FRAMES OF REFERENCE

Film Loop: Galilean Relativity II: Object dropped from aircraft.

Length: 3:40 min., Black and White, No sound

A Cessna 150 aircraft 23 feet long is moving at about 100 ft/sec at an altitude of about 200 feet. A flare is dropped from the aircraft; the action is filmed from the ground. Scene 1 shows part of the flare's motion; Scene 2, shot from a greater distance, shows several flares dropping into a lake; Scene 3 shows the vertical motion viewed head-on. Certain frames of the film are "frozen" to allow measurements. The time interval between freeze frames is always the same.

In the earth frame, the motion is that of a projectile whose original velocity is the plane's velocity. The motion should be a parabola in this frame of reference, assuming that gravity is the only force acting on it. (Can you check this?) Relative to the plane, the motion is that of a body falling freely from rest. In the frame of reference of the airplane, is the motion vertically downward?

The plane is flying approximately at uniform speed in a straight line,but its path is not necessarily a horizontal line. The flare starts with the plane's velocity in magnitude and direction. We expect the downward displacement to be d=1/2 a(t squared). But we cannot be sure that the first freeze frame is at the instant the flare is dropped. The time, t, is conveniently measured from the first freeze frame. If a time B has elapsed between the release of the flare and the first freeze frame, we have, d=1/2 a((t+B) squared). So if we plot square root of dagainst t, we expect a straight line. Why? If B=0, this straight line will pass through the origin.

Project Scene 1 on paper. At each freeze frame, when the motion on the screen is stopped briefly, mark the positions of the flare and the aircraft cockpit. Measure the displacement d of the flare below the plane. Use any convenient unit. The times can be taken as integers, t=0, 1, 2, . . .designating successive freeze frames. Plot d versus t. Is the graph a straight line? What would be the effect of air resistance, and how would this show up in your graph? Can you detect any signs of this? Does the graph pass through the origin?

Analyze Scene 2 in the same way. Make two graphs from Scene 2, plotting time intervals horizontally and displacements vertically. Use one color for horizontal displacement as a function of time, and another color for vertical displacement versus time.

From our equation square root of d = (square root(1/2 a)) (t+B), the acceleration is twice the square of the slope. To convert into ft/(sec)(sec) or m/(sec)(sec) use the length of the plane and the slow-motion factor.