VELOCITY

and

ACCELERATION

QUESTION SHEET

 

(To be done before the experiment by reading the introduction to the experiment. [below]]

 

1. What will you be analyzing in this experiment?

__________________________________________________________

__________________________________________________________

2. What is indicated when:

The dots are far apart on the timer tape?

__________________________________________________________

__________________________________________________________

The dots are close together on the timer tape?

__________________________________________________________

__________________________________________________________

3. IF the spaces between the dots are going to indicate how fast the tape is going, what do you have to assume about the rate at which the timer is moving, that you are going to use in this experiment?

    __________________________________________________________

        __________________________________________________________

4. What will be a tic of time in this experiment?

__________________________________________________________

__________________________________________________________

5. What unit will be used to label speed in this experiment?

__________________________________________________________

__________________________________________________________

 

LABORATORY INVESTIGATION #1

GRAPHICAL ANALYSIS OF MOTION

APPARATUS

 

laboratory cart,carbon paper discs [if waxed timer tape is not avalible]

recording timer,metric ruler

timer tape

 

 

 

Figure 1. The internal timer provides a record of the motion of the chart. Distance between dots is the distance the chart moved in that time interval.

The Investigation

 

During this investigation, you will analyze the varying motion of a body moving in a straight line. This will be done with the aid of an interval timer. You will use the timer tape to analyze a body’s speed and acceleration. Here are a few points that you must understand clearly for the experiment to be successful.

 

 

1. The time it takes a tape going through the timer to move from dot to dot is exactly the same for each interval between dots. If the distance between the dots is large, the tape was moving rapidly. If the distance between the dots is small, the tape was moving slowly.

2. Because the time intervals represented by successive dots are the same throughout the tape, it is possible to use this time period as a standard unit of time. In fact, we will use the time represented by two vibrations of the timer (two space intervals on the tape) as one time interval. We will call these time intervals "tics" of time (Figure 2).

 

 

 

Tics of Time

Figure 2. One tic represents two successive intervals.

 

 

 

 

 

 

 

 

 

Figure 3. The distance traveled in each tic of time represents speed in cm/tic.

If the distance is measured in centimeters, the speed of  the body is expressed in centimeters per tic.

1. Push the end of a length of timer tape (about 1.5 m.) into the timer. Attach the tape to the cart by removing the cup in the center of the cart, then replacing the cup with the tape between the cup and the cart, making sure the tape is on square and parallel to the cart. Start the timer. Holding the cart firmly, give it a strong push and allow it to move freely on a horizontal surface (the push should be hard enough so all the tape goes through the timer).

2. Mark the end of the tape that was attached to the cart "start" (Figure 4). Move back a few dots from this end and mark a dot as zero. Number every second dot after this 1, 2, 3, etc. These numbers represent the tics of time elapsed as the cart traveled the distance between dot 0 and each numbered dot.

3. Carefully measure the distance traveled during each successive tic of time. Because you are measuring, in each case, the distance traveled by the cart during one tic of time, the distance and the average speed for a given tic are numerically the same. Enter each value you measure for distance in the column for speed next to the corresponding tic number in Table 1.
103664

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LABORATORY INVESTIGATION #1 (cont’d)
4. The total distance traveled by the cart at the end of the first tic is just the distance you measure between the numbers 0 and 1 on you tape. The total distance traveled by the cart by the end of the second tic is the distance
traveled by the cart during the second tic (between the numbers 1 and 2) plus the distance traveled by the cart during the first tic. See Tables 1 and 2. The total distance is found in this manner all along the tape. Keep adding the sum of the previous distances to your current measurement as you go along. Record the total distance traveled by the cart during the corresponding number of tics in Table 2.

Interpreting the Investigation

 

Include answers to the following in your report.

1. Plot the speeds against the correspondingly numbered tic using the values in Table 1. Plot the speeds on the vertical axis. [The graph is labeled but not scaled. Choose a simple scale that uses most of the graph.] Draw a line through your plotted points that best fits most of the points. Do not connect the points with a series of straight lines.

