Victoria Rollins Lab 4 Vector Decomp

Name_________________________________ Force Table Lab Part 1: Vector Decomposition There are two basic types of quantities in physics: scalars and vectors. A scalar can be fully specified by a number and a unit (such as time, temperature, etc.), while a vector includes a direction as well (such as displacement and velocity). Any vector can be represented by an arrow that points in the direction associated with the quantity and has a length (magnitude) equal to the associated number. A vector in the x-y plane can be thought of as pointing partly in the x -direction and partly in the y -direction, and can be decomposed into these two parts. The part pointing in the x -direction is called the x -component, and the part pointing in the y -direction is called the y -component. Any such vector can be treated as the hypotenuse of a right triangle whose other two sides are parallel to the x - and y -axes. Given the magnitude of the vector (length of the hypotenuse) and the direction of the vector (the angle between the hypotenuse and one of the other two sides), you can use trigonometry to calculate the lengths of these two sides (the magnitudes of the components). If, instead, you are given the components and want to find the magnitude and direction of the original vector, you can again use trigonometry. The magnitude is equal to the length of the hypotenuse, which can be calculated from the lengths of the other two sides from the Pythagorean theorem. The direction (angle) can then be calculated by applying an inverse trigonometric function to the other two sides. In this lab procedure, a force (another vector quantity) will be applied to the ring in the center of a force table and then will be counterbalanced by forces exerted along the coordinate axes to experimentally decompose the force into its components. These experimental values of the components will then be compared with theoretical values calculated from the magnitude and direction of the original force using trigonometry. Secondly, force components will be set up on the force table by exerting two forces along the coordinate axes. To find experimental values of the magnitude and direction of the force having these two components, a third force will be exerted on the ring that balances out the other two. These values will be compared with the theoretical magnitude and direction calculated from trigonometry. Procedure Part A 1. Set up the mass table by screwing in the legs and the peg in the middle of the table. 2. Attach three pulleys to the rim of the force table: one at the 60-degree mark, one at the 180-degree mark, and one at the 270-degree mark. Note: Make sure the pulleys are at the same height and not touching the force table! 3. Tie three strings via loose loops to the white plastic ring. x y C C x C y θ C

Name_________________________________ 4. Thread these strings over the pulleys and tie the other end to a mass hanger. 5. Add 45 g to the hanger at the 60 degree mark, so that there is a total of 50 g hanging there. Add masses to each hanger of the other two hangers until the peg in the middle of the force table is centered in the ring. 6. Record the needed masses you added in the table below, and fill in the results of the associated calculations of experimental and theoretical force components (converting mass to units of kilograms before multiplying by g = 9.8 m/s 2 in order to calculate forces in standard units of newtons (N)). The forces exerted by the strings attached to these two hanging masses represent the x - and y -components of the force exerted by the string attached to the hanging mass at the 60-degree mark. 7. Record your data in the tables below and complete the calculations. Data (10 pts) All values in the tables below are magnitudes only (They should all be positive). Force Table. Vector in the first Quadrant (Positive x and y components) Angle Mass (Including Hanger) Force= mg (N) Theoretical Component From trig (N) % error Θ=60 ° 0.050 kg F exp = N/A N/A 180 ° (x-comp) (Do not use 180 degrees in your calculations) F x exp = F x theor = F exp cos 60= 270 ° (y-comp) (Do not use 270 degrees in your calculations) F y exp = F y theor = F exp sin 60= Force Table. Vector in the first Quadrant (Positive x and y components) Angle Mass (Including Hanger) Force= mg (N) Theoretical Component From trig (N) % error Θ=40 ° 0.060 kg F exp = N/A N/A 180 °(x-comp) (Do not use 180 degrees in your calculations) F x exp = F x theor = F exp cos 40= 270 °(y-comp) (Do not use 270 degrees in your calculations) F y exp = F y theor = F exp sin 40= Force Table. Vector in the second Quadrant (Negative x and positive y component) Angle Mass (Including Hanger) Force= mg (N) Theoretical Component From trig (N) % error f 1 x y f 2 f 3 x y x y x y x y x y

Name_________________________________