Lecture 2 Objects in Motion Aristotle and Motion Galileo’s Concept of Inertia Mass – a Measure of Inertia Net Force and Equilibrium Speed and Velocity Acceleration

Aristotle ( BC) Believed that natural laws could be understood by logical reasoning. Divided motion into 2 categories: –Violent motion – pushing or pulling forces –Natural motion – motion of stars, falling rocks, rising smoke, etc.

Aristotle ( BC) Two of Aristotle’s assertions that were thought to be correct for nearly 2,000 years: –Heavy objects fall faster than lighter objects. –Moving objects must have forces exerted upon them to keep them moving.

Galileo ( ) Revolutionized the laws of motion and tested his ideas by experiment. Experiment, not philosophical speculation, is the test of truth.

1.Observe – Recognize a question or a puzzle. 2.Question – Make an educated guess- a hypothesis to answer the question. 3.Predict – Consequences that can be observed if hypothesis is correct. 4.Test Predictions – Conduct experiments and make observations to see if predicted consequences are present. 5.Draw a Conclusion – The acceptance, modification, or rejection of the hypothesis based on extensive testing. Scientific Method: a process through which scientists gather facts through observations and formulate scientific hypotheses and theories.

In the absence of a force, objects once set in motion tend to continue moving indefinitely. –Assuming there are no opposing forces such as friction or air resistance. Force: a push or a pull that changes the motion of an object. Inertia: the property by which objects resist changes in motion. Galileo’s Concept of Inertia

No force is necessary to keep the cannonball moving in the horizontal direction once it has left the cannon. Galileo’s Concept of Inertia

Mass vs. Weight The inertia of an object depends on its amount of matter. Mass: the measure of the inertia or the quantity of matter in an object. –Measured in Kilograms (kg)

Weight of astronaut on the Moon = 1/6 that of his weight on Earth. However, mass remains the same!

Mass vs. Weight Weight: the force upon an object due to gravity. –Measured in units of force such as pounds. –Scientific unit is the Newton (N) –1 kg of any material at Earth’s surface has a weight of 9.8 N (2.2 lb) Mass and Weight are directly proportional.

Mass and Volume An object’s size is not always a good determination of its mass. Volume: the amount of space occupied by an object. Density = mass / volume: amount of matter per unit volume (g/cm 3, kg/m 3 )

Net Force Net Force: the combination of all forces acting upon an object. Forces are vector quantities. –Vector Quantity: has both magnitude and direction.

Net Force When net force is zero, an object is at mechanical equilibrium. Equilibrium Rule:ΣF = 0 An object either remains at rest or moves at a constant velocity (no change in motion).

If the scaffold is at rest, then the sum of the upward vectors must equal the sum of the downward vectors.

F (pushing) = 20 N F (friction) = 20 N ΣF = 0 A desk is being pushed across the floor at a constant velocity. What is the net force acting on it?

Net Force Support Force: force that supports an object against gravity, often called the normal force. Weight + Normal Force = 0 (ΣF = 0)

Weight and Support Force What happens if the supporting surface undergoes an acceleration?

Weight and Support Force

The Force of Friction Friction: the resistive force that opposes the motion or attempted motion of an object past another with which it is in contact. Friction occurs for all states of matter! (air resistance for example).

Friction The force of friction between 2 surfaces depends on: –The kind of materials. –The force with which they are pressed together.

Speed Before the time of Galileo, objects in motion were described as “slow” or “fast”. Speed: distance traveled per amount of travel time. Examples of units of speed: km/h, m/s, mi/h

Speed Instantaneous Speed vs. Average Speed –Average Speed = Total distance covered –Total distance covered = Average speed X Travel time Travel time

Velocity Velocity: both the speed and direction of an object. A quantity such as velocity that specifies both magnitude and direction is known as a vector quantity. Constant velocity = constant speed and constant direction.

Relative Motion: Are you standing still? Relative to the Sun? The Earth is orbiting the Sun at approximately 100,000 km/h! Relative to the Earth? Relative to the center of the galaxy? The Milky Way galaxy is rotating at a speed of 965,600 km/h! Relative to other galaxies? The Andromeda galaxy is approaching the Milky Way at a velocity of 100 to 140 km/s!

Acceleration Acceleration: a rate of change of velocity. Acceleration = Change in velocity = ΔV Example of units of acceleration: m/s 2 Time interval T

The velocity of a ball rolling down an inclined plane will gain the same amount of velocity in equal intervals of time = constant acceleration.

Acceleration A body experiences acceleration when there is a change in its state of motion: –Can either be an increase or a decrease in velocity! –Change in velocity = change in speed, direction, or both.

Acceleration Decreasing Velocity = acceleration in opposite direction of object’s motion. Increasing Velocity = acceleration in same direction as object’s motion.

Falling Objects Acceleration due to gravity on Earth = 10 m/s 2 (more precisely 9.8 m/s 2 ). g = 10 m/s 2 Distance of free fall from rest is directly proportional to the square of the time of the fall. d = ½gt 2

The rate at which velocity changes each second is the same. g (acceleration due to gravity) is always constant.

Note: acceleration due to gravity (g) is constant (same quantity and same direction). Direction of velocity Direction of g Direction of velocity Direction of g

A penny is dropped from the top of the Empire State Building (381 m). Ignoring the effect of air resistance, the penny will fall for approximately 9 s. What will be its final velocity in m/s? –Assume that the acceleration due to gravity (g) is 10 m/s 2 and that the penny starts from rest. Velocity will be 90 m/s or 324 km/h (203 mph)!