2. Below your graph, write a brief explanation of what the graph shows. Point out periods of accelerations and periods of relatively uniform motion. Explain any gradual accelerations of the cart.

3. Plot the total distance traveled by the cart against the corresponding number of tics using the values in Table 2. Plot the distances on the vertical axis. Draw the line through the plotted points that best fits the most points.
4. Below your graph, write a brief explanation of the meaning of the graph. Explain any change in the slope of the line of the graph.

1 Graphical Analysis of Motion

 

Objective: To analyze the motion of a laboratory cart by the  graphical method.

 

Data and Observations:

 

 

Table 1: Average Speed Per Tic of Time

	Tic Number	Average Speed (cm/tic)		Tic Number	Average Speed (cm/tic)
	1st			13th
	2nd			14th
	3rd			15th
	4th			16th
	5th			17th
	6th			18th
	7th			19th
	8th			20th
	9th
	10th
	11th
	12th

 

 

 

Table 2: Total Distance

	Total Number of Tics	Total Distance (cm)		Total Number of Tics	Total Distance (cm)
	1			13
	2			14
	3			15
	4			16
	5			17
	6			18
	7			19
	8			20
	9
	10
	11
	12

 

 

 

GRAPHICAL ANALYSIS OF MOTION: UNIFORM ACCELERATION

APPARATUS

 

recording timer, carbon paper discs

timer tape 200 g mass

metric ruler masking tape

 

 

Figure 1. The interval timer measures the change in speed of the falling mass. Measure the distance between the dots carefully.

The Investigation

During this investigation, you will demonstrate that a free-falling body undergoes constant acceleration. Your interval timer can be used to record the fall of a small object. The resulting tape can then be used to analyze uniformly accelerated motion.

 

Procedure

1. Push the end of a length of timer tape (about 1.5 m.) into the timer. Attach the tape to the cart by removing the cup in the center of the cart, then replacing the cup with the tape between the cup and the cart, making sure the tape is on square and parallel to the cart. Start the timer. Holding the cart firmly, give it a strong push and allow it to move freely on a horizontal surface (the push should be hard enough so all the tape goes through the timer).

2. Mark the end of the tape that was attached to the cart "start" (Figure 4). Move back a few dots from this end and mark a dot as zero. Number every second dot after this 1, 2, 3, etc. These numbers represent the tics of time elapsed as the cart traveled the distance between dot 0 and each numbered dot.

3. Carefully measure the distance traveled during each successive tic of time. Because you are measuring, in each case, the distance traveled by the cart during one tic of time, the distance and the average speed for a given tic are numerically the same. Enter each value you measure for distance in the column for speed next to the corresponding tic number in Table 1. 


4. The total distance traveled by the cart at the end of the first tic is just the distance you measure between the numbers 0 and 1 on you tape. The total distance traveled by the cart by the end of the second tic is the distance traveled by the cart during the second tic (between the numbers 1 and 2) plus the distance traveled by the cart during the first tic. See Tables 1 and 2. The total distance is found in this manner all along the tape. Keep adding the sum of the previous distances to your current measurement as you go along. Record the total distance traveled by the cart during the corresponding number of tics in Table 2.

Interpreting the Investigation

 

Data and Observations:

Include answers to the following in your report.

1. Plot the speeds against the correspondingly numbered tic using the values in Table 1. Plot the speeds on the vertical axis. Draw a line through your plotted points that best fits most of the points. Do not connect the points with a series of straight lines.

2. Below your graph, write a brief explanation of what the graph shows. Point out periods of accelerations and periods of relatively uniform motion. Explain any gradual accelerations of the cart.

3. Plot the total distance traveled by the cart against the corresponding number of tics using the values in Table 2. Plot the distances on the vertical axis. Draw the line through the plotted points that best fits the most points.

