AGENDA 31-OCT Binder check today! Binder check today! Notes - Projectile Motion Notes - Projectile Motion CW - Plotting Projectile Motion Activity & to play projectile motion Cyclops game! CW - Plotting Projectile Motion Activity & to play projectile motion Cyclops game! HW - Happy Halloween! HW - Happy Halloween!

Projectile Motion Chapter 8 Mrs. Falatek

Projectile Motion Projectile – any object projected by any means that continues in motion. Projectile – any object projected by any means that continues in motion. Determine what the speedometer will read for the free falling baseball at time = 0, 1, 2, 3, 4 Determine what the speedometer will read for the free falling baseball at time = 0, 1, 2, 3, 4

Projectile Motion IF there were no gravity – any object thrown horizontally will continue in a straight line path. IF there were no gravity – any object thrown horizontally will continue in a straight line path. Because there is gravity projectiles follow a curved path called a parabola. Because there is gravity projectiles follow a curved path called a parabola.

Parabolic Path A ball is thrown horizontally off the cliff. Forces acting on the ball Forces acting on the ball Constant horizontal motion Constant horizontal motion Accelerated vertical motion Accelerated vertical motion The combination of the two independent forces causes projectiles to follow a parabolic path. The combination of the two independent forces causes projectiles to follow a parabolic path.

Parabolic Path Two component Forces Two component Forces Vertical (gravity) Vertical (gravity) Horizontal (throw - constant) Horizontal (throw - constant)

AGENDA 3-NOV: No HW to submit No HW to submit Finish Projectile Motion Activity Finish Projectile Motion Activity HW HW Questions? Visit Questions? Visit

AGENDA 5-NOV: Notes – Projectile Motion Notes – Projectile Motion CW – Practice Vector Problems CW – Practice Vector Problems HW – Part 1: Projectile Motion Lab HW – Part 1: Projectile Motion Lab Determining the velocity of a projectile Determining the velocity of a projectile Questions? Visit Questions? Visit

So Far We Know… a projectile is any object upon which the only constant force is gravity, a projectile is any object upon which the only constant force is gravity, projectiles travel with a parabolic trajectory due to the influence of gravity, projectiles travel with a parabolic trajectory due to the influence of gravity,

So Far We Know… there are no horizontal forces acting upon projectiles and thus no horizontal acceleration, there are no horizontal forces acting upon projectiles and thus no horizontal acceleration, the horizontal velocity of a projectile is constant (never changing in value), the horizontal velocity of a projectile is constant (never changing in value), there is a vertical acceleration caused by gravity; its value is ~10 m/s 2, down, there is a vertical acceleration caused by gravity; its value is ~10 m/s 2, down, the vertical velocity of a projectile changes by ~10 m/s each second, the vertical velocity of a projectile changes by ~10 m/s each second, the horizontal motion of a projectile is independent of its vertical motion. the horizontal motion of a projectile is independent of its vertical motion.

Vector Diagrams represent how the x- and y- components of the velocity change with time represent how the x- and y- components of the velocity change with time length of the vector arrows are representative of the magnitudes of that quantity length of the vector arrows are representative of the magnitudes of that quantity Note: Horizontal vector DOES NOT CHANGE!

Calculating Displacement Vertical Displacement Vertical Displacement y = 0.5*g*t 2 Horizontal Displacement Horizontal Displacement x = v ix * t

Calculating Displacement Anna drops a ball from rest from the top of 80-meter high cliff. How much time will it take for the ball to reach the ground and at what height will the ball be after each second of motion? Anna drops a ball from rest from the top of 80-meter high cliff. How much time will it take for the ball to reach the ground and at what height will the ball be after each second of motion? A cannonball is launched horizontally from the top of an 80-meter high cliff. How much time will it take for the ball to reach the ground and at what height will the ball be after each second of travel? A cannonball is launched horizontally from the top of an 80-meter high cliff. How much time will it take for the ball to reach the ground and at what height will the ball be after each second of travel?

