Chapter 6 Projectile Motion
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Transcript of Chapter 6 Projectile Motion
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Apr 20, 2023 Physics 1 (Garcia) SJSU
Chapter 6 Projectile Motion
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Projectiles
• A projectile is any object that moves through space where the only force acting on the object is gravity.
• The path that a projectile follows is called a trajectory.
Apr 20, 2023 Physics 1 (Garcia) SJSU
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Apr 20, 2023 Physics 1 (Garcia) SJSU
Projectile Motion
A ball thrown across the room follows an arced trajectory.
Example of projectile motion, which combines horizontal and vertical motion.
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Apr 20, 2023 Physics 1 (Garcia) SJSU
Projectile MotionProjectile motion combines uniform horizontal motion (constant speed)with freefall vertical motion (constant acceleration.
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Apr 20, 2023 Physics 1 (Garcia) SJSU
Uniform Horizontal Motion
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EqualDistances
Rolling ball (with no friction) is an example of uniform motion.Velocity of the ball is constant so distance between “frames” (equal time between frames) is constant.
Arbitrary
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Accelerating Vertical Falling1 (Release)
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Falling is an example of accelerating motion.
Total distance from point of release increases in the ratios 1:4:9:16:25:… or 12:22:32:42:52…
Distance between frames increases as 1:3:5:7:9….
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Projectile Motion2 3 4
Arbitrary 5
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Ball rolling off of a table combines horizontal and vertical motion.Falling starts with frame #4, vertical distances increasing as 1:3:5:7:…Horizontal distances equally spaced as with uniform motion.Frames #4 to #7 are projectile motion.
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Apr 20, 2023 Physics 1 (Garcia) SJSU
Check Yourself
At the instant a cannon fires a cannonball horizontally over a level range, another cannonball held at the side of the cannon is released and drops to the ground.
Which strikes the ground first?
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Apr 20, 2023 Physics 1 (Garcia) SJSU
Demo: Fall and Fire1
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1 FALL FIRE
One ball is released and falls straight down.Other ball is fired horizontally.At all times the balls are at the same height.Hit the ground at the same time.
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Apr 20, 2023 http://www.youtube.com/watch?v=cxvsHNRXLjw
Movie: Shoot the Monkey
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Apr 20, 2023 Physics 1 (Garcia) SJSU
Distance Fallen
From Table 3.3 (page 47) we know that distance fallen in one second is 5 meters.
This distance fallen is the same whether falling straight down or in projectile motion.
0.5 s
1.0 s
1.5 s
5 meters
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Projectile Motion & Curvature
For initial speeds that are faster and faster, the range of the projectile is farther and farther.
For very large speeds, the curvature of Earth starts to be noticeable.
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Projectiles Launched at an Angle
With no gravity, projectile would follow a straight line.
Due to gravity, projectile falls beneath this line, just as if released from rest.
No Gra
vity
WithGravity
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Parabolic Arc
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Arbitrary 5
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Up and down motion is symmetric, as shown.Frame #4 is highest point of the parabolic arc of projectile motion.
Arbitrary
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Maximum RangeMaximum range is at 45 degrees (when air resistance is negligible).
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Demo: TrebuchetTrebuchet is a type of catapult popular in the 13th century.
ReleaseWarwolf45 degrees
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Movie: Trebuchet
Contestant in annual pumpkin throwing contest, Punkin Chukin
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Projectile Motion with Drag
Range reduced by air resistance.
Shape of the arc is changed.Object lands at steeper angle.
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Earth’s Curvature
Curvature of the Earth is about 5 meters over a distance of 8000 meters (which is about 5 yards over 5 miles).
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Missing the Ground
8000 m
NOT toScale
5 mCurvature
Suppose you throw a ball at a speed of 8000 m/s (about 18,000 mph).After one second, ball travels 8000 meters and falls 5 meters.In that distance, Earth curves by same amount (5 meters).
If nothing stops the ball, what happens?
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Newton’s Mountain
Newton drew a similar illustration, picturing cannons firing from a tall mountain.
If a cannon was powerful enough, the cannonball would orbit Earth.
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Apr 20, 2023 Physics 1 (Garcia) SJSU
Orbits and Centripetal Force
Gravity provides the centripetal force required for a satellite to move in a circle.
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Check Yourself
Satellites orbit at least 150 km (about 100 miles) above the surface of Earth because:
There is almost no gravity at that altitude?
There is almost no air resistance?
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Apr 20, 2023 Physics 1 (Garcia) SJSU
Getting into OrbitRocket needs to lift abovethe atmosphere and thenfire thrusters to acquire therequired orbital speed ofabout 8 kilometers persecond.
Returning to Earth, air resistance slows thespacecraft during reentry.
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Elliptical Orbits
For speeds higher than 8 km/s, the orbit is elliptical instead of circular.
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Escape Speed
If speed exceeds 11.2 km/s then object escapes Earth because gravity weakens (as object gets further away) and never slows the object enough to return it back towards Earth.
Circular
Elliptical
Hyperbolic
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Apr 20, 2023 Physics 1 (Garcia) SJSU
End of Part I:Mechanics