A Vulgar Mechanic can practice what he has been taught or seen done, but if he is in error he knows not how to find it out and correct it, and if you put him out of his road, he is at a stand; Whereas he that is able to reason nimbly and judiciously about figure, force and motion, is never at rest till he gets over every rub. Isaac Newton to Nathaniel Hawes, 25 May 1694
VI. FORCES ON A MASSIVE GLIDER FLOATING ON AIR TRACK
Anywhere the lab describes a large chunk of ‘Dry Ice’, please refer to the glider on the air track.
In the figure below, the separation between the air track and the glider has, of course, been exaggerated.
FORCES ON A GLIDER AT REST OVER AIR TRACK
1. Is there a contact force on the glider by the track? {Y, N, U, NOT} [HINT: What’s TOUCHING the glider? Move the glider to a new resting position over the air track and quickly slide a smooth piece of paper between the track and the glider!]
2. In the above figure, show ALL the force vectors acting on the glider. Draw velocity vectors if they exist.
With the glider initially at rest in the lab frame, give the glider a tap (an "impulsive force," i.e., a force acting only over a very small time interval ∆t) with your hand in a horizontal direction such that the glider slides over the air track. Sketch the glider over the air track at 3 positions while in motion after the glider has left your hand: near the start, middle, and end of its horizontal motion. Show all the F and v vectors in the snapshot sketches below.
FORCES ON AND VELOCITIES OF A GLIDER TAPPED AFTER INITIALLY BEING AT REST
1. Is the glider sketched above in equilibrium in the lab frame? {Y, N, U, NOT} [HINT: Please consider the definition of "equilibrium" in Sec. II-F before answering this question.]
2. In the above sketch, is there a NET horizontal force vector on the glider? {Y, N, U, NOT}
3. In the above sketch, is there a horizontal force vector on the glider? {Y, N, U, NOT}
Suppose you were to give the glider a push so that it moves along a straight line with a nearly constant velocity v . Can you propose a good method to continuously and uniformly slow the glider down to nearly zero velocity? ("Continuously and uniformly slow the glider down" means that the velocity of the glider decreases continuously by equal amounts in equal intervals of time, i.e., the acceleration is constant) {Y, N, U, NOT} The snapshot sketches below show the glider while in motion after the initial push: at times near the start, middle, and end of its uniformly decreasing-velocity motion. Show all the F and v vectors in the snapshot sketches below. Justify your above answer by indicating your method in the sketches.
PROPOSED METHOD FOR CONTINUOUSLY AND UNIFORMLY SLOWING THE GLIDER DOWN
1. Try out your method. Does it work? (You may or may not wish to reorient the V-H axes shown in the drawing.) {Y, N, U, NOT}
2. If you didn’t answer "Y" to the above question, then discover a good method experimentally and sketch the method below. Show all the F and v vectors in the snapshot sketches. ACTUAL METHOD FOR CONTINUOUSLY AND UNIFORMLY SLOWING THE glider DOWN
3. Explain your method in terms of N1.
Suppose the glider is initially stationary. Can you propose a good method to continuously and uniformly speed the glider up to some relatively high velocity? ("Continuously and uniformly speed the glider up" means that the velocity of the glider increases continuously by equal amounts in equal intervals of time, i.e., the acceleration is constant) {Y, N, U, NOT} (You may or may not wish to reorient the V-H axes shown in the drawing.) Show all the F and v vectors in the snapshot sketches below. Justify your above answer by indicating your method in the sketches.
PROPOSED METHOD FOR CONTINUOUSLY AND UNIFORMLY SPEEDING THE GLIDER UP
1. Try out your method. Does it work? {Y, N, U, NOT}
2. If you didn’t answer "Y" to the above question, then discover a good method experimentally and sketch the method below. Show all the F and v vectors in the snapshot sketches.
ACTUAL METHOD FOR CONTINUOUSLY AND UNIFORMLY SPEEDING THE GLIDER UP - Sketch this on the diagram above.
3. Explain your method in terms of N1.
1. Suppose that you were to hitch a flea to a glider which is initially at rest. Could the flea continuously increase the velocity of the glider up to some value easily visible to the unaided eye? {Y, N, U, NOT} (Your lab instructor will take bets.)
a. In considering this problem would you be justified in ignoring the small frictional force f on glider by gas? {Y, N, U, NOT}. [HINT: Pretend you are a flea trying to accelerate a glider. Would the frictional force be of any concern to you? {Y, N, U, NOT}]
b. Assume the glider is initially at rest. Can you figure out what physical parameters would determine whether or not the flea could accelerate the glider? {Y, N, U, NOT}
HINT #1: Sketch a thought experiment in which the flea is on the verge of accelerating the glider. HINT #2: Ignore mharness, since mharness<< mglider. Then the force Fon harness by flea is just equal to the tension T in the harness and Fon glider by harness = T = Fon harness by flea.
FLEA IS ON THE VERGE OF ACCELERATING THE GLIDER
c. Suppose the flea were able to move the glider with a constant acceleration a starting at a time t = 0. Can you figure out what physical parameters would determine the velocity v of the glider at some given time τ during the constant a motion? {Y, N, U, NOT}
HINT #1: Sketch a thought experiment in which the flea is accelerating the glider.