AGENDA 6-NOV: Projectile Motion Lab Projectile Motion Lab HW – HW – Part 2: Projectile Motion Lab Part 2: Projectile Motion Lab TEST IN ONE WEEK TEST IN ONE WEEK

AGENDA 7-NOV: Submit HW Submit HW No notes No notes CW- The Influence of Gravity on distance traveled & Projectile motion challenge problems CW- The Influence of Gravity on distance traveled & Projectile motion challenge problems HW – HW – p 130 #1-6, Review, #1-3 Exercises p 130 #1-6, Review, #1-3 Exercises Test Friday! Test Friday!

AGENDA 10-NOV: Submit HW Submit HW Notes – Gravity and Satellites Notes – Gravity and Satellites CW- The Force of Gravity & Exploration WS (if time) CW- The Force of Gravity & Exploration WS (if time) HW – p 130 #11, 13, 18 Review, p 113 #2, 5, 11 & TEST TUESDAY! HW – p 130 #11, 13, 18 Review, p 113 #2, 5, 11 & TEST TUESDAY!

Terms to know: Tangent – a line that touches a circular surface at only one point. Tangent – a line that touches a circular surface at only one point. Tangential Velocity – velocity whose direction is tangential to the Earth’s surface (parallel or in the x-direction). Tangential Velocity – velocity whose direction is tangential to the Earth’s surface (parallel or in the x-direction). Satellite – object with v x = 8 km/s. Trajectory follows curvature of the Earth’s surface Satellite – object with v x = 8 km/s. Trajectory follows curvature of the Earth’s surface

Newton’s Experiment: cannonball launched from an elevation > Earth’s atmosphere. cannonball launched from an elevation > Earth’s atmosphere. velocity x is GREAT & trajectory becomes a circle. velocity x is GREAT & trajectory becomes a circle. Air resistance minimal, velocity x remains the same Air resistance minimal, velocity x remains the same Object orbits Earth indefinitely Object orbits Earth indefinitely

More Terms to know: Ellipse – an oval-like path. Ellipse – an oval-like path. Elliptical orbit – an orbit followed by a projectile with a velocity-x greater than 8 km/s. Speed of an object decreases as it travels away from Earth and increases as it comes near. Elliptical orbit – an orbit followed by a projectile with a velocity-x greater than 8 km/s. Speed of an object decreases as it travels away from Earth and increases as it comes near. Escape speed – the speed at which a projectile can out run the force of gravity (11.1 km/s) Escape speed – the speed at which a projectile can out run the force of gravity (11.1 km/s)

Newton’s Discovery: The Law of Universal Gravitation Gravity acts between all things Gravity acts between all things Dependent on Mass and Distance Dependent on Mass and Distance Force of gravity INVERSELY proportional to the square of the distance between them. Force of gravity INVERSELY proportional to the square of the distance between them. F = [ G x (m 1 m 2 ) ] ÷ (d 2 ) Constant = G = 6.67 x Nm 2 /kg 2

Some ?’s for you: If the tangential velocity of the moon were zero, how would the moon move? If the tangential velocity of the moon were zero, how would the moon move? What happens to the force of gravity between two objects when the mass of one body is doubled? What happens to the force of gravity between two objects when the mass of one body is doubled? How does the force of gravity between the earth and a rocket change as the distance between them is doubled? How does the force of gravity between the earth and a rocket change as the distance between them is doubled?

Some ?’s for you: What other word do we use to describe the quantity achieved when m 1 is your mass, m 2 is the Earth’s mass, and d is the earth’s radius? What other word do we use to describe the quantity achieved when m 1 is your mass, m 2 is the Earth’s mass, and d is the earth’s radius? What must be true in order for a satellite to stay in orbit? What must be true in order for a satellite to stay in orbit?

