Apr 20, 2023 Physics 1 (Garcia) SJSU
Chapter 6 Projectile Motion
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
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.
Apr 20, 2023 Physics 1 (Garcia) SJSU
Projectile MotionProjectile motion combines uniform horizontal motion (constant speed)with freefall vertical motion (constant acceleration.
Apr 20, 2023 Physics 1 (Garcia) SJSU
Uniform Horizontal Motion
1 2 3 4 5
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
Apr 20, 2023 Physics 1 (Garcia) SJSU
Accelerating Vertical Falling1 (Release)
2
3
4
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….
Apr 20, 2023 Physics 1 (Garcia) SJSU
Projectile Motion2 3 4
Arbitrary 5
1
6
7
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.
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?
Apr 20, 2023 Physics 1 (Garcia) SJSU
Demo: Fall and Fire1
2
3
4 4
2
3
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.
Apr 20, 2023 http://www.youtube.com/watch?v=cxvsHNRXLjw
Movie: Shoot the Monkey
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
Apr 20, 2023 Physics 1 (Garcia) SJSU
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.
Apr 20, 2023 Physics 1 (Garcia) SJSU
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
Apr 20, 2023 Physics 1 (Garcia) SJSU
Parabolic Arc
2
3
4
Arbitrary 5
1
6
7
Up and down motion is symmetric, as shown.Frame #4 is highest point of the parabolic arc of projectile motion.
Arbitrary
Apr 20, 2023 Physics 1 (Garcia) SJSU
Maximum RangeMaximum range is at 45 degrees (when air resistance is negligible).
Apr 20, 2023 Physics 1 (Garcia) SJSU
Demo: TrebuchetTrebuchet is a type of catapult popular in the 13th century.
ReleaseWarwolf45 degrees
Apr 20, 2023 Physics 1 (Garcia) SJSU
Movie: Trebuchet
Contestant in annual pumpkin throwing contest, Punkin Chukin
Apr 20, 2023 Physics 1 (Garcia) SJSU
Projectile Motion with Drag
Range reduced by air resistance.
Shape of the arc is changed.Object lands at steeper angle.
Apr 20, 2023 Physics 1 (Garcia) SJSU
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).
Apr 20, 2023 Physics 1 (Garcia) SJSU
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?
Apr 20, 2023 Physics 1 (Garcia) SJSU
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.
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.
Apr 20, 2023 Physics 1 (Garcia) SJSU
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?
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.
Apr 20, 2023 Physics 1 (Garcia) SJSU
Elliptical Orbits
For speeds higher than 8 km/s, the orbit is elliptical instead of circular.
Apr 20, 2023 Physics 1 (Garcia) SJSU
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
Apr 20, 2023 Physics 1 (Garcia) SJSU
End of Part I:Mechanics