4. Below your graph, write a brief explanation of the meaning of the graph. Explain any change in the slope of the line of the graph.

Table 1: Average Speed Per Tic of Time

	Tic Number	Average Speed (cm/tic)		Tic Number	Average Speed (cm/tic)
	1st			13th
	2nd			14th
	3rd			15th
	4th			16th
	5th			17th
	6th			18th
	7th			19th
	8th			20th
	9th
	10th
	11th
	12th

 

 

Table 2. Total Distance

Tics Squared (t2)	Total # of tics	Total Dis. (cm)		Total # of tics	Total Dis. (cm)
	0				2			15
	3			16
	4			17
	5			18
	6			19
	7			20
	8
	9
	10
	11
	12

 

 

WHAT ARE THE CHARACTERISTICS OF ACCELERATED MOTION?

[All problems must be done with diagram, formula, substitution method on a separate piece of paper to be handed in.]

 

Uniform Motion

WHAT ARE THE CHARACTERISTICS OF ACCELERATED MOTION?

Uniform Motion

1. Motion may be defined as a continuing change of ______________.
If the path of the motion is known, the motion can be described by giving the __________________ from the starting point for  each instant of _________________. For some kinds of motion, this relationship can be expressed as a mathematical equation.
The symbol usually used for distance is __________________; the symbol used for time is __________________.

2. The rate at which the distance changes is called the __________ of the motion. If the distance changes by equal amounts for equal time intervals, the speed is _______________ and the motion is said to be _____________________.

3. When speed is constant, the speed can be found by dividing the ______________________ traveled by the _______________________.
When the speed is not constant, the result of dividing the  distance by the time is called the __________________________.

4. The quantity that includes both the speed and the direction of motion is called _______________________. In straight-line motion, the two terms may be used interchangeably.

5. If v is the symbol for velocity or speed, complete the following formulas to show how velocity is related to distance and time: For uniform, straight-line motion:
v = s =

For nonuniform, straight-line motion:
vav = s =

6. At 30 mi/hr, how far will you travel in 3 hrs.? _______________

7. On a trip, a man traveled the first 120 miles in 4 hours. The next 120 miles took 3 hours. What was the average speed for the entire trip? 
Ans. _______________________

8. Since the complete specification of a velocity includes a magnitude and a _____________________, velocity is a _______________________ quantity.

9. A river is flowing south at 5 km/hr. A motorboat is headed east across the river at 12 km/hr. Find the resultant velocity and the change in position relative to the shore after ½ hour.
Ans. _______________________
Position: _______________ km east and ________________ km south

Uniformly Accelerated Motion

1. When the velocity of motion is not constant, the rate at which the velocity is changing is called the _____________________. If the velocity changes by equal amounts in equal times, the acceleration is said to be __________________. In the following discussion, we will assume that all accelerations are uniform and that the motion is in a straight line.

 

[Accelerations in curved motion will be considered in a later problem.]

2. An automobile changed its velocity from 30 mi/hr. to 50 mi/hr. in 5 sec. The change in velocity was ______________________. the changer per second was __________________. therefore the acceleration was ______________________.

3. In the preceding example, the initial velocity (v_o) was ________

The velocity increased by _______________ each second. If we let t be zero for the initial velocity, the velocity at any later time can be calculated from the formula

v_f = v_o +

The velocity when t = 3 sec was _______________________________

The velocity when t = 5 sec was _______________________________

(Does this result agree with the given data?)

4. In the special case when v_o = o (a body accelerating from rest), the formula for velocity reduces to

v_f =

5.EXTRA CREDIT [you need to know algebra] When acceleration is uniform, the average velocity (over any given time interval) is equal to the average of the initial and final velocities:

v_av = v_o + v_f

---

2

If we substitute for v_f its formula found in Question 3, we obtain:

v_av

7. A car moving at 20 m/sec is uniformly slowed down to 5 m/sec

in 3 sec.

a. What is its acceleration? _________________________________

b. What distance did it cover during the 3 seconds? __________(EXTRA CREDIT)

Acceleration Due to Gravity

1. The acceleration due to gravity near the earth’s surface is

_______________m/sec/sec. (The unit m/sec/sec may be shortened

to m/sec².)

