Force Table: Force Vector Components

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Physics Bridging Course 0885-398-01 Adding Vectors By Components Topic: Adding Vectors By Components Preparation: GR&R: Read Chapter 2 WebAssign: To followup this workshop, do Week 2: Force and

1 Physics Bridging Course Adding Vectors By Components Topic: Adding Vectors By Components Preparation: GR&R: Read Chapter 2 WebAssign: To followup this workshop, do Week 2: Force and Equilibrium Purpose: To learn the properties of scalar quantities and vector quantities and to learn to add vector components. Force Table: Force Vector Components Introduction: Adding Vectors by components: In another workshop you added vectors graphically, that is by drawing them to scale and measuring the resultant. Now you will add vectors by components, and confirm your calculations with the force tables. All vectors are a combination of two vectors, one on the x-axis and one on the y-axis. A very simple example is shown below: V 1 is on the positive x-axis (it is horizontal, pointing right) and V 2 is on the positive y-axis (it is vertical and pointing up). You can either measure or use the Pythagorean Theorem to determine that the resultant is 5 units long. Keep this page. 1

2 That 5-unit vector has two components. They are a positive-x vector of 4 units and a positive-y vector of 3 units. If you add those two components together, you get a 5 unit vector at 49 o. How do we find components? The trigonometric functions sine, cosine and tangent will be very useful here. As the unit circle rotates from its initial position at 0 o, It generates a sine wave and a cosine wave. (Look at < to see a movie of how these functions appear. You can find the component of a vector by using trigonometry. F = o F x F y On the right is a force vector of 10 newtons at 150 o. This force is the vector sum of F x and F y. (If you added F x and F y graphically or using the Pythagorean Theorem, you'd get force F.) To calculate F x and F y, we'll use cosine and sine. F x = F cos 150 o F x = 10 N (cos 150 o ) = N F y = F sin 150 o = 10 N (sin 150 o ) = 5.0 N Note: Just to check our work, let's add these up using the Pythagoren Theorem. Keep this page. 2

F = (5.0 N) 2 + ( 8.66 N) 2 = 25 N 2 + 75 N 2 = 100 = 10 N It works! The Force Table The Force Table is a flat, circular disk.

A ring fits over the center pin. Ring Pin Strings are tied to the ring and extend over the pulleys. Masses are hung from the strings.

3 F = (5.0 N) 2 + ( 8.66 N) 2 = 25 N N 2 = 100 = 10 N It works! The Force Table The Force Table is a flat, circular disk. It is marked off in degrees around the edge. In the center is a pin. It can be removed. The edge has three or four pulleys. A ring fits over the center pin. Ring Pin Strings are tied to the ring and extend over the pulleys. Masses are hung from the strings. Each string and mass represents a force. The force is applied to the ring around the pin. So, a problem from your book that might look like this: 90 o 180 o 0 o 270 o Keep this page. 3

4 On the force table, the problem would look like this: Purpose: For this lab you will determine the resultant of several force vectors theoretically (on paper). Then you will verify your results by finding the resultant of the same forces on the force table. Method: Below you will find two force addition problems. Use the vector component method to find the sums of the vectors. Do this before you do the lab. Bring this information with you on workshop day. Problem 1: A = o B = o Problem 2: Keep this page. 4

5 A = o B = o C = o When you come into lab, your group will have a force table and mass hangers. Each hanger has a mass of 50 g. Remember this, it will make a difference. Set up the force table for Problem 1. Set one of the pulleys at 60 o and another at 280 o. Add appropriate slotted masses to the hangers. Estimate where the resultant of A + B will be. (You should know exactly where to expect it, from your problem solutions.) Pull gently on a string in the opposite direction of the resultant. Adjust the direction that you are pulling until the ring is centered on the pin. Place another pulley on the force table at this position. Add masses to the hanger until the ring is balanced, centered on the pin. Do this so that if you take the pin out, the ring will stay where it is. Example: R This is the that you have calculated. This is you pulling on a string to balance the resultant. Keep this page. 5

6 The force that you apply to balance the resultant must be equal and opposite to the resultant. Record the magnitude and position that you calculated for the resultant. Record the magnitude of the balancing force, and the position of the balancing force. Now, do the same thing for Problem #2, with Vectors A, B and C. Problem Calculated Calculated Balancing Force Balancing Force Experimental Experimental 1 2 Remember that the balancing force is equal and opposite to the resultant. Write down the magnitude and the position of the resultant, as you found it on the force table. Compare your experimental results with your calculated results. Does the trigonometric method of resolving vectors work? Did you get an accurate solution? Keep this page. 6

7 Name: Team members: WS 4.1 Scalars and Vectors Neatness counts! If I can't easily follow your work, I won't grade it. Attach your scale drawings to this sheet. Figure out the components of the forces, and calculate the resultants and equilibrants for both problems. Draw your diagrams and show your work here and on the next page. Turn this in. 7

8 Problem Calculated Calculated Balancing Force Balancing Force Experimental Experimental 1 2 Remember that the balancing force is equal and opposite to the resultant. Write down the magnitude and the position of the resultant, as you found it on the force table. Compare your experimental results with your calculated results. Does the trigonometric method of resolving vectors work? Did you get an accurate solution? Turn this in. 8

Name: Lab Partner: Section: In this experiment vector addition, resolution of vectors into components, force, and equilibrium will be explored.

Name: Lab Partner: Section: In this experiment vector addition, resolution of vectors into components, force, and equilibrium will be explored. Chapter 3 Vectors Name: Lab Partner: Section: 3.1 Purpose In this experiment vector addition, resolution of vectors into components, force, and equilibrium will be explored. 3.2 Introduction A vector is