Date Period Name

k-\s Lab

Objectives

Observe the interaction of concurrent forces.

Apply vector addition to obtain the resultant of forces in equilibrium.

Demonstrate equivalent ways to add vectors.

Addition of Vector Forces When two or more forces act at the same time on an object and their vec­tor sum is zero, the object is in equilibrium. Each of the arrangements shown in Figure A illustrates three concurrent forces acting on point P. Because point P is not moving, the three forces produce no net force on point P, and the systems are in equilibrium. In this experiment, you will determine the vector sum of two of the concurrent forces, called the resul­tant, and investigate the relationship of the resultant to the third force.

Procedure Your teacher wil l demonstrate the apparatus you wil l be using^—either Method 1 or Method 2.

String

Ring stand

Method 1—force table and 3 spring scales

Method 2—2 spring scales, 2 ring stands, cross support, and 500-g mass

metric ruler

heavy string

pencil

protractor

paper

Figure A You can use a variety of methods to measure forces. Your apparatus will probably be similar to one of these.

Method 1 1. Set up the apparatus shown in Figure A l . Each spring scale should

read zero when no load is attached. Attach the spring scales to the force table so that each scale registers a force at approximately midrange.

2. Place a piece of paper beneath the spring scales. Using a sharp pencil, mark several points along the line of action (the string) of each force.

3. Remove the paper and, using the points that you marked, construct lines A, B, and C, representing the direction of force action for scales A, B, and C.

Physics: Principles and Problems Laboratory Manual 17

Name

Physics Lab

p c 5.0 N

- - C 5.0 N

C

Scale: 1 N = 2 cm

Figure B 1 2 3

4. Record the reading of each spring scale next to its corresponding line, as shown in Figure B l . 5. Select a suitable scale, such as 1 N = 2 cm, and record your scale near line C. Construct vectors, of

proper scaled length, along lines A, B, and C to represent each force. If the spring scales are not cal­ibrated in newtons, convert the measurements to newtons by multiplying the mass in kilograms by 9.8 m/s^. Figure B2 shows how to scale these vectors.

6. Add vector A to vector B by reproducing A parallel to itself but with its tail at the head of B (the head-to-tail method), as shown in Figure B3.

7. Draw a vector representing the vector sum of A -I- B, the resultant.

8. Repeat steps 1-7 so that each lab partner has a set of data to analyze.

1. Set up the apparatus shown in Figure A2. With a protractor, measure each of the three angles at the intersection of the three strings.

2. Using these angle measurements, construct a diagram on paper of the forces acting on point P by drawing three lines to represent the lines of action of the three forces. Label the lines A, B, and C, as shown in Figure B l .

3. Record the values of the two spring-scale readings and the weight in newtons of the 500-g mass next to lines A, B, and C on your paper. I f the scales measure mass, convert the mass readings to newtons by multiplying the mass in kilograms by 9.8 m/s^.

4. Selert a suitable scale, such as 1 N = 2 cm, and record your scale near line C. Using your scale, construct vectors along lines A, B, and C to represent the forces acting along each line of force, as shown in Figure B2.

5. Add vector A to vector B by reproducing A parallel to itself but with its tail at the head of B (the head-to-tail method), as shown in Figure B3.

6. Draw a vector representing the vector sum A + B, the resultant.

7. Repeat steps 1-6 so that each lab partoer has a set of data to analyze.

18 Laboratory Manual Physics: Principles and Problems

Method 2

Name

Physics Lab

Data and Observations On a separate sheet of paper, draw the vectors from your experiment. Follow the format in Figure B.

Analysis and Conclusions 1. What scale did you select for your model? Compute the resultant using your number scale.

2. Compare the magnitude and direction of the computed resultant force of A + B with the mea­sured or known magnitude of force C. Explain your findings. Calculate the relative error in the magnitudes using force C as the reference value.

3. On a separate street of paper, reconstruct vertors A, B, and C and add them. Do this by placing a piece of paper over your first diagram and tracing the vertors. Place the tail of B at the head of A, and then place the tail of C at the head of B (the head-to-tail method). Label your vertors.

4. Explain the results of the graphical addition of A -H B -I- C from question 3.

5. Suppose that you had added B to C. What result would you expert?

6. What result would you expert if you added C to A?

7. On the same paper you used for question 3, add your three vertors in the order C -f- B -I- A. What is the resultant?

Physics: Principles and Problems Laboratory Manual 19

Name

Physics Lab

Extension and Application 1 . Using a different method, repeat the investigation, setting the angle between A and B at an angle

other than 90°. Solve for C both mathematically and graphically.

2. A sky diver jumps from a plane and, after falling for 11 s, reaches a terminal velocity (constant speed) of 250 km/h. Changing her body configuration, she accelerates to a terminal velocity of 320 km/h. Finally, after releasing her parachute, she again accelerates and reaches a final terminal velocity of 15 km/h. Explain how it is possible to obtain the different terminal velocities.

20 Laboratory Manual Physics: Principles and Problems