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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
This lab provides a heads- and hands-on learning experience in applying Newton’s First (N1) and Newton’s Third (N3) Laws to simple mechanics experiments. It will also provide practice in drawing force motion-vector diagrams and time-sequential snapshot sketches which are very helpful in understanding mechanics. You will learn "to reason nimbly and judiciously about figure, force and motion...(thus being)...never at rest...(and getting) ...over every rub." As you go through this lab you may wish to refer to the NI and N3 diagrams hanging above your table.
A. OBJECTIVES – To Understand:
1. how to draw color-coded force-motion-vector diagrams and time-sequential snapshot sketches; 2. operational definitions: vertical, horizontal, force, up, down, equilibrium;
3. the two kinds of forces considered in elementary mechanics problems: contact (touching) and action-at-a-distance (non-touching);
4. the application of Newton’s first and third laws to simple mechanics experiments: a. an iron disk held stationary,
b. an iron disk lifted vertically upward at constant velocity,
c. an iron disk lifted vertically upward with an increasing velocity,
d. an iron disk carried horizontally at constant velocity,
e. a block at rest on a table,
f. a block pushed across a table at constant velocity,
g. a block sliding to rest on a table,
h. a block projected horizontally into the air,
Instructions (similar to webpage)
Print Document (Has all of the Images from below, no questions)
How to Prepare for Lab
How to Prepare for Lab
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Newton’s first law (N1L)
Newton’s third law (N3L)
Forces:
Equilibrium - we adopt the conventional definition of "equilibrium" such that a body is in equilibrium in a reference frame if and only if its vector velocity v as observed in that reference frame is constant in time).
I. Introduction
I. Introduction
A. HOW TO DRAW A FORCE VECTOR
A. HOW TO DRAW A FORCE VECTOR
In order to draw a vector representing, say, the force F on a block by a stick, draw a RED arrow (Vector) with the Vector Tail On the Body (VTOB) and label it F on block by stick as shown in the figure below. The vector tail should be indicated by a large dot •.
Fig. 1. A woman pushes on a stick which in turn pushes on a block, so that there is a force F on the block by stick, written with subscripts as F on block by stick. Please practice the color code by coloring the block yellow and the force vector red.
It is helpful in understanding Newtonian mechanics if:
We focus on just one body, in this case the BLOCK, and then systematically apply Newton’s First (N1) or Second (N2) laws to that body. Application of N1 or N2 requires drawing in ALL the forces acting ON the body, and then taking the vector sum of all those forces. To assist this focus, please color the the block of Fig. 1 YELLOW. In this way, the usual "free-body diagram" can be embedded in a "touch-body diagram" (see Fig. 2) which shows the body and all objects which touch the body. Most of the diagrams you will draw in SDI labs will be of the touch-body type.
We distinguish between contact (TOUCHING) forces and non-contact (NON-TOUCHING, or "action-at-a-distance," or "field") forces. Thus, we do NOT say that the force is "on the block by the woman." The reason is that the woman is NOT touching the block, and we want to classify forces as either touching forces or non-touching forces. The force F on block by stick is a touching force which is applied on the block by the stick.
Questions to Consider:
1. Is there any possibility of other significant touching forces acting on the block of Fig. 1? {Y, N, U, NOT} {Yes, No, Uncertain, None Of These}
2. Is there any possibility of some significant non-touching forces acting on the block of Fig. 1? {Y, N, U, NOT}
The length of the vector arrow should be proportional to the magnitude of the vector quantity. Thus in Fig. 1, if the magnitude of the frictional force f on block by floor (the use of the lower case f for frictional forces is fairly conventional) is about the same as the magnitude of the force F on block by stick, then the vector force diagram should show these two vectors with about the same lengths as shown below in Fig 2.
