Question

Describe how to go about building a force table and comment on the importance of unit vectors in this process..

Answer 1

"The Force Table" is a simple tool for demonstrating Newton’s First Law and the vector nature of forces. This tool is based on the principle of “equilibrium”. An object is said to be in equilibrium when there is no net force acting on it. An object with no net force acting on it has no acceleration. By using simple weights, pulleys and strings placed around a circular table, several forces can be applied to an object located in the center of the table in such a way that the forces exactly cancel each other, leaving the object in equilibrium. (The object will appear to be at rest.)

The force table, shown in Fig. 4-3, is an apparatus that allows the experimental determination of the resultant force produced by a combination of forces. The rim of the circular table is calibrated in degrees. Weight forces are applied to a central ring by means of strings running over pulleys and attached to mass hangers. Adding or removing slotted masses varies the magnitude of a force and changing the angle of the pulley varies the direction. Each pulley with its suspended mass represents a vector. On a force table, the resultant of two or more forces (vectors) is found by balancing the forces by adding weight to the hangers and by changing the angles of the pulleys so that the ring becomes centered at the central pin. The balancing force is not the resultant R, but rather its opposite, called the equilibrant vector, a force of equal magnitude to FR but in the opposite direction, as shown in Fig. 4-4.

PROCEDURE

A. Graphical Method of Vector Addition

Given two vectors F1 = 250 g-dynes at 60o and F2 = 250 g-dynes at 150o , find their vector sum or resultant FR = F1 + F2 by the following procedures.

1. Using the head-to-tail method of vector addition, draw a vector diagram for Part A. Use a scale for which the finished vector diagram fills about half a sheet of graph paper.

2. Measure the magnitude and direction of the resultant with a ruler and protractor; record the results in the data table.

3. Use your scale to convert the magnitude of the vector in centimeters to a force in units of gdynes.

B. Addition of Two Forces on the Force Table Find the resultant vector FR = F1 + F2 of Part A.

1. Check to see if the force table is level. Ask your instructor for a level if this has not been done. Make any necessary adjustments by means of the leveling screws in the tripod base of the table. Orientation angles of vectors are measured from the 0o reference line or x-axis.

2. On the force table, clamp two pulleys at 60o and 150o .

3. Make sure the strings will move freely on the ring and allow the strings to pull directly away from the center

. 4. Add enough weights to each weight hanger to total 250 g, to give weight forces of F1 = F2 = 250 g-dynes in these directions. (Weigh the mass of each hanger. Weight hangers usually have masses of 50 g.)

5. Add weights to a third pulley positioned opposite the first two until the central ring is centered around the center pin. These weights are the vector sum, or resultant.

6. Record the magnitude and direction of the resultant in the data table. Remember that the resultant has the same magnitude as the equilibrant but is in the opposite direction.

7. When the forces are balanced, the ring is centered around the central pin. To confirm its position, the pin should be carefully removed to see if the ring is centered exactly around the central hole. Make adjustments if necessary. Record the results in Table 4-1.

8. Determine the percent difference of the experimental and graphical results in Parts A and B for the magnitude and direction of the resultant and record the value at the bottom of Table 4-1.

Importance of vector

All measurable quantities can be classified as either a scalar or a vector. A scalar has only magnitude while a vector has both magnitude and direction. Examples of scalar quantities are the number of students in a class, the mass of an object, or the speed of an object, to name a few. Velocity, force, and acceleration are examples of vector quantities. The statement "a car is traveling at 60 mph" tells us how fast the car is traveling but not the direction in which it is traveling. In this case, we know the speed of the car to be 60 mph. On the other hand, the statement "a car traveling at 60 mph due east" gives us not only the speed of the car but also the direction. In this case the velocity of the car is 60 mph due east and this is a vector quantity.Unlike scalar quantities that are added arithmetically, addition of vector quantities involves both magnitude and direction.