Lab 1: Force and motion I Physics 193 Fall 2006
Lab 1: Force and motion I
I. Introduction
In today’s lab, you will describe the motion of an object using a motion diagram and describe the forces that other objects exert on this object of interest using a free-body diagram. You will then confirm that the changing velocity of the object is in the same direction as the net force that other objects exert on that object.
II. Theory
Motion Diagrams
A motion diagram nicely describes linear motion—an object moving along a straight line. (See the Reasoning Skills: Constructing a Motion Diagram in Chapter 1 of the Active Learning Guide). Dots are placed at the location of the object at equal time intervals. Arrows attached to each point indicate the direction of motion and the relative speed of the object. If the velocity is changing, a velocity change arrow indicates how one velocity arrow has to change in order to make the next velocity arrow. There are three common situations:
Constant velocity: The dots are equally spaced and the velocity arrows are equally long and in the same direction, as shown below. There is no velocity change.
Increasing speed: The object moves faster and faster and the dots are separated farther as time progresses. The velocity arrows get longer and longer. The velocity change arrow points in the same direction as the velocity.
Decreasing speed: The object moves slower and slower and the dots are separated by less distance as time progresses. The velocity arrows get shorter and shorter. The velocity change arrow points opposite the velocity arrows.
Free-Body Diagrams
A free-body diagram represents the forces that other objects exert on an object of interest. (The Reasoning Skills box for Constructing Free-Body Diagrams from Chapter 1 of the Active Learning Guide is provided below.) You choose an object of interest and identify other objects that interact with that object of interest (exert forces on it). Each interaction is represented by an arrow and labeled by a symbol with two subscripts indicating the other object exerting the force and the object on which the force is exerted.
1. Sketch the situation described in the problem.
The Net Force is in the Direction of the Velocity Change
We will confirm with the experiments today that the sum of all forces exerted on an object of interest is in the direction of the change in its velocity. We can use the free-body diagram and a graphical vector addition method (illustrated at the right for the diagram above) to estimate the direction of the net force exerted on the object of interest. To add the vectors, place them tail to head and draw the resultant or net force vector from the tail of the first vector to the head of the last. The vectors can be added in any order.
In our future analysis, we should find that the net force (the sum of the forces exerted on the object) points in the same direction as the velocity change, as shown in a motion diagram for that object.
III. Procedure
A. Practice making motion diagrams
Equipment: toy car, Nerf ball, sugar packets, meter stick, and stopwatch.
Motion of a Toy Car
· You will use a stop watch to indicate equal time intervals. One person in the group can observe the watch and each second abruptly says “now”.
· Another person starts the toy battery operated car so that it moves in a straight line.
· After it has reached a steady speed, the second person walks beside the car and places sugar packets beside the car each second—at the locations when you hear “now”.
· Repeat the process until you get a nice sugar packet distribution of the car’s location each second.
· Now, construct a coordinate axis to measure with a meter stick the car’s location each second. The coordinate axis should have a positive direction (toward the right in this example), an origin, and a scale (10-cm units will be good for this activity).
· Use a meter to measure the locations of the sugar cubes at one-second time intervals relative to this coordinate axis.
Time (s) / Position (cm)· Place the data in a data table with one heading time in seconds (the independent variable) and the other heading position in centimeters (the dependent variable).
· You should find that the distance between adjacent sugar packets is approximately the same, since the car has constant velocity motion. Is this what you observe?
· Make a motion diagram to represent this motion—equally spaced dots and equal length velocity arrows.
Motion of a Nerf Ball
· Again use the stop watch to indicate equal time intervals with one person indicating one second time intervals with abrupt “nows”.
· A second person rolls the Nerf ball so that it rolls with reasonable speed in a straight line.
· The second person or a third person walks or runs beside the ball and places sugar packets at the ball’s location each second. If the ball curves near the end of its trip, ignore that part of the trip—include only positions where it is moving straight.
· Repeat the process until you get a nice sugar packet distribution of the ball’s location each second.
· Use a meter to measure the locations of the sugar packets at one-second time intervals relative to the coordinate axis developed in the previous activity.
· Place the data in a data table with one heading for
Time (s) / Position (cm)time in seconds (the independent variable) and the other heading for position in centimeters (the dependent variable).
· Note the distance between adjacent sugar packets as recorded in your data table.
· Construct a motion diagram for the motion of the Nerf ball. Include position dots, velocity arrows, and a velocity change arrow (assume that the velocity changes the same amount during each time interval—velocity change motion with constant velocity change). You might want to include every other measurement from your data table.