Fig. 2. A touch-body diagram showing the block and all the objects which touch the block. The magnitudes of the friction force f on block by floor and the force F on block by stick are about the same, as indicated by the equal lengths of the two vector arrows representing these two forces. Please practice the color code by coloring the block yellow and the force vectors red.
You will find that Newton’s-third-law action-reaction pairs are relatively easy to distinguish if you always use the "on A by B" designation indicated above. Then remember that AN ACTION REACTION PAIR NEVER ACTS ON THE SAME BODY, and that Newton’s third law can be stated succinctly as
F on A by B = – F on B by A . .............................................................. (N3)
In introductory mechanics, one can ALWAYS (!!) obtain the Newton’s-third-law action reaction pair by using the "A-B-Switch" method! (We ignore, for the moment, transient effects associated with wave propagation.)
II. FORCES EXERTED ON A DISK BY YOUR HAND
II. FORCES EXERTED ON A DISK BY YOUR HAND
A. DISK AT REST
A. DISK AT REST
Hold an iron disk (a standard lab disk of mass1-kg) stationary in the lab frame on the palm of your hand at about eye level. In the space below show ALL the force vectors (colored red !) acting on the disk (colored yellow!). Draw the velocity vector (colored green) if you think it exists or as a green dot on the disk if you think it is zero.
You will move a long way towards the Newtonian world if you can determine ALL the forces acting ON a BODY. To do this successfully always ask yourself TWO KEY QUESTIONS*:
(1) What objects TOUCH the BODY? Only these can transmit contact forces. (It must be realized that touching is a necessary but not a sufficient condition for the transmission of a contact force, i.e., two bodies may touch without there being significant contact forces between them.)
(2) What non-touching ("action-at-a-distance") forces act on the BODY? Usually only the gravitational force F on body by Earth (i.e., the "weight," often labeled W on body by Earth) is significant.
FORCES ON A DISK HELD STATIONARY IN YOUR HAND
Fig. 4. A touch-body FRONT VIEW of a disk held stationary on your hand in the lab frame. The clock symbol is meant to show that the spatial positions of the disk and hand are constant in time.
Near the surface of the Earth the 1.0 kg iron disk weighs 9.8 N or 2.2 lb. Complete the following sentences which describe the above simple experiment:
1. A downward force of magnitude 9.8 N is exerted on the disk by________________ . (It may help in answering subsequent questions to label the force as W on A by B in the above diagram.)
2. An upward force of magnitude _____ is exerted on the ______ by the hand. (It may help in answering subsequent questions to label the force as N on A by B in the above diagram.)
* This touch method of determining the forces is due to Joan Heller and Fred Reif (HR) who showed its remarkable effectiveness in carefully controlled experiments at Berkeley. The "HR Strategy" also involves checking to make sure that ∑F and the acceleration (a) of the body are in the same direction, as will be discussed in SDI Lab #2.3. Do the two forces W and N constitute a Newton’s-third-law (N3) action-reaction pair? {Y, N, U, NOT} [HINT: Please carefully STUDY (a) "How to Determine the Newton’s Third Law Action-Reaction Pair," and (b) the Newton’s Third Law diagram hanging above your table (or at the back of this manual) before answering this question!]
4. That forces W and N are equal and opposite is an example of Newton’s law. Does the equality of these forces depend on the fact that the disk has a constant (zero) vertical velocity? {Y, N, U, NOT}
5. The reaction force (call it F 5) to force N is a force of magnitude _________ , exerted on _____ by ______ . Its direction is ______________ .
(It may help in answering subsequent questions to label the force as F 5 on A by B in the diagram below. The "5" refers to the number of this question."
N3 ACTION-REACTION PAIR N AND F 5 (A labeled sketch of the N3 pair is worth a teraword.)
6. That forces N and F 5 are equal and opposite is an example of Newton’s law. Does the equality of these forces depend on the fact that the disk has a constant (zero) vertical velocity? {Y, N, U, NOT}
7. The reaction force (call it F 7) to the forceW is a force of magnitude ________ , exerted on the ______ by the _______. Its direction is ____________________ .
