addition of vectors lab
DESCRIPTION
Addition of Vectors LabTRANSCRIPT
Name: _______________________________
Vector Addition Lab
Overview: In this activity, you will use both the head-to-tail method and the analytical method of vector addition in order to determine the resultant displacement of a plane trip, which have three individual "legs." You will then use these skills to resolve force vectors that are in equilibrium on a Force Table apparatus. Materials: ruler, protractor, pencil, calculator, copy of a New Zealand map Part 1:Head-to-Tail Method of Determining the Resultant: On the attached map, use the indicated scale to add the following three vectors (A, B, C) in a head-to-tail fashion. Include an arrowhead on each vector and label them clearly as A, B and C. Draw the resultant of A + B + C on the diagram and label it as R1. Begin in Auckland. All angles are measured clockwise from north. Scale on map: _____ cm = 250 km
A B C 350 km at 150° 259 km at 224° 641 km at 213°
scale length = ____ cm scale length = ____ cm scale length = ____ cm Length of resultant (Δx) = _____ cm (scale) = _____ km direction = _____°
The resultant of A + B + C is _________________________ (include magnitude and direction). The final destination appears to be in or at least close to the city of _________________.
Name: _______________________________
Analytical Method of Determining the Resultant: Now use a calculator, trigonometric functions, and principles of vector resolution to determine the components of each vector; include both magnitude and direction for each component. Show your work in each of the cells of the first three rows of the data table. Finally, add all the components to determine the horizontal and the vertical components of the resultant of A + B + C.
Vector Horizontal or E-W Component Vertical or N-S Component
350 km at 150°
259 km at 224°
641 km at 213°
Resultant
Now use the components of the resultant to determine the magnitude and the direction of the resultant. Once you have determined the resultant, make a measurement on the map to determine where this displacement would place a traveler. Length of resultant (Δx) = _____ km (actual) = _____ cm (scale) with the direction = _____°
According to the analytical method, the resultant of A + B + C is ____________________(include magnitude and direction).
Name: _______________________________
When this resultant displacement is measured on the provided map, the final destination appears to be in or at least close to the city of Compare the results of the two methods of vector addition and use a few complete sentences to evaluate the effectiveness of the methods and the accuracy of your measurements.
Name: _______________________________
Part2: Equilibrium of Forces Acting at a Point
An object is said to be in equilibrium when the vector sum of all the forces acting on it is zero. In this experiment we shall study the translational equilibrium of a small ring acted on by several forces on an apparatus known as a force table, see Fig. 1.
This apparatus enables one to cause the forces of gravity acting on several masses (F = mg) to be brought to bear on the small ring. These forces are adjusted until equilibrium of the ring is achieved. You will then add the forces analytically by adding their components and graphically by drawing the vectors and determining if they add to zero using the rules for the addition of force vectors listed above.
Setup
1. Assemble the force table. Use three pulley clamps (two for the forces that will be added and one for the force that balances the sum of the other two forces).
2. Arrange the strings from the String Tie over the pulleys.
3. Hang the following masses over two of the super pulleys and clamp the pulleys at the given angles.
Table 1.1:
Vector Mass (kg) Force = mg (N) Angle (°)
FA 0.050 (50g) = 0.050 x 9.81= 0.490 0
FB 0.100 (100g) 120
FE 0.200 (200g)
g = 9.81 ms-2
Fig. 1. A force table in equilibrium
Name: _______________________________
Procedure (Experimental Method)
4. By trial and error, find the angle for the third super pulley clamp and the 200g mass that must be suspended over the pulley so that its weight will balance the forces exerted on the strings by the other two masses.
This third force will the be called the equilibriant (FE) because it establishes equilibrium. The equilibriant is the negative of the resultant.
To test whether the system is in equilibrium, make sure that the ring is not maving and centered on the central peg as in Fig. 1.2
5. Record the angle for the third pulley to put the system into equilibrium into Table 1.1
Analysis
To theoretically determine what mass should be suspended over the third pulley, and at what angle, calculate the magnitude and direction of the resultant by the component method and the graphical method. The equilibriant (FE) will have the same magnitude, but it will be opposite in direction. In other words, the direction will be 180° from the direction of the resultant.
Component Method
On a separate sheet of paper, add the vector components of Force A and Force B to determine the magnitude of the equilibriant. Record the components Rx and Ry in Table 1.2. Use trigonometry to find the direction of the equilibriant (remember, the equilibriant is exactly opposite in direction to the resultant.) Record the results in Table 1.2.
Graphical Method
On a separate sheet of paper, construct a tail-to-head diagram of the vectors of Force A and Force B. Use a metric ruler and protractor to measure the magnitude and direction of the resultant. Record the results in Table 1.2. Remember to record the direction of the equilibriant as opposite in direction to the resultant.
Fig. 1.2
Name: _______________________________
Table 1.2:
Equilibriant (FE)
Method Magnitude Direction
Experimental
Component
Graphical
Rx = ______________ Ry = ______________
Question
How do the theoretical values for the magnitude and direction of the equilibriant compare to the actual magnitude and direction?