Motion II

1 / 18

# Motion II - PowerPoint PPT Presentation

Motion II. 2 and 3 dimensional motion. Components of Motion . Motion in 2 dimensions X component Y component Motion in 3 dimensions X component Y component Z component. Motion in x direction is independent of motion in y direction and z direction.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Motion II' - benoit

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Motion II

2 and 3 dimensional motion

Components of Motion
• Motion in 2 dimensions
• X component
• Y component
• Motion in 3 dimensions
• X component
• Y component
• Z component

Motion in x direction is independent of motion in y direction and z direction.

Separate set of equations of motion for each direction.

Equations of Motion
• ax= Fx/ m
• vx = vox + axt
• x = xo+ voxt + (1/2)axt2
• vx2 = vox2 + 2ax(x – xo)
• ay= Fy/ m
• vy = voy + ayt
• y = yo+ voyt + (1/2)ayt2
• vy2 = voy2 + 2ay(y – yo)

az= Fz/ m

• vz = voz + axzt
• z = zo+ vozt+ (1/2)azt2
• vz2 = voz2 + 2az(z – zo)
Independence of x, y, z motion
• Motion in the x direction is independent of motion in the y or z directions.
• Motion in the y direction is independent of motion in the x or z directions
• Motion in the z direction is independent of motion in the x or y directions.
Nerf Gun Experiment
• In class, a nerf gun was fired horizontally from a height of 3’10” and struck the ground at a distance of 16’10”.
• Calculate the muzzle velocity of the projectile.
• Calculate the time of flight of the projectile.

Neglecting aerodynamic drag, the projectile leaves the muzzle with a velocity vo = vox.

• The projectile as it leaves the muzzle has no velocity in the y-direction, i.e. voy = 0.
• The only force on the projectile after it leaves the muzzle is the force of gravity.
• The acceleration in the y direction (up and down) is g = 32.2 ft/s2.

Knowing the initial y component of velocity is 0, the acceleration in the y direction is 32.2 ft/sec2, and the distance to the floor is 3’10”,

• 3’10” = 3.833 ft = y – yo
• ay = 32.2
• y = yo+ voyt +0.5ayt2
• 3.833 = 0.5 x 32.2 x t2
• t = 0.488 sec

In that time of 0.488 sec, the projectile travels

• 16.833 ft in the horizontal direction.
• vx = 16.833/0.488 = 34.49 ft/sec
• So the muzzle velocity is 34.49 ft/sec
Elevated Nerf Gun
• Consider the same nerf gun, but now elevated at an angle of ϴ⁰ to the horizontal.
• The muzzle velocity is vo
• The horizontal velocity vox = vocosϴ
• The vertical velocity is voy= vosinϴ
• vyvo
• vx

The only force acting on the projectile after it leaves the muzzle is gravity – in the y-direction.

• The projectile will arc up, stop rising, and arc down to hit the ground.
• We can then calculate how high the projectile will rise and the time it takes to reach that maximum height.

vy2 = voy2 + 2ay(y – yo)

• voy = vosinϴ
• ay = - g
• vy2 = vo2sin2ϴ + (2)(-32.2)(y – yo)
• If ϴ = 30⁰ and vo = 28.0 ft/sec
• 0 = (28.0)2 (0.5)2 – 64.4 (y – yo)
• (y – yo) = 3.04 ft

To calculate the time for the velocity in the y-direction to go from (14) ft/sec to 0,

• vy = voy + ayt
• 0 = 14 – (32.2)t
• t = 0.435 sec
• The projectile then begins to fall and it takes another 0.435 sec for it to hit the ground. A total time of flight of (2)(0.435) = 0.87 sec

During that entire 0.87 sec, the projectile is moving in the x-direction at its initial speed.

• There is no force in the x-direction causing it to speed up or slow down.
• Its speed in the x- direction is (28)(0.866) ft/sec = 24.25 ft6/sec
• In 0.87 sec, the projectile travels (0.87)(24.25)
• = 21.1 feet in the x-direction before it impacts the ground!
Review
• Motion in 2 dimensions
• X component
• Y component
• Motion in 3 dimensions
• X component
• Y component
• Z component

Motion in x direction is independent of motion in y direction and z direction.

Separate set of equations of motion for each direction.

Class Activity
• Consider a rifle with a muzzle velocity of 3,000 ft/sec firing at ϴ⁰ to the horizontal.
• Calculate the range and time to impact as a function of ϴ.
• Create an excel worksheet and plot range vsϴ.
• At what value of ϴ would you get the maximum range? Analytically and graphically!