(It may help in answering subsequent questions to label the force as F 7 on A by B in the diagram below.) N3 ACTION-REACTION PAIR W AND F 7 (A labeled sketch of the N3 pair is worth a teraword.)
8. In this experiment, what are the forces which are directly felt by your hand? (Indicate them as F on A by B.)
B. FORCES ON A DISK LIFTED VERTICALLY UPWARD AT CONSTANT SPEED
B. FORCES ON A DISK LIFTED VERTICALLY UPWARD AT CONSTANT SPEED
Fig. 4. Snapshot sketches of a disk at equal time intervals during its motion. The disk is lifted vertically upward at a constant speed with respect to (wrt) the lab frame. As a result, the disk travels the same distance in the second time interval as it did in the first time interval.
Show ALL the force vectors (red) acting on the disk at these three positions. Show the vector tails as dots "•" near the center of the disk.
Draw velocity vectors (green) at each of the three positions. Again, show the vector tails as dots "•" on the disk, but offset the dots from the center so that they do not lie on top of the force vector tails.
Since your 3 sketches show the disk at 3 instants of time ("clock readings") during its motion, these drawings might be called "snapshot sketches" because they’re similar to snapshots taken with a camera. Henceforth, in SDI labs we shall often refer to such drawings as "snapshot sketches."
1. Is the disk sketched above in equilibrium in the lab frame? {Y, N, U, NOT} [HINT: Please consider the definition of "equilibrium" 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. How would the answers you gave in the disk stationary in the palm of your hand change for this case in which the disk is moving at a constant non-zero vertical velocity in the palm of your hand?
3. Specifically, for the non-zero constant vertical velocity case, is the force on the block by the hand equal to the force on the hand by the block? {Y, N, U, NOT} This is an example of Newton’s _______ law.
C. FORCES ON A DISK LIFTED VERTICALLY UPWARD AT A UNIFORMLY INCREASING SPEED
C. FORCES ON A DISK LIFTED VERTICALLY UPWARD AT A UNIFORMLY INCREASING SPEED
Fig. 5. Snapshot sketches of a disk at equal time intervals during its motion. The disk is lifted vertically upward at a uniformly increasing speed with respect to the lab frame. As a result, the disk travels a greater distance in the second time interval than in the first time interval.
Lift the disk vertically upward so that its speed wrt the lab frame continuously and UNIFORMLY increases, i.e., the velocity increases continuously by equal amounts in equal intervals of time (this is the definition of motion at constant acceleration). Fig. 5 shows the disk and your hand while they are in motion at 3 positions: near the start, middle, and end of the increasing velocity v motion. Show ALL the force vectors acting on the disk at these 3 positions. Draw velocity vectors at each of the 3 positions.
1. Is the disk 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: 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. Is the force exerted on the disk by your hand equal and opposite to the force exerted on the disk by the Earth? {Y, N, U, NOT} (This illustrates Newton’s ____ law.)
3. Is the force exerted on the disk by the Earth equal and opposite to the force exerted on the Earth by the disk? {Y, N, U, NOT} (This illustrates Newton’s ____ law.)
4. Is the force exerted on the disk by your hand equal and opposite to the force exerted on your hand by the disk? {Y, N, U, NOT} (This illustrates Newton’s ____ law.)
5. Is it necessary that the force exerted on the disk by your hand be continuously increasing with time in order that the disk’s velocity be continuously increasing in time? {Y, N, U, NOT}
6. In this experiment, what are the forces which are directly felt by your hand? (Indicate them as F on A by B.)
D. CARRYING THE DISK AT CONSTANT HORIZONTAL VELOCITY
D. CARRYING THE DISK AT CONSTANT HORIZONTAL VELOCITY
Holding the disk at about eye level walk about 2 m at a nearly constant horizontal velocity v (i.e., in a straight line at constant speed). The figure below shows the disk at three positions in its constant v motion. Show ALL the force vectors acting on the disk at these 3 positions. Draw velocity vectors at each of the 3 positions. Here again, these are "snapshot sketches."
