Motions in Space

What forces act on falling objects? Gravity Air resistance Is Free fall only to objects moving downward? NO

What is the acceleration due to the gravitational force on Earth? Picket Fence Lab -9.8 m/s2

Calculating Acceleration To calculate the acceleration of an object, the change in velocity is divided by the length of time interval over which the change occurred. vf - vi a t

Acceleration, Speed and Velocity Acceleration is how quickly velocity changes. When the velocity of an object changes, the object is accelerating. Symbol: a Unit: m/s2 http://glencoe.mcgraw-hill.com/sites/dl/free/0078600510/161752/00035808.html

Acceleration Change in velocity Initial velocity is the beginning velocity ( starts from rest= zero). Symbol: vi Unit: m/s Final velocity is the ending velocity (if the object ends at rest= zero). Symbol: vf

Speeding Up and Slowing Down Acceleration Speeding Up and Slowing Down When you think of acceleration, you probably think of something speeding up. However, an object that is slowing down also is accelerating. Acceleration also has direction, just as velocity does. Acceleration can be speeding up, slowing down, or changing direction

Practice = Notes

Hammer and Feather What happens on the Moon if you drop a feather and hammer? http://er.jsc.nasa.gov/seh/feather.html

Terminal Velocity The terminal velocity is the highest speed a falling object will reach. The terminal velocity depends on the size, shape, and mass of a falling object. Happens when Gravity = air resistance

Air Resistance The amount of air resistance on an object depends on the speed, size, and shape of the object. Air resistance, not the object’s mass, is why feathers, leaves, and pieces of paper fall more slowly than pennies, acorns, and apples.

Calculating Displacement (assuming object is dropped) Acceleration Calculating Displacement (assuming object is dropped) To calculate the acceleration of an object, the change in velocity is divided by the length of time interval over which the change occurred. x 0.5a t2

Projectile Motion When something is launched near Earth’s surface, it experiences a constant vertical gravitational force. Motion under these conditions is called projectile motion. It occurs whenever an object is given some initial velocity and thereafter travels in a trajectory subject only to the force of gravity.

Projectile Motion A sphere is fired horizontally from and simultaneously another sphere is dropped from the same height. Which sphere hits the ground first? A student—Galileo?—has two balls. He drops both, one falls straight down and the other forward a bit. Which ball hits the ground first? The answer is: both spheres, and both balls, will hit the ground at the same time. Vertical motions can be treated as separate from horizontal!

A Trip to Narang To further our understanding of projectile motion, we will perform some simple experiments here on Earth, record the results, and go to Narang, a planet with No Air Resistance And No Gravity.

A Trip to Narang Paths of bullets fired horizontally on Narang and Earth. The distance d between the two paths is always equal to the distance an object would free- fall during the same elapsed time. The horizontal motion of the bullet is exactly the same on each planet.

A Trip to Narang The same experiment, only now with the bullet fired at an upward angle, shows the same results. Horizontal movement is unaffected by the presence or absence of gravity. The distance d is equal to free-fall.

A Trip to the Moon A golf drive showed the same horizontal motion. Moon path A golf drive showed the same horizontal motion. The vertical motion is different, Why? (approximately 6 times higher) How does this change the range?

Projectile Motion Strobe drawing of a thrown ball’s motion. Note that the horizontal motion has a constant speed.

Conceptual Question: Projectile Motion Upon your return to Earth you decide to slingshot a banana to a hungry gorilla. Suddenly you see a gorilla wearing a bright red button hanging from a limb. At the instant you release the banana, the gorilla lets go of the limb. Fresh back from Narang, you have made a mistake in dealing with a gravitational world! You miss. Where should you have aimed to hit the gorilla’s red button? Answer: Directly at the button! The dart and the gorilla would have fallen at the same rate.

Launching an Apple into Orbit On our first attempt, we throw the apple with an ordinary speed. The apple follows a projectile path. On our next attempt, imagine that we throw the apple much faster. The apple still falls to the ground, but the path is unlike the first one. If the apple travels very far, Earth’s curvature becomes important. The force of gravity points in slightly different directions at the beginning and end of the path. An unsuccessful launch results in projectile motion.

Launching an Apple into Orbit Normally, we are not aware of the curvature of Earth’s surface, because Earth is so huge. If we were to construct a large perfectly horizontal plane resting on the surface of a perfectly spherical Earth, Earth’s surface will be 5 meters below the plane at a distance of 8 kilometers. Imagine what would happen if on our next attempt to launch the apple, we throw it with a speed of 8 km/sec (18,000 mph!) During the first second, the apple drops 5 meters.

Launching an Apple Into Orbit The result is that the motion during the next second is a repeat of that during the first. And so on. The apple is in orbit. By throwing the apple far enough, we have changed the motion from projectile to circular. This illustration was used in Newton’s Principia in the discussion of launching an object into orbit around Earth.

Flawed Reasoning about Orbits A newspaper report reads in part, “The space shuttle orbits Earth at an altitude of nearly 200 miles and is traveling at a speed of 18,000 mph. The shuttle remains in orbit because the gravitational force pulling it toward Earth is balanced by the centrifugal force (the force of inertia) that is pulling it away from Earth.” Explain why this newspaper should hire a new reporter.

Flawed Reasoning about Orbits Answer: All forces are exerted by one object on another object. Earth exerts the gravitational force on the shuttle. We have great difficulty, however, finding an object responsible for exerting a centrifugal, or outward, force on the shuttle. This is our first clue that such a force does not exist and, indeed, is not needed. Circular motion requires a net force acting toward the center of the circle, and the gravitational force provides this force. There is also no such force as a “force of inertia.” Objects travel at constant velocity in the absence of a force, not because of a force.