2. Try the above experiment and use force-motion-vector snapshot sketches to indicate the results in the space on the next page. Show the harness and the flea. Do your results agree with your prediction? {Y, N, U, NOT} (If you can’t find a flea or have trouble making a harness, then conduct and sketch a "thought experiment.")
CHECK ONE:
A FLEA DOES ______ , DOES NOT____ ACCELERATE AN INITIALLY STATIONARY GLIDER
1. Can a truck driver ‘pin’ (stuck) kids to their seats by driving his truck at very high constant velocity v as suggested in the cartoon above? {Y, N, U, NOT} [HINT: It may help to consider your earlier experience, Sec. III-D, in carrying a disk across a room at constant speed in a straight line.]
2. The schematic diagram below shows a kid in her seat in a truck. Three successive positions of the kid and seat are shown in the Earth’s frame of reference, as the truck moves forward at very high constant horizontal velocity v . Draw ALL the force vectors acting on the kid at these 3 positions. Show the velocity vectors in the 3 positions if they exist.
FORCES ON A KID SITTING IN A TRUCK MOVING AT A HIGH CONSTANT VELOCITY
3. Is the kid sketched above in equilibrium as seen by an observer in the Earth frame of reference? {Y, N, U, NOT} [HINT: In answering this and latter questions please recall that in SDI labs we adopt the conventional definition of "equilibrium" such that a body is in equilibrium in a given reference frame if and only if its vector velocity v as observed in that reference frame is constant in time.]
4. Is the kid sketched above in equilibrium as seen by an observer in the Truck frame of reference? {Y, N, U, NOT}
5. Is the Truck frame of reference an inertial reference frame (IRF) (i.e., a frame in which Newton’s First Law is obeyed as determined by an observer riding with the frame)? {Y, N, U, NOT}
6. Is there a NET horizontal force vector acting on the kid? ("NET horizontal force vector" means the vector sum of all horizontal forces acting on the kid.) {Y, N, U, NOT}
7. Is it possible that a horizontal force vector could act on the kid? {Y, N, U, NOT} 8. Is the kid pinned to her seat? {Y, N, U, NOT}
A. HOLD TWO MAGNETS.
Hold two permanent magnets, one in each hand and as far apart as possible. Slowly bring the two magnets together. Play around so as to determine magnet orientations for maximum attraction and magnet positions so close (a millimeter or so) that you can barely keep them from touching.
In order to understand the physics of this situation, it is essential that you draw a LARGE LABELED DIAGRAM. In the space below draw a "FRONT VIEW" ( i.e., the view of an observer whose line of sight is horizontal) of both magnets [labeled "#1"(solid lines) and " #2"(dashed lines)] in this maximum attraction position. For simplicity orient the magnets so that the magnetic force (call it M) between them is horizontal. Draw the fingers of the hand holding magnet #1.
According to N1 and N2, the motion of magnet #1 depends on ALL the forces acting ONLY on magnet #1. Therefore, show ALL the force vectors acting ONLY on this magnet #1 (don’t forget the subscript designation "on #1 by________").
Hint #1: To assist your concentration in applying N1 to magnet #1, color ONLY that body yellow.
Hint #2: Don’t forget the reference axis V-H!
Hint #3: It’s useful to consider separately the vertical and horizontal components of the forces.
Hint #4: Although your fingers may pinch the magnet with relatively large opposing forces, it’s simplest to only show the unbalanced forces F net vertical on magnet #1 by hand (call this simply N on #1 by hand) and F net horizontal on magnet #1 by hand (call this simply f on #1 by hand) .
FORCES ON MAGNET #1 HELD VERY CLOSE TO ATTRACTING MAGNET #2
1. Is magnet #1 in equilibrium in the lab frame? {Y, N, U, NOT} [HINT: Please consider the definition of "equilibrium" in Sec. II-F before answering this question: a body is in equilibrium in a given reference frame if and only if its vector velocity v as observed in that reference frame is constant in time.]
2. What body or bodies are TOUCHING magnet #1? (Study your diagram !!) (Only these can exert contact forces!!).
3. Are there any force vectors shown in your drawing which are due to interaction with bodies which DO NOT TOUCH magnet #1? (Study your diagram!!) {Y, N, U, NOT}
4. Are the relative force-vector magnitudes (as shown by the relative lengths of the vector arrows) in your sketch above consistent with Newton’s first law (NI)? {Y, N, U, NOT} [HINT #1: Study the Newton’s First Law diagram hanging above your table (also at the back of this manual). HINT #2: Consider N1 first along the vertical axis and then along the horizontal axis.]
5. Are there any "magnetic" forces acting on magnet #1? {Y, N, U, NOT} If so, indicate them in an F on A by B manner:
6. Are there any "gravitational" forces acting on magnet #1? {Y, N, U, NOT} If so, indicate them in an F on A by B manner:
7. If you answered "No" to both "5" and "6," or "No" to one of "5" and "6," please explain your reasoning. If you answered "Yes" to both "5" and "6," should the lengths of the vectors in "5" and "6" be about the same? {Y, N, U, NOT} Can you think of an experimental method which would roughly indicate the relative magnitudes of the magnetic and gravitational forces acting on magnet #1? {Y, N, U, NOT}
8. In this experiment, what are the forces which are directly felt by your hand? (Indicate them as F on A by B.)
9. Considering your answers to questions 1 - 8 above, do you think that non-touching (i.e., "non contact," "action-at-a-distance," or "field" ) forces actually exist? {Y, N, U, NOT}