Fig. 6. Snapshot sketches of a disk at equal time intervals during its motion. The disk is carried horizontally at a constant speed with respect to the lab frame. As a result, the disk travels the same distance in the second time interval as it did in the first time interval.
1. Is the disk 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: 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. Is there a NET horizontal force ("NET horizontal force means the vector sum of all the horizontal forces) acting on the disk? {Y, N, U, NOT}
3. Is there a horizontal force acting on the disk? {Y, N, U, NOT}
4. If your answer to "3" is "Yes" explain how your answers to "2" and "3" are consistent. If your answer to "3" is "No," can you think of any special way of carrying the disk at constant v with respect to the lab frame of reference so that there would be a horizontal force on the disk? {Y, N, U, NOT}
5. Is the net force exerted on the disk by your hand equal and opposite to the force exerted on the disk by the Earth? {Y, N, U, NOT} (This illustrates Newton’s law.)
6. Is the force exerted on the disk by the Earth equal and opposite to the force exerted on the Earth by the disk? {Y, N, U, NOT} (This illustrates Newton’s ______ law.)
7. Is the net force exerted on the disk by your hand equal and opposite to the net force exerted on your hand by the disk? {Y, N, U, NOT} (This illustrates Newton’s ______ law.)
8. In this experiment, what are the forces which are directly felt by your hand? (Indicate them as F on A by B.)
III. FORCES EXERTED ON A WOODEN BLOCK BY A TABLE
III. FORCES EXERTED ON A WOODEN BLOCK BY A TABLE
A. BLOCK AT REST
A. BLOCK AT REST
Place a wooden block so it is at rest (with respect to the lab frame) on a table. The figure below shows the block and the table top. Show ALL the force vectors acting on the block. Draw velocity vectors if you think they exist.
FORCES ON A BLOCK AT REST ON A TABLE
Fig. 7. A touch body FRONT VIEW of a block at rest on a table in the lab frame. The clock symbol is meant to show that the spatial positions of the block and table are constant in time.
1. Is the block 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: 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. Is the force exerted on the block by the table equal and opposite to the force exerted on the block by the Earth? {Y, N, U, NOT}* (This is an example of Newton’s law.
- *Here and throughout this lab, please recall the and abide by the ground rules for SDI labs set forth in the Introduction and recall that a curly bracket {.......} indicates that you should ENCIRCLE O a response within the bracket and then, we INSIST, briefly EXPLAIN or JUSTIFY your answers in the space provided on these sheets. The letters {Y, N, U, NOT} stand for {Yes, No, Uncertain, None Of These}.
B. BLOCK PUSHED AT CONSTANT VELOCITY
B. BLOCK PUSHED AT CONSTANT VELOCITY
Push the block across the table with a nearly constant horizontal velocity v . Fig. 7 shows your hand and the block at 3 positions on the table while it is in motion: near the start, middle, and end of the constant-velocity motion. Show ALL the force vectors acting on the block at these three positions. Draw velocity vectors at each of the three positions if you think they exist.
FORCES ON A BLOCK PUSHED AT CONSTANT VELOCITY ON A TABLE
Fig. 7. Snapshot sketches of a block at equal time intervals during its motion. The block is pushed across a table at a constant horizontal velocity v with respect to the lab frame. As a result, the block travels the same distance in the second time interval as it did in the first time interval.
1. Is the block 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. Is there a NET horizontal force vector acting on the block? (Remember that NET horizontal force means the vector sum of all the horizontal forces.) {Y, N, U, NOT}
3. Is there a horizontal force vector acting on the block? {Y, N, U, NOT}
4. Is the NET force exerted on the block by the table equal and opposite to the force exerted on the block by your hand? {Y, N, U, NOT} [Hint: A labeled sketch in one of the snapshots of Fig. 7 would be worth a teraword!]
