22-Oct-15 Physics 1 (Garcia) SJSU Chapter 6 Projectile Motion

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.



Projectile Motion

A ball thrown across the room follows an arced trajectory.

Example of projectile motion, which combines horizontal and vertical motion.


Projectile MotionProjectile motion combines uniform horizontal motion (constant speed)with freefall vertical motion (constant acceleration.


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


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….


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.


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?


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

http://www.youtube.com/watch?v=cxvsHNRXLjw


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


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.


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


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


Maximum RangeMaximum range is at 45 degrees (when air resistance is negligible).


Demo: TrebuchetTrebuchet is a type of catapult popular in the 13th century.

ReleaseWarwolf45 degrees


Movie: Trebuchet

Contestant in annual pumpkin throwing contest, Punkin Chukin


Projectile Motion with Drag

Range reduced by air resistance.

Shape of the arc is changed.Object lands at steeper angle.


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).


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?


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.


Orbits and Centripetal Force

Gravity provides the centripetal force required for a satellite to move in a circle.


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?


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.


Elliptical Orbits

For speeds higher than 8 km/s, the orbit is elliptical instead of circular.


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


End of Part I:Mechanics

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22-Oct-15 Physics 1 (Garcia) SJSU Chapter 6 Projectile Motion