Lecturer: Clare OFarrellModule: Physics 1Major: BEng Offshore and Mechanical EngineeringAssessment: Lab Report 1Student: Rui Alexandre Bastos Ferreira MoreiraDate: 15th of October, 2014

Introduction:To realize this lab report, knowledge about moments was necessary to understand the aim of this experiment. Moments are the product of force and perpendicular distance and are given by the formula:

The perpendicular distance mentioned is the distance from the point where the moments are measured from to the line of action. Although there are two types of moments, which are bending and turning, this experiment will only be looking at one type of moment which is the turning moment. Turning moment is defined as how much force in an either clockwise or anticlockwise direction is necessary for an object to turn in a specific direction as well as, at what perpendicular distance from the line of action does the force need to placed to turn an object. Calculating moments is useful. By calculating moments, knowing to what extent forces act on different structures and how much force is being applied is possible. Also, the calculation of moments are used to know of which materials should the structure be made of, to effectively prevent the forces acting on the structure to permanently deform the structure. All in all, the aim of this experiment is to investigate moments as well as compare theoretical values against experimental values. Method and Apparatus:All the materials used in the experience belong to a Principle Moments Kit. For the experiment, four different methods were used in order to investigate moments. The first method consisted of investigating how to achieve equilibrium. Equilibrium happens when the sum of all the moments is equal to zero. In these specific methods equilibrium is achieved when the beam is completely horizontal.

Steps for method 1:1. Attach beam with a hinge to the board;2. When attached, the beam is able to turn 3603. Hangers are put on the beam and spaced equally from the middle of the beam where the hinge has been put to hold the beam against the board. (Hangers have an initial weight of 10 g).4. 4 disks weighing 10 g each are added to each side totalling a weight of 50 g on each side. 5. Distance is measured from the where the weights were hung until the centre of the beam. Steps for method 2: 1. The structure is identical as the first method with only one difference. The difference is that, one of the hangers is now hung by a string on the beam.2. Due to one of the hangers being hung by a string, the beam will decline to the side where the hanger is being hung by the string.3. To reach equilibrium between both sides, apply weight to the side which is not hung by a string. 4. Take the length from the string until the centre of the beam and from the hanger until the centre. 5. When lengths are obtained, calculate the weights on each hanger to achieve the weight necessary on which side to achieve equilibrium in the beam.Steps for method 3:1. To the previous method, a pulley is added and this change creates an angle between the beam and the string that goes through the pulley. 2. Add 25 disks each weighing 10 g totalling 260g with the initial weight of the hanger which is 10 g. 3. Left side of the hanger has also disks totalling a weight of 30 g.4. Measure distance from pulley to the hinge and angle the pulley forms from the beam. 5. When all the information above is collected calculate moment about the hinge. Steps for method 4:1. Structures are put equidistant from the middle of board. 2. From these structures, spring balances are hung.3. From one spring balance to the other spring balance, a beam is hung. 4. Following that, a weight of 100 g is put on the beam at different distances to find out the effect on the spring balances. 5. Record results from the spring balance and due further calculations on reactions on the spring balance.

Data Collection and Processing:

1st Method: In the first method there was no calculation to be performed. Data was collected and then the following step was simply to observe the beam in equilibrium.

18 cm18 cm

Beam

Hinge

LoadLoad

This diagram of the experiment helps in the understanding of the method used to investigate moments. The diagram shows two equal loads standing equidistantly from the hinge therefore resulting in the beam being at equilibrium.

2nd Method:After adding more 50 grams to the left side totalling a weight of 100 g, and adding an unknown value to the right which is hung by a string, the loads were put at different distances from the hinge on the beam to achieve equilibrium. 10 cm13 cm

Load: 100 g

Load: Unknown

Gravitational Constant

F1 = 0.1 kg * 9.81 = 0.981L1 = 0.13 mF2 = Unknown * 9.81 = 9.81 UL2 = 0.10 m F1 * L1 = F2 * L2F2 = (F1 * L1)/ L2 F2 = 0.981 * 0.13 / 0.10 = 1.275 N

m = F/g m = 1.275 * 9.81 = 0.13 kg Unknown load is 0.13 kg.

3rd Method: 18 cm

8 cm

35o

30 g

260 g

There are two ways of calculating the moments on the right side of this apparatus. The first one is by resolving the forces and the second one is with the aid of the perpendicular distance from the beam to the continuation of the force exerted by the string. (Shown in the dotted line in the diagram.

First Method:

Second Method:

The two methods used give quite a different answer but, this could be reasoned out by the fact that there is random error in the data collected.Finally, in this method, the moments on the left side will be calculated by resolving vectors.

Theoretically, the moments on both left and right side have to be equal as the beam is in equilibrium. (Sum of all forces is equal to 0). However, there is human error in the data collected resulting in faulty data.

4th Method: Spring Balances

18 cm 18 cm

RBRA

100 g

This is the diagram for the first positioning of the load. After the data had been collected from the load in this positioned it was moved around in order to obtain different resultant forces at the spring balance.

First position of the load: F = 0.1 * 9.81 = 0.981 N D = 0.18 m D2 = 0.36 m (from spring balance on the left to the one on the right).

This is the force recorded at the right spring. The force recorded on the left is the same as the beam is in equilibrium. Using the same formulas and equations, the other values when the load was positioned at a different spot in the beam are as follow:When the load was put at 6.5 cm from the left side: Left side = 0.81 N Right side = 0.18 NWhen the load was put 25 cm from the left side:Left side = 2.99 NRight side = 0.68 N

Conclusion:This experiment involved 4 different methods, 3 of which included calculations of moments. Although the calculations have been successfully completed, some problems regarding human error were encountered. The ability of reading of instruments was an issue when collecting data, therefore, the difference between the theoretical values obtained during the experiment and the experimental values is great.Nevertheless, moments are very useful in the modern world regarding construction and so forth. This experiment showed possible uses of moments and most importantly, how to achieve equilibrium.