5. How does the force on the block by the hand compare with the force on the hand by the block?
C. BLOCK SLIDING TO REST
C. BLOCK SLIDING TO REST
Give the block a tap (impulsive force) with your hand in a horizontal direction such that it slides about 3 ft (1 m). In Fig. 8 below show ALL the force vectors acting on the block at the 3 positions shown. Draw velocity vectors at each of the three positions.
FORCES ON A BLOCK SLIDING TO REST ON A TABLE
Fig. 8. Snapshot sketches of a block at equal time intervals. The block is given an initial tap so that it slides to rest on the table. The block is shown on the table at 3 positions after it has left your hand and while it is in motion: near the start, near the middle, and near the end of its slide. That the block is slowing down is shown by the fact that the displacement during the second time interval (t3 - t2) is less than the displacement during the first time interval (t2 - t1). (Compare the snapshot sketches for Ground Rule #5 in Sec. I- C of SDI #0.1 where a block is speeding up.)
1. Is the block 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: 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. Is the NET force exerted on the block by the table equal and opposite to the force exerted on the block by the Earth? (here "NET force exerted on the block by the table" means the vector sum of all force components exerted on the block by the table). {Y, N, U, NOT} [Hint: A labeled sketch in one of the snapshots of Fig. 8 would be worth a teraword!]
3. Is the NET force exerted on the block by the table equal and opposite to the NET force exerted on the table by the block? {Y, N, U, NOT} This is an example of Newton’s Law.
D. BLOCK PROJECTED INTO THE AIR
D. BLOCK PROJECTED INTO THE AIR
Suppose you were to give the block a vigorous push (an "impulsive force," i.e., a force acting only over a very small time interval ∆t ) with your hand in a horizontal direction so that it slides across the table, is projected horizontally into the air, and hits the floor at a distance from the base of the table which is about equal to the height of the table. In the space below show your prediction for the path of the block along the table top and through the air to the floor. (Always represent paths as continuous straight or curved lines, not a series of arrows.)
PREDICTION: PATH OF BLOCK PROJECTED HORIZONTALLY INTO THE AIR
1. Now have your lab partner perform the above experiment AFTER you have stationed yourself so that you can carefully observe the path of the block from a position such that your line of sight is perpendicular to the plane of the motion. Draw the observed path as a continuous line in the space on the next page. Does it agree with your prediction? {Y, N, U, NOT}
EXPERIMENTAL RESULTS: PATH OF BLOCK PROJECTED HORIZONTALLY INTO THE AIR.
2. In the above figure, sketch the block at 4 positions along the path after it has left the table: at the instant it leaves the table; 1/4, 1/2, and 3/4 of the distance to the floor. At these (or any other positions along the path), is there any necessary relationship between the direction of the path and the direction of of the block’s velocity v ? {Y, N, U, NOT}
3. Draw horizontal vx , vertical vy , and resultant vR (same as v in "2") velocity vectors at these 4 positions. Here it is convenient to show the velocity vector tails at the center of the block.
4. Show ALL the force vectors acting on the block at these 4 positions with their tails on the block but displaced from its center. (At these low speeds the frictional force on the block by the air is negligible.)
5. Is the block 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: 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.]
6. Is there a NET horizontal force acting on the block? {Y, N, U, NOT}
7. Is there a horizontal force acting on the block? {Y, N, U, NOT}
8. Is there a NET vertical force acting on the block? {Y, N, U, NOT}
9. Is there a vertical force acting on the block? {Y, N, U, NOT}
10. At the instant (call it t = 0) that the block leaves the table (first snapshot above), does the block (regarded as a point particle, i.e., in the limit as the block becomes very small with respect to other lengths in the experiment):
a. experience a vertical force? {Y, N, U, NOT}
b. have a vertical acceleration? {Y, N, U, NOT}
c. have a vertical velocity? {Y, N, U, NOT}
V. BLOCK PROJECTED INTO THE AIR - PhET Simulation
Please complete the preceding Section IV "Forces Exerted on a Wooden Block ....." and discuss them with your teacher before starting this section!
