1 / 18

Motion II

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.

jules
Download Presentation

Motion II

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Motion II 2 and 3 dimensional motion

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

  3. Motion in x direction is independent of motion in y direction and z direction. Separate set of equations of motion for each direction.

  4. 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)

  5. az= Fz/ m • vz = voz + axzt • z = zo+ vozt+ (1/2)azt2 • vz2 = voz2 + 2az(z – zo)

  6. Independence of x, , 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.

  7. 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.

  8. 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.

  9. 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

  10. 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

  11. 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

  12. 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.

  13. 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

  14. 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

  15. 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!

  16. Review • Motion in 2 dimensions • X component • Y component • Motion in 3 dimensions • X component • Y component • Z component

  17. Motion in x direction is independent of motion in y direction and z direction. Separate set of equations of motion for each direction.

  18. 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!

More Related