Triangle of Forces

SPACE AND VECTOR DIAGRAMS

Table of Contents

AIM....………....................................................................................................................... 3
INTRODUCTION………....…………………………........................................................ 3
EQUIPMENT and COMPONENTS USED ........................................................................ 3
EXPERIMENTAL METHOD AND PROCEDURE .......................................................... 3

FINDINGS and RESULTS ................................................................................................. 4
Measured….......................................................................................................................... 4
Calculated….................................................................................. ….................................. 5
Data findings........................................................................................................................ 6

RECOMMENDATIONS and CONCLUSIONS ................................................................ 7

AIM
To show that three forces acting upon a body, in equilibrium, may be represented by a triangle of forces. (Vector addition)
INTRODUCTION
With this experiment we will show that a body in a state of equilibrium, with three forces acting in a singular plane. The following conditions must be met: * Moment of all three forces must pass through the same point. * Magnitudes of the forces can be represented by the sides of a triangle, each as a vector with the side of the triangle being the magnitude of the force and the angle being the heading of the force.
EQUIPMENT and COMPONENTS USED * Vertical fixed force * String * A3 drawing paper * 2x free running pulleys * Assorted masses * Straight edge and set square * Protractor
EXPERIMENTAL METHOD AND PROCEDURE

Part 1 1. Tape the drawing paper to the vertical board and attach pulleys to the edges of the board near the top. 2. Run the string through the two pulleys, hang two masses at the ends of the string and the third mass between the two pulleys. Recording the weight of each mass. 3. Once system is in equilibrium (not moving) making sure the pulleys are free and none of the masses are resting on the board.
If the centre of string is not on the drawing paper adjust the system as needed so that the centre point is on the paper. 4. Draw lines on the paper. Each line following the string, note the direction and the magnitude of each force.
Part 2 1. Draw the Space diagram, then the Vector diagram with one known force and all known angles. 2. Compare measured results with calculated results

FINDINGS and RESULTS

Measured Mass | Grams | Direction | 1 | 352.2 270246.3 44245.7 132 | 2 | | 3 | |

Percentage of error calculations

7.36 = 9.90 Sin 48

12.26 = 12.33 Sin 84
7.36N
9.90 x 100 = 80.29 12.33 12.26N 42 100 - 80.29 = 19.71% error 42 48 7.36N

The triangle of forces diagram is close to being connect but not enough to back up the objective. With an error % of 19.71 being slightly too high to outright claim the object is in equilibrium

Experiment 2 Force | Newton’s (N) | Angle from horizon | 1 | 11.28 907.36 2810.07 49 | 2 | | 3 | |

Percentage of error calculations

7.36 = 11.22 Sin 41

11.28 = 11.58 41 Sin 77 10.07N 10.07 = 11.40 Sin 62 11.28N 11.22 x 100 = 96.89 11.58 49 62 28 100 – 96.89 = 3.11% error 7.36N

Experiment number two improves from the first experiment greatly. If you follow the above vectors it shows the total forces acting on the body end up were they started showing is not in motion.

Experiment 3 Force | Newton’s (N) | Angle from horizon | 1 | 9.27 9010.07 279.31 19 | 2 | | 3 | |

Percentage of error calculations

9.27 = 12.89 Sin 46

10.07 = 10.65 Sin 71 71 9.31 9.31 = 10.45 Sin 63 9.27N 19 10.45 x 100 = 81.07 27 12.89 63 10.07N 100 – 81.07 = 18.93% error

Another triangle of forces diagram that is not closed, not enough to back up our second experiment. Findings
The results show one very low 3.11 error percentage and two that are slightly higher than desired 18.93 and 19.71 percent. These errors could have come from many sources, mostly from the collecting of raw data. This is not enough to outright backup the statement in the objective. That is: To show that three forces acting upon a body, in equilibrium, may be represented by a triangle of forces.

RECOMMENDATIONS and CONCLUSIONS

In this lab experiment I learned that the results can be close to what you expect but have some contradictions as well. Seeing the body in equilibrium in each experiment and recording data each time, one set of results supporting the body is in equilibrium and two that contradict that fact. For the week before the experiment we had been mathematically calculating resultant and equilibrium forces for various scenarios. The sum of the applied forces is derived by splitting the individual forces into x and y axis values, then totalling each axis. If the resultant equals zero the body is in equilibrium, if resultant has a value the inverse of the resultant is the equilibrant force. In doing this I was expecting all experiments to show a less than 10% error.
These unexpected results I believe are inaccuracies in our recorded data, or possible contact between the weights and vertical board and the string not sitting correctly in the pulleys. Spending the time to double check the recording of raw data, measuring weights and angles twice and minimalizing parallax error would improve the accuracy of all data. With the improvement of raw data inherently an increase in accuracy of the finial data will
The current data shows the hypothesis is not completely reinforced, it could be accepted if you find the reasons for the inaccuracies are plausible. With the improvements to the experiment the next attempt will conclusively show that three forces acting on a body can be shown by a triangle of forces diagram.