Open PhET Projectile Motion. On the LAB tab, play around with the program until you understand the various controls and readouts. Trajectory displays a ball, but the physics of a projected block is the same as that of a projected ball for the experiment.
Note that the range of selectable values for the the mass of the ball (block) m (1 - 31 kg), launch angle θ (-5° - 90°), launch height H (0 - 15 m), and launch speed vo( 0 - 30 m/s) span the actual values as experienced in the lab. Thus simulations of the motion investigated in Sec. IV-D are possible, except that the motion as seen on the computer screen is slower than in the lab. (Note, however, that the time readout on the computer screen is the elapsed time interval ∆t for the actual lab motion, not the much larger time interval ∆T as observed by someone watching the slow-motion animation.) The magnitude of the acceleration a due to the earth’s gravitational force W on block by Earth is normally set at g = 9.8 m/s2, but can be changed over the range 0.1 < g < 20 m/s2 if you wish to simulate, say, the motion of the block on the moon (g = 1.7 m/s2) or on Jupiter (g = 19 m/s2).
1. Simulate the experiment done in Sec. IV-D by setting the time t = 0, g = 9.8 m/s2, m = 0.10 kg, launch angle θ = 0.00°, and launch height H = 1.00 m. Set the launch speed vox such that the Range R = 1.0 m. Here R is defined to be the horizontal distance moved from takeoff to landing as indicated by the black trajectory curve. For future reference, record in the blank the required value vox = m/s.
a. Click on the Action "Fire." Indicate the computer’s reading of the time interval T = sec for the block to traverse this trajectory. Qualitatively describe the time dependence of the horizontal, vertical, and resultant velocities:
(1) v x
(2) v y
(3) v R
b. Are the above time dependencies above consistent with your snapshot sketches in Block Projected into Air? (Use the time slider to move the ball to any point on its trajectory. Select the option Track Ball to keep all vectors visible throughout the trajectory.) {Y, N, U, NOT} If your answer is not "Yes," please justify the lack of consistency.
c. The computer picture at t = 0.00 sec duplicates the conditions of question #10 in Block Projected into Air: the ball/block (considered as a point particle) is shown at the instant it leaves the table. Are your responses to #10 consistent with the computer picture? {Y, N, U, NOT} If your answer is not "Yes," please justify the lack of consistency.
2. Return to the parameter values of "1". Can you predict the qualitative influence on the trajectory if the mass m is increased to 0.20 kg, leaving all the other parameters the same? {Y, N, U, NOT}
a. Increase the mass m as above and watch the position of the black trajectory curve. Is your prediction verified? {Y, N, U, NOT} Can you explain the results? {Y, N, U, NOT}
3. Return to the parameter values of "1". Indicate in the blank your prediction for the time T = sec taken for the block to traverse a longer trajectory with a range R = 4.0 m (obtained by increasing vox, leaving all other parameters the same.
a. Increase the range R as above by increasing the launch speed vo. Click on the Action "Throw Ball." Is your prediction verified? {Y, N, U, NOT} Can you explain the results? {Y, N, U, NOT}
4. Return to the parameter values of "1". Can you predict the qualitative influence on the trajectory of decreasing the value of g to its value on the moon, g = 1.7 m/s2, leaving all other parameters the same? {Y, N, U, NOT}.
a. Decrease g as above and click on "Throw Ball." Adjust the Zoom as necessary to view the trajectory. Is your prediction verified? {Y, N, U, NOT} Can you explain the results? {Y, N, U, NOT}
Newton's First Law
Newton's First Law
Newton's Third Law
Newton's Third Law
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