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If the force exerted by a horse on a cart is equal and opposite to the force exerted by a cart on the horse, as required by Newton’s third law, how does the horse manage to move a cart? A soft-drink sits at rest on a table. Which of the Newton’s laws explains why the upward force of the table acting on the can is equal and opposite to Earth’s gravitational force pulling down on the can? A book sits at rest on a table. Which force does Newton’s third law tell us is equal and opposite to the gravitational force acting on the book?

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Circular Motion An object moving along a circular path at a constant speed must have a net force acting on it.

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It is important to distinguish between adjectives centripetal (center-seeking) and centrifugal (center-fleeing). The force, we are discussing , the centripetal force, is directed toward the center of the circle.

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**There is no centrifugal force!!!!**

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A Car, Rounding a Curve

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**Acceleration revisited**

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**Velocity and acceleration are perpendicular each other at each point of this circle.**

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**V = 2pR/T (meters/second)**

Frequency f (revolutions per second) Period T = 1/f ( seconds) The linear velocity of the object V = 2pR/T (meters/second)

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**Dynamics of Uniform Circular Motion**

S F = ma = m V2/R Centripetal force is just a term, which means that there is the acceleration pointed to the center.

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Skidding on a Curve

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Banking Corners

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Projectile Motion

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**When something is thrown or launched**

near the Earth surface, it experiences a constant vertical gravitational force. Motion under these conditions is called projectile motion.

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Important: The study of projectile motion is simplified because the motion can be treated as two mutually independent, perpendicular motions, one horizontal and the other vertical.

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Question Suppose a bullet is fired horizontally from a pistol and simultaneously another bullet is dropped from the same height. Which bullet hits the ground first?

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Important:The object projected horizontally will reach the ground in the same time as the object released vertically from the rest.

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Object, Thrown Upward

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**You are hunting gorillas with a rifle that shoots tranquilizer darts**

You are hunting gorillas with a rifle that shoots tranquilizer darts. Suddenly you see a gorilla wearing a bright red button, hanging from a limb. At the instant, you pull the trigger , the gorilla lets go of the limb. Where should you have aimed to hit the gorilla’s red button?

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**Fast Moving Projectiles: Satellites**

The Earth satellite is simply a projectile that falls around the Earth rather than into it.

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**A common misconception is that satellites orbiting at high altitudes are free from gravity.**

The high altitude only allows the satellites to go above atmosphere, but they are in the field of the Earth gravity.

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Question 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.

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Questions What is the force that allows a person on roller-blades to turn a corner? What happens if this force is not strong enough? A child rides on a carousel at constant speed. In which direction does each of the following vectors point? a. velocity b. change in velocity c. acceleration d. net force.

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Questions A vine is just strong to support Tarzan when he is hanging straight down. However, when he tries to swing from tree to tree, the same vine breaks at the bottom of the swing. How could it happen?

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Circular Motion and the Law of Universal Gravitation.

Circular Motion and the Law of Universal Gravitation.

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