exactly same shape and size but very different masses, which ball has the greater force acting on it?

Why proportional to the mass? All objects, regardless of their mass, fall with the same acceleration. Because F = ma, To keep the acceleration constant, the force must vary proportional to the mass.

Discussion If I swing a ball in a circle over my head with a short string and a long string with each ball moving at the same speed, which ball has the greater force acting on it? Explain why.

Why the square of the distance? An inverse square central force law is required to get stable orbits that are conic sections, i.e. orbits that are elliptical.

Discussion A ball held on a string is coasting around in a large horizontal circle. The string is then pulled so the ball coasts in a smaller circle. When coasting the smaller circle its speed is Greater Less Unchanged