B Practice constructing free-body diagrams
Equipment: Bowling ball and Nerf ball
· Hold the Nerf ball stationary in your hand. Then hold the bowling ball the same way.
· In the center cell of the box below these instructions, you have a sketch showing “you” holding one of the balls in your hand. Circle the ball lightly to indicate that it is the object of interest for your free-body diagram.
· You also see a solid dot in the left cell of the table and a second solid dot on the right cell. The left dot represents the Nerf ball and the right dot represents the bowling ball.
· Place a short downward arrow on the left dot and label it FE on b. This arrow represents the gravitational force that the Earth exerts on the Nerf ball.
· Place an equally long upward pointing arrow on the left dot and label it FH on b. This arrow represents the upward force of your hand on the ball. These are the only two objects that interact with the Nerf ball while resting in your hand.
· Repeat the procedure for the bowling ball and label the forces FE on B and FH on B. However, make the lengths of the arrows somewhat longer to represent the greater forces of the Earth and your hand on the bowling ball.
Free-body diagram for the Nerf ball / Sketch of you holding one of the balls / Free-body diagram for the bowling ballC. The net force exerted on an object is proportional to its velocity change
Equipment: Bowling ball, mallet, sugar packets.
We would like to verify the following rule.
Rule relating net force and motion: The sum of all forces that other objects exert on an object of interest (the net force that other objects exert on it) is in the same direction as the CHANGE in velocity of that object.
To verify this, perform the following experiments. For each experiment, draw either a motion diagram or a free-body diagram or both for the bowling ball and decide if the diagrams are consistent with the rule above.
Motion diagram / Free-body diagram.
Are the diagrams consistent? Explain.
Experiment 1 Place the bowling ball at rest on the floor. A motion diagram for the ball is shown at the right. Draw a free-body diagram for the ball. Is the free-body diagram consistent with the rule above and with the motion diagram? Explain.
Motion diagram / Free-body diagramAre the diagrams consistent? Explain.
Experiment 2 You start tapping the ball with a rubber mallet so that it moves toward the right faster and faster. A free-body diagram for the ball is shown at the right (the FMonB arrow represents the average force of the mallet on the ball). Draw a motion diagram for the ball. Is the motion diagram consistent with the free-body diagram and with the rule above? Explain.
Motion diagram
/ Free-body diagramAre the diagrams consistent? Explain.
Experiment 3 Once the ball starts moving fast, stop tapping it and let it roll as constant velocity. A motion diagram for the ball is shown at the right. Draw a free-body diagram for the ball. Is the free-body diagram consistent with the motion diagram and with the rule above? Explain.
Motion diagram / Free-body diagramAre the diagrams consistent? Explain.
Experiment 4 Finally, start tapping the ball with the mallet toward the left opposite its direction of motion. It moves slower and slower because of the tapping. Draw a motion diagram and a free-body diagram for the bowling ball while it is being tapped opposite its direction of motion. Are the motion diagram and the free-body diagram consistent with the rule above? Explain.
Conclusion: Note that your diagrams confirm that the net force that other objects exert on an object of interest (for example, on the bowling ball) point in the same direction as the change in the velocity of that object. If they don’t, it is likely that you invented a fictitious force. Remember that you always have to be able to identify the other object exerting a force on the object of interest.
IV. Homework: Lab 2 is a quantitative lab. To be successful there, you will need to be knowledgeable about experimental uncertainties. To help you learn about them, we wrote a special document, attached to this lab. Please read the document carefully. After you finish reading, proceed to the following problems. They will help you learn how to estimate uncertainties and how to use them to evaluate experimental results. Please complete these problems at home on a separate sheet of paper before coming to lab 2. We will read your answers and provide feedback. If you are not satisfied with the grade, you can always improve it (see the syllabus).
1. The following instruments are available in your laboratory:
a) ruler b) protractor
c) watch d) scale
What would you estimate as the absolute uncertainties in measurements made using these instruments?
2. Measure the length of the pencil. Estimate the relative uncertainty in the measurement.
3. Suppose that by using the instruments from the Problem 1, you determined that it takes 3 s for a toy car to travel a distance of 162 cm. What are the relative uncertainties of the distance and the time measurements? Which measurement is more precise? Explain.
4. Calculate the average speed of the toy car. Decide whether you can use the weakest link rule to determine the relative uncertainty in this speed estimation. Determine the range within which you know the speed.
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