College Physics Lab
PH 141
Vectors
Return to Lab Main Page Purpose: The purpose of this lab is for you to gain experience working with vector quantities. Discussion: For this lab you will use an instrument called a force table. A ring is placed around a pin in the center of the force table. Strings attached to the ring pull it in different directions. The magnitude (strength) of each pull and the direction of the pull can be varied. The magnitude of the string tension (strength of the pull) is determined by the amount of mass which is hung from the other end of the string. The value of the pull in the string equals m*g, where m is the mass hanging from the string and g equals 9.8 m/s2.

The force table allows you to demonstrate when the sum of forces acting on the ring equals zero. Under this condition called equilibrium, the ring, when released, will remain centered on the post. When the forces on the ring do not add up to zero, the ring will be pulled to one side until stopped by hitting the post.

Your task is to confirm that forces add as vectors. You will apply three different forces to the ring and add them up. From this information you will predict the magnitude and direction of a fourth vector that you need to apply to the ring in order to bring into equilibrium. You will make this prediction by two methods: graphical addition of vectors and algebraic addition of vector components. Finally, you will check your prediction empirically.

Procedure:

1. Make sure the force table is level, and that you have four strings attached to the ring.

2. Hang known masses (200-400 g) from three of the strings, and position the corresponding pulleys at known angles. The choice of masses is up to you, but they should all differ by at least 20%. None of the angles may be 0o, 90o, 180o, or 270o, and their differences may not be any of these either. Calculate the tensions in the strings in Newtons. You may call the magnitudes of these forces F1, F2, F3 and the corresponding angles q1, q2, q3, respectively. You are going to figure out the magnitude F4 and direction q4 of a fourth force which should be applied to the ring in order to establish equilibrium.

3. Decide on a convenient scale factor that will allow you to draw vectors representing your forces on your sheet of paper. For example, you could try a scale conversion factor , for example 10 cm : 1 N, to figure out how long to draw each force vector. Draw a diagram of the forces acting on the ring. You will not know F4or q4, just make an educated guess.

4 Make a scale drawing representing the addition of the force vectors F1, F2, F3, and F4. Determine the magnitude F4 and angle q4 from your drawing.

5. Calculate the x and y components of F1, F2, F3. Set up the equations SFx = 0 and SFy = 0, and solve them for F4x and F4y, respectively. Calculate F4 and q4 from the components.

6. Hang the mass necessary to produce F4 on the fourth string, and place its pulley at the calculate angle q4.

7. By making small variations in the mass and angle, decide what combination will best keep the ring in equilibrium at the center of the table. You should also decide how much uncertainty there is in these values. If there is any detectable difference between your experimental value of F4 and your theoretical value calculated from the components, you should calculate the % difference.

Summary:

When you are finished you should have constructed or determined the following items:
• A diagram for your chosen experimental arrangement. Force vectors must be clearly indicated and defined.
• Two predictions for the expected value of F4 and q4. One prediction is made graphically and one is made algebraically. Your reasoning process is what I want to see.
• Experimental determination of F4 and q4.
• Conclusion: How does observation compare to prediction?