AGENDA 11-NOV: Notes – Gravity and Satellites Notes – Gravity and Satellites Notes – Gravity and Satellites Notes – Gravity and Satellites CW- Newton’s Law of Universal Gravitation CW- Newton’s Law of Universal Gravitation HW – p 115 Problems #1-7 & 9 p 132 Problem #1 HW – p 115 Problems #1-7 & 9 p 132 Problem #1

AGENDA 12-NOV: Submit HW Submit HW Review Review HW – STUDY! HW – STUDY!

AGENDA 13-NOV: CW – Review Packet CW – Review Packet HW – Study!!! Test Tomorrow! PJAS #5 Due 11/21! HW – Study!!! Test Tomorrow! PJAS #5 Due 11/21!

AGENDA ?-JAN: Review big ideas in Projectile Motion & Gravity Review big ideas in Projectile Motion & Gravity CW – Projectile Motion Review CW – Projectile Motion Review HW HW Finish Projectile Motion Review – STUDY! Finish Projectile Motion Review – STUDY! Organize Binder Organize Binder QPA Thursday!!!!! QPA Thursday!!!!!

Projectile Motion Describe for a projectile the changes in the vertical and horizontal components of its velocity. Describe for a projectile the changes in the vertical and horizontal components of its velocity. Vertical component changes at a rate of (-) 9.8 m/s 2 due to gravity. Vertical component changes at a rate of (-) 9.8 m/s 2 due to gravity. Horizontal component DOES NOT change. Horizontal component DOES NOT change.

Projectile Motion Calculate time or distance traveled by an object in free-fall. Calculate time or distance traveled by an object in free-fall. Vertical component use d y = ½ a x t 2. Vertical component use d y = ½ a x t 2. Horizontal component use d x = v i x t Horizontal component use d x = v i x t

Projectile Motion Show the connection between a fast-moving projectile and an Earth satellite. cannonball launched from an elevation > Earth’s atmosphere. cannonball launched from an elevation > Earth’s atmosphere. velocity x is GREAT velocity x is GREAT trajectory becomes a circle. trajectory becomes a circle. Air resistance minimal Air resistance minimal velocity x remains the same velocity x remains the same Object orbits Earth indefinitely Object orbits Earth indefinitely

Projectile Motion Describe how the speed of a satellite changes for different portions of an elliptical orbit. Describe how the speed of a satellite changes for different portions of an elliptical orbit. Circular orbit – constant speed Circular orbit – constant speed Elliptical orbit – changing speed Elliptical orbit – changing speed Describe what it is meant by escape speed. Describe what it is meant by escape speed. The horizontal speed at which an object will not become a satellite The horizontal speed at which an object will not become a satellite

Gravity State Newton’s law of universal gravitation. State Newton’s law of universal gravitation. Gravity acts between all things Gravity acts between all things Dependent on Mass and Distance Dependent on Mass and Distance F = [ G x (m 1 m 2 ) ] ÷ (d 2 ) Constant = G = 6.67 x Nm 2 /kg 2

Projectile Motion Describe the how the force of gravity changes with … Describe the how the force of gravity changes with … Distance – as distance increases, force decreases by change in distance squared! INVERSE RELATIONSHIP Distance – as distance increases, force decreases by change in distance squared! INVERSE RELATIONSHIP Mass – as mass increases, force changes directly by change in mass of object(s). Mass – as mass increases, force changes directly by change in mass of object(s).

Some ?’s for you: If the tangential velocity of the moon were zero, how would the moon move? If the tangential velocity of the moon were zero, how would the moon move? What happens to the force of gravity between two objects when the mass of one body is doubled? What happens to the force of gravity between two objects when the mass of one body is doubled? How does the force of gravity between the earth and a rocket change as the distance between them is doubled? How does the force of gravity between the earth and a rocket change as the distance between them is doubled?

Some ?’s for you: What other word do we use to describe the quantity achieved when m 1 is your mass, m 2 is the Earth’s mass, and d is the earth’s radius? What other word do we use to describe the quantity achieved when m 1 is your mass, m 2 is the Earth’s mass, and d is the earth’s radius? What must be true in order for a satellite to stay in orbit? What must be true in order for a satellite to stay in orbit?