Forces and Motion CHAPTER 6

Gravity and Motion Aristotle (round 400 BC) believed that heavier objects fell to the earth faster than lighter objects. But he never dropped objects to test his theory. In the late 1500s a young Italian scientist named Galileo Galilei ( ) questioned Aristotle's theory about falling objects. Galileo believed that the mass of an object did not affect the rate at which it fell to the earth.

Proving a Theory According to one story, Galileo proved his theory by dropping two cannonballs of different masses from the top of the Leaning Tower of Pisa (183 feet tall) in Italy. People watching from below were amazed to see the two cannonballs land at the same time. Whether or not this story is true, Galileo’s work changed people’s understanding of gravity and falling objects.

Gravity and Acceleration Objects fall to the ground at the same rate because the acceleration due to gravity is the same for all objects. Why is this true? Acceleration depends on both force and mass. Heavier objects experience a greater gravitational force than a lighter object does. But a heavier object is also harder to accelerate because it has more mass. The extra mass of the heavy object exactly balances the additional gravitation force.

Acceleration due to Gravity Acceleration is the rate at which velocity changes over time. V f – V i /s = m/s 2 All objects accelerate toward Earth at a rate of 9.8 m/s 2 or 9.8 m/s/s.

Velocity of Falling Objects You can calculate the change in velocity of a falling object by using the following formula: Δ v = g  t Where Δ v is change in velocity. Where g is the acceleration due to gravity on Earth which is 9.8 m/s 2. Where t is the time the object takes to fall (in seconds).

Two Formulas To find a change in velocity (how fast was it going after a certain length of time): Δ v = g  t To find time (how long did it take to travel a specific distance): t = Δ v / g

Air Resistance When an object falls there are two forces acting on it. 1. The force of gravity pulling down the object down. 2. The force of air resistance pushing the object up. The net force on the falling object is the force of gravity minus the force of air resistance.

Terminal Velocity As the speed of a falling object increases, air resistance increases. The upward force of air resistance continues to increase until it is equal to the downward force of gravity. At this point, the net force is 0 N and the object stops accelerating. The object then falls at a constant velocity called terminal velocity.

Free Fall An object is in free fall only if gravity is pulling it down and no other forces are acting on it. Because air resistance is a force, free fall can occur only where there is no air or air resistance. Two places that have no air are in space and in a vacuum. A vacuum is a place in which there is no matter.

Orbiting Objects An object is orbiting when it is traveling around another object in space. Orbiting involves two motions: 1. The object moves forward at a constant speed in a straight line. 2. Gravity pulls the object down. Because of these two motions, the object moves in a curved path known as orbiting.

Floating in Space A spacecraft experiences the two motions mentioned in the previous slide. The spacecraft is in a state of free fall. Astronauts and objects in a spacecraft float and appear to be weightless because they are in a state of free fall, but they are not weightless.

Projectile Motion Projectile motion is the cured path that an object follows when thrown, launched, or otherwise projected near the surface of Earth. For example, when a ball is thrown as it leaves the hand it is traveling in a horizontal velocity. But gravity acts on the ball pulling it downward vertically. The two motions combine to form a curved path known as projectile motion. Vertical motion does not affect horizontal motion.

Newton’s Laws of Motion Newton’s First Law of Motion An object at rest remains at rest, and an object in motion remains in motion at a constant speed and in a straight line unless acted on by an unbalanced force. Consider this law in two parts.

First Law / Part 1 Part 1: Objects at Rest An object that is not moving is said to be at rest. Newton’s first law says that objects at rest will stay at rest unless they are acted on by an unbalanced force.

First Law / Part 2 Part 2: Objects in Motion The second part of Newton’s first law is about objects moving with a certain velocity. Such objects will continue to move forever with the same velocity unless an unbalanced force acts on them. When an object is moving across the floor and comes to a stop, it is friction that is the unbalanced force that acts on it that brings the object to a stop.

Inertia Newton’s first law of motion is sometimes called the law of inertia. Inertia is the tendency of an object to resist being moved or, if the object is moving, to resist a change in speed or direction until an outside force acts on the object. Mass is a measure of inertia. An object that has a small mass has less inertia than an object that has a large mass. Changing the motion of an object that has a small mass is easier than changing the motion an object with a large mass.

Newton’s Laws of Motion Newton’s Second Law of Motion The acceleration of an object depends on the mass of the object and the amount of force applied. Newton’s second law describes the motion of an object when an unbalanced force acts on the object. As with Newton’s first law, you should consider the second law in two parts.

Second Law / Part 1 Part 1: Acceleration Depends on Mass If you are pushing an empty cart, you have to exert only a small force on the cart to accelerate it. If the cart is full the same amount of force will not create the same amount of acceleration. As mass increases, acceleration decreases (if force remains the same).

Second Law / Part 2 Part 2: Acceleration Depends on Force As the force on an object increases, the acceleration of that object also increases. As the force on an object decreases, the acceleration of that object also decreases. The acceleration of an object is always in the same direction as the force applied.

Mathematical Expression The relationship of acceleration to mass and force can be expressed mathematically as follows: a = F/m or F = m  a Where: a is acceleration due to gravity = 9.8 m/s 2 F is force = measured in Newtons (kg  m/s 2 ) m is mass = measured in g or kg

Objects Fall at Same Rate Newton’s Second Law explains why objects fall to Earth with the same acceleration. See page 162 in your textbook.

Newton’s Laws of Motion Newton’s Third Law of Motion Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. All forces act in pairs. If a force is exerted, another force occurs that is equal in size and opposite in direction.

Momentum Momentum is a quantity defined as the product of the mass and velocity of an object. To find momentum multiply mass by velocity. (p = m  v) Momentum is expressed in Newtons. 1 Newton = kg  m/s

Conservation The Law of Conservation of Momentum states that when two object collide, momentum is transferred from one object to another. In a collision some or all of the momentum is transferred from one object to another.