2. A body initially at rest is dropped and allowed to fall freely.

At the end of 4 sec, its velocity will be ____________________.

3. A body is thrown upward with an initial velocity of -50 m/sec.

Find its velocity,

a. After 5 sec _____________________

b. After 10 sec ____________________

(Be sure to use the proper algebraic sign to indicate upward or downward velocity.)

4. A body is thrown downward with an initial velocity of 12 m/sec.

How far will it fall in 3 sec?

(EXTRA CREDIT) Ans. _______________________

 

PROBLEM SUMMARY

PROBLEM SUMMARY

In motion at constant speed in a straight line, the distance(s) traveled during a time interval (t) is related to the speed or velocity (v) in accordance with the following formulas:

s = v = t =

If the velocity is changing at a constant rate, we say that the _{motion has uniform _________________________________________________}

Distance (s) and final velocity (v_f) are related to initial velocity

(v_o), acceleration (a), and time (t) as follows:

In terms of a and t, v_f = v_o +

In terms of a and t, s =

In terms of a and s, v_f =

Method D: a_g from Falling Water Drops

You can measure the acceleration due to gravity ag simply with drops of water falling on a pie plate.

Put the pie plate or a metal dish or tray on the floor and set up a glass tube with a stop clock, valve, or spigot so that drops of water from the valve will fall at least a meter to the plate. Support the plate on three or four pencils so that each drop sounds distinctly, like a drum beat.

 

Adjust the valve carefully until one drop strikes the plate at the same instant the next drop from the valve begins to fall. You can do this most easily by watching the drops on the valve while listening for the drops hitting the plate. When you have exactly set the valve, the time it takes a drop to fall to the plate is equal to the time interval between one drop and the next.

 

Method D: a_g from Falling Water Drops (cont’d)

 

With the drip rate adjusted, now find the time interval t between drops. For greater accuracy, you may want to count the number of drops that fall in half a minute or a minute, or to time the number of seconds for 50 to 100 drops to fall.

 

Your results are likely to be more accurate if you run a number of trials, adjusting drip rate each time, and average your counts of drops or seconds. The average of several trials should be closer to actual drip rate, drop count, and time intervals than one trial would be.

 

Now you have all the data you need. You know the time (t) it takes a drop to fall a distance (d) from rest. From these you can calculate a_g, since you know that d = ½a_gt² for objects falling from rest.

 

1. What value did you get for ag?

2. What is your percentage error? How does this compare with your percentage error by any other methods you have used?

3. What do you think led to your error? Could it be leaking connections, allowing more water to escape sometimes? How does this affect your answer?

Distance of fall lessened by a puddle forming in the plate: How would this change your results?

Less pressure of water in the tube after a period of dripping: Would this increase or decrease the rate of dripping? Do you get the same counts when you refill the tube after each trial?

Would the starting and stopping of your counting against the watch or clock affect your answer? What other things may have shown up in your error?

4. Can you adapt this method of measuring the acceleration of gravity so that you can do it at home? Would it work in the kitchen sink? or if the water fell a greater distance, such as down a stairwell?

BIBLIOGRAPHY

 

Weisler, Jules J. Physical Science. NY, NY: Amsco School

Publications, Inc.

 

Murphy, James T., and Smoot, Robert C. Physics Principles and

Problems. Columbus, OH: Charles E. Merrill Publishing

Co.

 

Turner, Hallie F., and Carpenter, George P. Discovery Problems

in Physics. Fairfield, NJ: Cebco Standard Publishing.

 

Murphy, James T. Laboratory Physics. Columbus, OH:

Charles Merrill Publishing Co.

 

Directors of Harvard Project Physics. Project Physics. NY:

Holt, Rinehart and Winston.