OBJECTIVE
This experiment will provide an opportunity to set up and measure seve
OBJECTIVE
This experiment will provide an opportunity to set up and measure several actual force systems and to compare results with calculated vector forces found by graphical methods.
EQUIPMENT Force Table with ring, pin, cord, pulleys and weight hangers
Set of slotted weights
Ruler and protractor
Graph paper INTRODUCTION
A scalar is a physical quantity with only magnitude. (Examples are length, mass and density.) A vector is a physical quantity with both magnitude and direction. (Examples are force, velocity and acceleration.)
A scalar quantity is represented by a single number (including units) giving its size or magnitude. A vector quantity is represented by a number amount and a direction or angle. Graphically, a vector force is represented by an arrow whose direction gives the direction of the vector. The length of the arrow is proportional to the size of the vector. In physics there are many important vectors. For example, a force, which is a push or pull, may be represented by a vector. If a set of two or more forces is balanced with no motion, it is said to be in equilibrium. Vectors may be combined using methods of graphing. When a set of forces is replaced by a single force, the single force is called a resultant, as shown in Figure 2. A force equal and opposite to a resultant is called an equilibrant, which is a single force that will cause a system of forces to be in equilibrium. The process of finding a single vector force to replace several others is called “composition” of vector forces. The process of replacing a single vector force with others is called “resolution” of vector forces.
Several methods may be used to solve vector force problems. In the “graphical” method, vectors are added by connecting the head of the previous vector (A) to the tail of the next vector (B). The resultant (R) is then from the tail of the first to the head of the last (see Figure 2). For more than two vectors, a polygon can be graphically constructed to find a resultant or equilibrant as in Figure 3.
Figure 2 Figure 3
Graphical Method Polygon Method
Analytical methods consist of applying trigonometry to resolve several vectors into right angle components, summing these in the x and y directions, and finding a resultant using the Pythagorean Theorum. For non-right triangles, the Law of Sines or Cosines may be used.
In this experiment, actual force systems will be set up and measured on the force table. Calculated vector forces using graphical and analytical methods will be compared to measured forces found by using the force table.
PROCEDURE
The following was observed when using the Force Table:
Confirmed that the table was leveled “by eye” and that the pulleys spin freely.
The pulley assembly was against the machined edge of the table.
When measuring, the ring was centered on the pin and that the strings extended radially outward from the center pin. The weight of the hangers was determined using a scale and was included as shown below.
The angles were measured counterclockwise and recorded below.
Either the S.I. unit of Newtons or the gram may be used as the force unit as long as consistency is maintained.
The instructor will assign one of the following Assignments to students:
Non-Rectangular Part I
Three concurrent, coplanar forces Part III
#
Component A
Component B
Equilibrant
Force A
Force B
Force C
Equilibrant
5
350g/70˚
402g/195˚
340g/320˚
140g/112˚
170g/345˚ 150g/249˚
90g136.927˚
Part I – Non-Rectangular vector components
1. The two pulleys were placed on the force table at the angles given shown in the above table. The required component weights A and B were added to the pulleys.
2. A third line and pulley with a weight force to balance the first two weight forces was used such that the ring was centered and did not touch the center pin. This is the actual or experimental value of the equilibrant. (A light tap to jog the system minimized friction and assured a correct value.)
3. The equilibrant was record in above Table. (Weight force may be measured in grams (g) or newtons (N). To convert from grams to newtons, multiply grams by 0.0098cm/s.)
Table I
Non-Rectangular Vector Components
Sketch
Weight (g)
Force (N)
Angle (degrees)
Component Vector A
350
3.43
70
Component Vector B 402
3.94
195
Equilibrant (from force table)
340
3.332
320.065
Resultant
340
3.332
140.065
4. Make a vector sketch in the space in Table I for this force system showing the resultant and its components A and B using the graphical method. Using graph paper, make a complete to-scale diagram which should be included in your lab report.
Part II – Rectangular vector components
1. A 300g weight force at 0˚ and a 400 g weight force at 90˚ were suspended. Experimentally found the equilibrant using the force table. The values of the experimental equilibrant were recorded in Table II. 2. Make a vector sketch showing the components and their resultant in the space below. Using graph paper, make a complete to-scale diagram which should be included in your lab report.
Sketch Calculations
3. Calculate the value of the resultant using the given components. Show this calculation above and in Table II below.
Table II
Rectangular Vector Components
Sketch
Weight (g)
Force (N)
Angle (degrees)
Equilibrant (experimental)
505
Resultant (experimental)
Resultant (calculated)
Find the % difference error, in magnitude only, for the experimental resultant using its calculated value as the accepted value. Show this calculation.